third asian-pacific regional meeting of the international astronomical union: september...

THIRD ASIAN-PACIFIC REGIONAL MEETING OF THE INTERNATIONAL ASTRONOMICAL UNION

Third Asian-Pacific Regional Meeting of the International

Astronomical Union

September 30- October 51984, Kyoto, Japan Part 2

Edited b,Y

M. KITAMURA Tokyo Astronomical Observatory

and

E. BUDDING Carter Observatory, Wellington

Reprinted from Astrophysics and Space Science, Vol. 119, No.1

D. REIDEL PUBLISHING COMPANY

A MEMBER OFTHE KLUWER ~ ACADEMIC PUBLISHERS GROUP

DORDRECHT / BOSTON / LANCASTER / TOKYO

Library of Congress Cataloging-in-Publication Data

International Astronomical Union. Asian-Pacific Regional Meeting (3rd : 1984 : Kyoto, Japan) Third Asian-Pacific Regional Meeting of the International Astronomical Union.

Bibliography: p. 1. Astronomy - Research _. Asia -Congresses. 2. Astron

omy - Research - Pacific Area -Congresses. 3. Astrophysics- Research - Asia-Congresses. 4. Astrophysics-Research-Pacific Area -Congresses. 1. Kitamura, Masatoshi, 1926- II. Bud-ding, E., 1943- III. Title. QB61.156 1984 520 86-469

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TABLE OF CONTENTS

Part 2

G. YA. SMOLKOV, A. A. PISTOLKORS, T. A. TREsKov, B. B. KRISSINEL, V. A. PUTILOV, and N. N. POTAPOV / The Siberian Solar Radio Telescope: Parameters and Principle of Operation, Objectives and Results of First Observations of Spatio-Temporal Properties of Development of Active Regions and ~~ 1

B. LOKANADHAM, and P. K. SUBRAMANIAN, A. L. KIPLINGER, and B. R. DENNIS / High Energy Observations of June 1980 Solar Flares 5

E. HIEI, Y. SHIMIZU, H. MIYAZAKI, H. IMAI, K. SATO, S. KUJI, and W. SINAMBELA / Coronal Structure Observed at the Total Solar Eclipse of 11 June 1983 in Indonesia 9

T. NISHIKAWA / Continuum Absorption in the Solar EUV Spectra 17 K. SHIBASAKI I Height Measurements of S-Components 21 B. LOKANADHAM, and P. K. SUBRAMANIAN I Variations in Quiet Sun Radia-

tion at Centimetre Wavelengths during Solar Maximum Period 27 Y. SAITO, and M. SAITO I Analysis of a Magnetohydrodynamic Stellar Wind 33 M. TAKEUTI / Study of Time-Evolving Hydrodynamic Cepheid Models 37 B. A. YAO I Unusual Variable Stars in the Globular Cluster M4 41 M. TAKAHARA, and K. SATO I The Phase Transitions of Superdense Matter

and Supernova-Explosion 45 P. VENKATAKRISHNAN I Supercritical Winds From Cool 'Canonical' Stars

Caused by Evolution on the Main Sequence 51 M. KATO / Steady Mass-Loss from Supermassive Stars 57 J. Woo / Effective Temperatures, Radii and Luminosities of O-Emmission,

Be and Ae Stars 61 T. MIKAMI / Absolute Magnitudes of Late-Type Stars 65 M. SUZUKI, and T. KOGURE / Active Phenomena of the Be Star EW Lac Ob-

served in 1978-82 69 J. H. JEONG, C. W. SUH, and I. L-S. NHA / Photometric Behaviour of the Be

Star EW Lacertae 73 T. HIRANO, S. HAYAKAWA, F. NAGASE, and Y. TAWARA / Iron K-Emission

Line from Cygnus X-2 77 N. SATO, S. HAYAKAWA, and F. NAGASE / X-Ray Emissions from Vela X-I

During Its Eclipsing Period 81 O. KABURAKI / Electrodynamical Synchronization of AM Her-Type Stars 85 A. OKAZAKI, and A. YAMASAKI I Spectroscopic and Photometric Observa-

tions of Nova Aquilae 1982 89 S. J. WILSON, and K. K. SEN I Moment Method for the Inverse Radiative

Transfer in Inhomogeneous Media 93 W. J. COUCH, and H. J. TROD ALL / Photometric Determination of Variations

in the Surface Conditions for Pulsating Stars 97 X. Wu, G. QIAO, X. XIA, and F. LI / The Estimation of Some Parameters of

Pulsars and Their Applications 101

v

vi TABLE OF CONTENTS

S. SHIBATA / Pulsar Magnetosphere with Conspicuous Trans-Field Flow 105 A. T. OKAZAKI, and S. KATO / One-Armed Oscillations of a Non-Self-Gravi-

tating Polytropic Disk 109 B. J. ROBINSON, R. N. MANCHESTER, and W. H. MCCUTCHEON / CO Obser-

vations Geometry and Galactic Structure 111 T. OKUDA, and S. IKEUCHI / Hydrodynamical Models of the Orion-KL Ne-

bula 115 M. SHINOHARA / Radio Recombination Lines of Hydrogen Atoms Associa-

ted with Stimulated Emissions in Ionized Regions 123 T. HANDA, and Y. SOFUE / The Scutum Ring of HII Regions 127 S. YOSHIDA, S. MIZUNO, M. NAKANO, T. KOGURE, K. SAKKA, T. SASAKI, and

S. D. WIRAMIHARDJA / Surface Photometry of Simple HII Regions 131 Y. KOBAYASHI, J. JUGAKU, H. OKUDA, S. SATO, and T. NAGATA, / Infrared

Polarimetry of the Stars in the Inner Galaxy 135 S. S. HONG, and B. C. Koo / Effect of Magnetic Field on the Shock-Induced

Thermal Instability 141 M. FUKUNAGA / On the Radial Distribution of Molecular Clouds in Galaxies 143 T. TANABE, F. KAMIJO, T. ONAKA, A. SAKATA, and S. WADA / Grain For-

mation Experiments by a Plasma Jet Apparatus 147 T. HASEGAWA / Hydrostatic Models of BOK Globules 151 S. S. HAYASHI, N. KAIFU, and T. HASEGAWA / Cep A: A Possible Proto-

Cluster 155 J. J. RAWAL / Formation of the Solar System 159 Y. SABANO, and M. TOSA / Thermal-Chemical Instability in a Pre-Galactic

Gas Cloud 167 T. MURAl, and M. FUJIMOTO / Dynamics of the Magellanic System and the

Galaxy - Present Status of Theoretical Understanding 169 A. J. TURTLE, and W. D. PENCE / Emission Line Velocity Survey of Spiral

Galaxies with Bright Nuclei 173 H. OHTANI, J. MEABURN, C. GOUDIS, A. EL-BASSUNY, and M. SOLIMAN /

Optical Light Variation of the Seyfert Galaxy NGC 4151 177 M. SASAKI, and M. SAITO / Emission Line Velocity Field in the Central Re-

gion of M82 181 S. MIYOSHI, S. HAYAKAWA, H. KUNIEDA, and Y. TAWARA / X-RayObserva-

tion of AGN's from TENMA 185 Y. SOFUE, U. KLEIN, R. BECK, and R. WIELEBINSKY / Large-Scale Configuc

ration of the Magnetic Field in Spiral Galaxies 191 S.-W. KIM, and M.-S. CHUN / Correlation Between the Physical Parameters

and Morphological Type of Spiral Galaxies 195 T. FUJIWARA, and S. Hozumi / Global Instability of Thin Stellar Discs 199 B. BASU / A Mathematical Model of the Initial Stage in the Formation of a

Disk Galaxy 201 Y. D. TANAKA, S. IKEUCHI, andA. HABE / Evolution of Disk Galaxies Regu-

lated by Supernova Remnants 207 Y. KUMAI, and M. TOSA / On the Effects of Compression of a Gaseous Disc

by Thermal and Dynamical Pressures of Intergalactic Gas 211 M. YOKOSA WA / Formation of Collimated Beams 213

TABLE OF CONTENTS

F. TAKAHARA, and M. KUSUNOSE / Electron-Positron Pairs in a Mildly Rela-tivistic Plasma in Active Galactic Nuclei

T. ISHIZA WA / Simulation of Compact Groups of Galaxies M. FUJISHITA / Motion of Quasar Images by Gravitational Lens Galaxies Y. CHU, X. ZHU, and H. BUTCHER / Optical Identification of QSOs with Flat

Radio Spectrum

A. SAVAGE / United Kingdom Schmidt Telescope (UKST) Objective Prism

Searches for Quasars

A. SAVAGE / Optical Identifications of Radio Sources with Accurate Posi

tions Using the United Kingdom Schmidt Telescope (UKST) IIIa-J Plates

M. UMEMURA, and S. IKEUCHI / Formation of a Void and Galaxies in a Neu

trino Dominated Universe

L. FANG, S. XIANG, S. LI, Y. CHU, andX. ZHU / Dark Matter and the Formation of Large-Scale Structure in the Universe

D. A. LEAHY, S. NARANAN, and K. P. SINGH / X-Ray Detection of the Monoceros Supernova Remnant

H. T. MACGILLIVRAY, and R. J. DODD / Alignment of Spiral Galaxies in the Local Supercluster

K. AIzu, H. TABARA, T. KATO, and M. INOUE, / Log N - Log S of Radio Sources at 10 GHz with Flat Spectra

Announcement

List of Unpublished Papers T ABLE OF CONTENTS

Part 1

(Astrophysics and Space Science Vol. 118, No. 112)

M. KITAMURA and E. BUDDING / Introduction DONALD C. MORTON / Remarks by the Chairman of the Scientific Organizing Committee

SECTION 1: A VIEW OF ASIAN-PACIFIC ASTRONOMY

VII

217 221 227

231

233

239

243

247

249

253

257

262

1 3

K. KODAIRA and T. KOGURE / The Japanese National Large Telescope (JNLT) Project 5 SHI-HUI YE / Solar Studies in China 9 SHu-Mo GONG / New Telescopes in China 15 G. YA. SMOLKOV, V. E. STEPANOV, V. M. GRIGORYEV, and V. G. BANIN / The East-Siberian

Complex of Sibizmir Solar Observatories 21 DONALD C. MORTON / Recent Developments with the Anglo-Australian Telescope 31 BUNSHIRO TAKASE / Galactic and Extragalactic Studies with the Kiso Schmidt 35 T. KOGURE / Cooperation in Astronomy Between Indonesia and Japan 39 J. C. BHATTACHARYYA / New Telescopes in India

45 HAMID M. K. AL-NAIMIY / The Iraqi National Astronomical Observatory 51 B. J. ROBINSON / The Australian Radio-Telescope 57 MASAKI MORIMOTO / Results From Nobeyama Radio Observatory (NRO) - A Progress Report 63 MINORU ODA / Space Astronomy in Japan 67 IAN R. TUOHY / STARLAB: An Ultraviolet/Optical Space Telescope 71 J. B. HEARNSHAW / The Mt John 1 Metre Telescope Project 79 A. J. TURTLE / Radio Astronomy at the University of Sydney 83 I. A. IssA and A. I. GAMAL EL DIN / Astronomical Research Activities with the 74 Inch Telesco-

pe at Kottamia Observatory 87

viii TABLE OF CONTENTS

P. B. BABADZHANOV / Astronomy in Tadjikistan 95 M. S. A. SASTROAMIDJOJO / Present and Future of Astronomical Science at Gadjah Mada Uni-

versity, CentraiJava, Indonesia 99

SECTION 2a: THE SUN

KATSUO TANAKA / High-Energy Observations of Solar Flares 101 R. T. STEWART / Dynamical Processes in the Solar Corona and Interplanetary Space (Invited Re-

view) 115 YUTAKA UCHIDA / Magnetodynamic Phenomena in the Solar and Stellar Outer Atmospheres 127 H. KUROKAWA, T. KITAHARA, Y. NAKAI, Y. FUNAKOSHI, and K. IcHIMOTO / High Resolution

Observation of Ha Solar Flares and Temporal Relation Between Ha and X-Ray, Microwave Emission 149

TAKASHI WATANABE and TAKAKIYO KAKINUMA / Three-Dimensional Properties ofInterplane-tary Disturbances in 1978-1981 153

YAOTIAO JIANG AND ZHENTAO Xu / On the Sporer Minimum 159 MITSUGU MAKITA, SHlGEO HAMANA, KEIZO NISHI, MINORU SHIMIZU, TAKASHl SAKURAI and

KIYOTO SHlBASAKI / Solar Vector Magnetograms of the Okayama Astrophysical Observatory 163 H. M. ANTIA, S. M. CHITRE, and D. NARASHIMA / Solar Five-Minute Oscillations of Low, Inter-

mediate, and High Degree 169 H. S. YUN and H. A. BEEBE / Reference Models of Sunspot Chromospheres 173 HIROYASU ANDo / Resonant Excitation of the Solar g-Modes Through Coupling of 5-Min Oscil-

lations 177

SECTION 2b: SOLAR-STELLAR CONNECTIONS

R. G. HEWITT and D. B. MELROSE / Plasma and Radiation Processes (Invited Review) 183 YOJI OSAKI and HIROMOTO SHIBAHASHI / Oscillations and Pulsations in the Sun and Stars (Invi-

ted Review) 195

THEODORE SIMON / Stellar Chromospheres, Coronae, and Winds (Invited Review) 209 WASABURO UNNO and MASA-AKI KONDO / Nonlinear Hydrodynamical Models of Stellar Con-

vective Zones 223 TAKASHl TSUJI / Turbulence, Convection, and Mixing in Red Giant Stars: Some Empirical Ap-

proaches Based on High Resolution Spectroscopy 227 SE-HYUNG CHO, NORIO KAIFU, NOBUHARU UKITA, MASAKI MORIMOTO, and MAsAHlKo

HAYASHI/High Sensitivity SiO Maser Survey for Mira Variables 237

SECTION 3: STARS

EDWIN BUDDING / Classical Algol Systems (Invited Review) 241 W. SUTANTYO / Massive X-Ray Binaries: Their Physics and Evolution 257 BRIAN WARNER / Rapid Oscillations in Cataclysmic Variables 271 ATsUMA YAMASAKI, AKIRA OKAZAKI and MASATOSHI KITAMURA / Short-Period Noncontact

Binaries 279 'MASAOMI NAKAMURA and YASUHlSA NAKAMURA / The Effect of Back Pressure on the Contact

Evolution of a Close Binary System 283 D. T. WICKRAMASINGHE and S. MEGGITT / The Electron Temperature of AM Herculis Type Sys-

tems 287 1. R. TUOHY, N. VISVANATHAN and D. T. WICKRAMASINGHE / Photometry, Polarimetry, and

Spectroscopy of AM Herculis Variables 291 B. LOUISE WEBSTER, L. H. TAAFFE and A. J. MLNAJS / Line Profiles in Symbiotic Stars 295 IL-SEONG NHA and J OON-YOUNG OH / Light Curves of V711 Tauri (HR 1099) 299 KEN'ICHl NOMoTo, FRIEDRICH-K. THIELEMANN, KOICHl YOKOI and DAVID BRANCH / Carbon

Defiagration Models for Type-I Supernovae and Theoretical Optical Spectra 305

T ABLE OF CONTENTS ix

SUHARDJA D. WIRAMIHARDJA, TOMoKAzu KOGURE, MAKOTO NAKANO, SHIGEOMI YOSHIDA and KEN'ICHI TATEMATsu / A Survey of Emission-Line Stars in the CMa Star Formation Region 311

YUZURU TAwARA, SATIO HAYAKAWA, HIDEYO KUNIEDA and DE-YUWANG / X-Ray Spectra of Various Bursts from the Rapid Burster 317

G. N. SALUKVADZE / Trapezium-Type Multiple Systems 321 HONG BAE ANN and YONG HEE KANG / Age-Metallicity Relation for F-Stars 325

SECTION 4a: COMPACT STARS, AND GALACTIC STRUCTURE

V. RADHAKRISHNAN and C. S. SHUKRE / The Pulsar Velocities and Their Binary Origins (Invited Review) 329

K. C. FREEMAN I Dynamics of Disk Galaxies (Invited Review) 337 A. R. HYLAND / The Galactic Centre (Invited Review) 343 V. M. BLANCO and B. M. BLANCO I Expected and Observed Late Giant Star Counts in the Milky

Way Bulge 365 SHOGO INAGAKI I Post-Collapse Evolution of Small-N Clusters 367 Y. SOFUE, T. HANDA, I. SuwAand Y. FUKuI/The Galactic Center Radio Lobe-A Cosmic let in

Our Galaxy? 371 T. KII, S. HAYAKAWA and F. NAGASE / Tenma Observations ofthe X-Ray Pulsar 4U1626-67 375 WANG DE-Yu, PENG Qlu-HE and CHEN TING-YANG / A Model of the Galactic Centre with Mag-

netic Monopoles 379

SECTION 4b: GALACTIC STRUCTURE

CHRISTOPHER F. McKEE / The Injection of Energy into the Interstellar Medium by Stars (Invited Review) 383

SOREN-AKSEL SORENSEN / The Shape of Spiral Arms 395 TOSHIHIRO OMODAKA, MASAHIKO HAYASHI, SAEKO SUZUKI, TETsuo HASEGAWA and

RYOSUKE MIYAWAKI / High-Resolution Observations ofthe Orion Bright Bar 401 MAsATosHl OHlSHl, No RIO KAIFU, HIROKO SUZUKI, and MASAKI MORIMOTO / Excitation ofIn-

terstellar Molecules in the ORI-KL Source 405 YOSHIO TOMITA / Large-Scale Structures of High Galactic Latitude Dark Clouds 409 T. ONAKA, Y. NAKADA, T. TANABE, A. SAKATA and S. WADA / A Quenched Carbonaceous

Composite (QCC) Grain Model for the Interstellar 220 NM Extinction Hump 411 HSIN HENG Wu / Photographic and Spectrographic Observations with a Reducing Camera on

the 61 CM NCU Telescope 415 R. S. STOBIE, K. ISHIDA, Y. YosHllandH. T. MACGILLIVRAY / Star Count ofthe North Galactic

Pole Region in the UBV Colour Bands 419

SECTION 5a: GALACTIC STRUCTURE AND COSMOLOGY

TETSUO HASEGAWA I Star Formation Associated with High-Velocity Mass Outflows (Invited Review) 421

SIDNEY VAN DEN BERGH / Globular Clusters and Galactic Evolution (Invited Review) 435 1. R. WALSH / The Structure of the R Monocerotis, NGC 2261, and HH39 Nebular Complex 439 KAZUNARI SHIBATA and YUTAKA UCHIDA / Formation of Astrophysical lets by a Contracting

Magnetic Accretion Disk 443 OSAMU KAMEYA, TATSUHlKO HASEGAWA, NAOMI HIRANO, MUNEZOSEKI, MAKOToTosA, Yos-

HlAKI TANIGUCHI, and KEIYA TAKAKUBO / CS, C34S, and CH30H Observations of the Mole-cular Cloud Associated with NGC 7538 449

C. A. CHRISTIAN AND 1. N. HEASLEY / Deep(est) Colour-Magnitude Diagrams of Clusters 453 GUO-XUAN SONG / Elliptical Galaxies Under Perturbation 457 TOMoHlKo YAMAGATA and HIDEO MAEHARA / A Photometric Study of Poor Clusters of Gala-

xies 459 MAKoTo TosA and MAsATAKA FUKUNAGA / N-Body Simulation of Giant Molecular Clouds in a

Galaxy 463

x TABLE OF CONTENTS

TSUNEAKI DAISHIDO, KUNIYUKI ASUMA, TOHRU OHKAWA, HIRA YOSHI OBARA, SHINICHI KOMATsu-and KIYOSHI NAGANE / A Design for Digital Signal Processing in a Large Field Radio Pa-trol Camera 467

ALAN T. TOKUNAGA and ROBERT G. SMITH / A Faint Object Spectrometer for the Infrared 471

SECTION 5b: GALAXIES AND COSMOLOGY

JIAN-SHENG CHEN / QSO Absorption Lines (Invited Review) 473 ALAN STOCKTON / The Environment of QSOs (Invited Review) 487 1. G. ROBERTSON, R. F. CARSWELL and P. A. SHAVER / Heavy Element Abundances in Absorp-

tion Line Systems Towards Q2206--199N 499 H. S. MURDOCH, R. W. HUNSTEAD,J. C. BLADES andM. PETTINI / An Absorption Line Study of

Galaxies at High Redshift 501 R. W. HUNSTEAD, H. S. MURDOCH, M. PETTINI andJ. C. BLADES / QSOs As Probes of the Eariy

Universe 505 SATORU IKEUCHI / The Baryon Clump Within an Extended Dark Matter 509 CHI YUAN, CHlH-KANG CHOU and TA-JEN LEE / The Effects of Self-Gravity on the Solar Nebula 515 M. lYE and M.-H. ULRICH / Echelle Spectroscopy of Narrow Line Regions of Seyfert Galaxies 523 YOSHIAKI TANIGUCHI, KATSUNORI SHIBATA and KEN-IcHl WAKAMATSU / New Polar Ring Gala-

xies in Rich Clusters of Galaxies 529 SHRINIVAS R. KULKARNI and R. MATHIEU / Distance to the Anti-Center Shell 531

Index of Contributors 535

Announcement 537

THE SIBERIAN SOLAR RADIO-TELESCOPE: PARAMETERS

AND PRINCIPLE OF OPERATION, OBJECTIVES AND

RESUL TS OF FIRST OBSERVATIONS OF SPATIO·TEMPORAL

PROPERTIES OF DEVELOPMENT OF ACTIVE REGIONS AND

FLARES*

G. YA. SMOLKOV, A. A. PISTOLKORS**, T. A. TRESKOV, B. B. K R ISS I N E L, V. A. P U TI L 0 V, and N. N. POT A P 0 V

SibIZMIR, Irkutsk, U.S.S.R.

(Received 8 March, 1985)

Abstract. At the SibIZMIR, the Siberian Solar Radio·Telescope (SSRT)has been devised, built and aimed to diagnose the state of solar activity in the microwave band, and to study the structure and development of active regions and flares in the solar atmosphere with high two-dimensional resolution on a real-time basis. The SSRT is a 256-element 5.2 cm cross interferometer oriented in E-W and N-S directions. Each linear interferometer consists of 128 antennas spaced by 4.9 m, with parabolic dishes 2.5 m in diameter. The brightness distribution of circularly polarized and nonpolarized emission is recorded. Radio-images are synthesized in the course of solar scanning as a consequence of co-rotation with the Earth of the multi-lobe antenna pattern of the SSRT along with multi-frequency recording of the radio brightness distribution in the angle of elevation. All SSRT systems control, data collection, operative representation and preprocessing are automatized. Solar observations have been carried out simultaneously with adjustment work during a stepwise commisioning of the SSRT since 1981. The observations revealed sudden, considerable changes of active regions and allowed us to keep track of the process of microwave emission source polarization, localization, and development of flare processes, and of other phenomena.

Within the framework of the program of creation of a complex of SibIZMIR observatories designed to study solar activity simultaneously with all possible groundbased methods (Smolkov, 1982), construction work on the Siberian Solar RadioTelescope (SSRT) (Smolkov et al., 1983) has been completed this year. Its main parameters and the principle of operation were chosen such that the characteristic properties of solar activity could be taken into account. The most effective manifestation of local sources (LS) of radio-emission from active regions (Molchanov, 1962; Akhmedov et al., 1966) and flares (Kundu and Vlahos, 1982) at 5 or 6 wavelengths have determined the selection of about 5.2 cm as the working wavelength of the SSRT.

The SSRT antenna system is a 256-element cross interferometer oriented in the E-W and N-S directions. Each linear interferometer consists of 128 antennas, spaced by 4.9 m, with parabolic dishes 2.5 m in diameter. The interferometer baselines are 622 m each, permitting a resolution of up to 20". A rather broad range of spatial frequency

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** Scientific Council on Radio Astronomy, Moscow, U.S.S.R.

Astrophysics and Space Science 119 (\986) 1-4. © 1986 by D. Reidel Publishing Company

2 G. YA. SMOLKOV ET AL.

Fig. 1. Surface part of the west beam of the S SRT.

spectrum of the SSRT makes it possible to study the quite different-scales of structure of the solar atmosphere, and to diagnose the state of solar activity as a whole.

Signals from the antennas are collected in a receiving 180-channel complex via waveguides connected to a parallel-stage circuit placed in an underground tunnel. The

R L

,,'":,-'----;I.ori~.,.. , \ \ I \j

031183

06h2.f'

." : \ . , lcF··

:/~-

Fig. 2. Variations of the structure of polarized emission distributions above a sunspot group owing to flare 031183.

THE SIBERIAN SOLAR RADIO-TELESCOPE 3

brightness distribution of circularly polarized and unpolarized emission is recorded. The dynamic range of the receiver is 104 . The system's phase adjustment is performed using solar radio emission with the localization of active regions taken into account. Automatic phase adjustment of long waveguide lines is provided, beginning with connections of 16-antenna interferometers. SHF-amplifiers located after each such group compensate for signal damping in subsequent waveguide plumbings.

The solar radio-image is synthesized in the course of solar scanning by a fan of interference lobes of the SSRT antenna pattern during a multifrequency parallel recording of the radio brightness distribution in the angle of elevation.

All SSRT systems control, data collection, operative representation and preprocessing are automized.

The design solutions have been tested for functioning using working models of all SSRT systems. The adjustment work on the SSRT E-W line is now complete while that on the N-S line is in progress. Figure 1 shows a view of the surface part of the West beam.

Upon adjustment of the first 16-antennagroup of the West beam in the spring of 1981, daily records were taken of one-dimensional distributions (scans) of radio brightness over the solar disk. The angular resolution was increased from 2' up to 20" as subsequent antenna groups were incorporated. Repeated acquisition of previously known evidence indicates a normal performance of the instrument. However, even during the adjustment stage we were successful in obtaining new interesting data on spatio-temporal evolutionary properties of active regions and flares.

We have detected sudden and significant changes in the brightness of active regions, providing evidence that the slowly varying component of solar radio-emission from continuous high-resolution observations is indeed a highly variable one. Circular polarization of the LS appears within half an hour. It reverses sign in a jump-like fashion, due to a change in orientation of the sunspot group's magnetic field with respect to the observer; or because of a change in physical conditions of the LS associated with the development of sunspot groups or flares. Accordingly, the LS intensity either remains unchanged or forms patterns after the character of variation in sunspot area, or in the development of a flare.

Sources of microwave bursts are able to arise above the trailing or leading parts of a sunspot group, to migrate from one part to the other and to cover the entire sunspot group simultaneously. At the time of flares, the LS structure may give rise to a new feature, with no sunspots present beneath. Such was the case, for example, also during the 3 February, 1983 flare (Figure 2). As that flare progressed, the structure of the polarized emission distribution (dots) above a sunspot group underwent substantial variations. The polarization reversed its sign. The polarized source in the later stage of the burst was of significant extent.

The great 'informativity' of observations with the SSRT enables us to effectively follow the general picture of active regions and detailed processes occurring in them, thus providing new insights into the state of solar activity as a whole.

4 G. YA. SMOLKOV ET AL.

References

Akhmedov, Sh. B., Borovik, V. N., Korzhavin, A. N. et al.: 1966, Solnechnye dannye, No.2, p. 62. Kundu, M. R. and Vlahos, L.: 1982, Space Sci. Rev. 32, 405. Molchanov, A. P.: 1962, Solnechnye dannye, No.2, p. 53. Smolkov, G. Ya.: 1982, in W. Fricke and G. Teleki (eds.), The Solar Complex ofSibIZMIR Observatories:

Instruments and Main Results of the Investigations', Sun and Planetary System, D. Reidel Pub!. Co., Dordrecht, Holland, p. 121.

Smolkov, G. Ya., Treskov, T. A., Krissinel, B. B., and Potapov, N. N.: I 983,lssledovaniya po geomagnetizmu, aeronomii ijizike Solntsa, Vo!' 64, Nauka, Moscow, p. 130.

HIGH ENERGY OBSERVATIONS OF JUNE 1980 SOLAR

FLARES*

B. LOKANADHAM,P. K. SUBRAMANIAN

Centre of Advanced Study in Astronomy, Osmania University, Hyderabad, India

ALLAN L. KIPLINGER, and B. R. DENNIS

Goddard Space Flight Centre, Greenbelt, Maryland, U.S.A.


Abstract. The paper presents a detailed study of the high energy X-ray observations of the most unusual solar events observed on 4 and 7 June, 1980 with the Hard X-Ray Burst Spectrometer (HXRBS) on Solar Maximum Mission (SMM) satellite. The hard X-ray data of the events are also compared with the radio microwave fluxes.

The X-ray time profiles of these flares are characterized by the occurrence of impulsive phase superposed with a number of narrow spikes before the occurrence of the main energetic events. Studies of the temporal and spectral properties of these events indicated a quasi-oscillatory nature of the sources. Various models for explaining the evolution of the events are considered and the sequential firing loop model seems to be consistent with the observations of the events.

1. Introduction

High resolution studies of solar hard X-ray bursts offer the possibility of understanding the basic flare processes. The hard X-ray burst observations carried out by the recent 'solar maximum' space missions provided a unique opportunity for such studies (Orwig et aI., 1980; Tsuneta, 1983). This paper presents the hard X-ray observations of the most prominent events, which occurred in June 1980, recorded by the hard X-ray spectrometer, in the range 28-482 keY, on the Solar Maximum Mission (SMM).

2. Observations

Hard X-ray observations, in the form of 15 channel pulse-height analysed spectra, over the energy range of 28-480 keY, recorded every 128 ms were obtained by the Hard X-Ray Burst Spectrometer (HXRBS) on SMM (Orwing et aI., 1980). During the first week ofJune 1980 the active region AR 2495, which first appeared on the disk on 4 June, produced a number of X-ray flares of M4 and M 7 , associated simultaneously with strong microwave bursts.

Figures 1 and 2 show the hard X-ray time profiles of the flares which occurred on 4 and 7 June, respectively, in different energy ranges. These profiles clearly exhibit impulsive phases with spiky structures superposed, which could be clearly brought out with smoothed data over the entire energy range for these two events. The most

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984.

Astrophysics and Space Science 119 (1986) 5-8. © 1986 by D. Reidel Publishing Company

6 B. LOKANADHAM ET AL.

I} 2~(\ .... \.1.) ';OC' ':-0 ", loe') ~ 200 1 4 (' 0 1600

3.0 !. 0 G

C 2. S 0 U N T

5 2.0

p E II

S 1.5 E C 0 N D 1.0

0.'S 0750 0800 0810 V. T

Fig. 1. Hard X-ray time profiles of the solar flare of 4 June, 1980 with one impulsive phase.

105

1Q4 28-54 kev

103

1Q4

U w (/)

(/)

~ ::> 0 103 u (.!) 0 ~

102

10·' L-L-'--''-'-.L...L...........i-'-'--'-.................. -'-'-'-.J.....L ............ ~ ~14 ~16 ~18 3:12 UNIVERSAL TlME

Fig. 2. Hard X-ray time profiles of the flare of 7 June, 1980 with multiple impulsive phases.

HIGH ENERGY OBSERVATIONS OF JUNE 1980 SOLAR FLARES 7

outstanding features of these time profiles of the flares is the presence of a series of intense pulses occurring at regular intervals before the outburst of a major flare, which was associated with the most energetic events.

Power-law spectral fits computed for these events showed that their spectra, in general, follow a power law with an index of ~ 4. By comparing their spectral indices with hard X-ray time profiles it is seen that the spectra are harder during the peaks. A close temporal correlation between hard X-ray emissions and the impulsive microwave and y-ray bursts, associated with a 7 June event, has been reported by Kiplinger et al. (1983). The microwave spectra, derived from the peak flux densities of the associated microwave bursts of these two events, are presented in Figure 3.

3000 .-----~----~-r-,~_T~~------_r--_,--_.~------_.

1000 L June 1980 108LO UTI

.: ,

r 1 GH:)

", ' Ju", 1980 106SS U! I ..

? Jun. '980 103'1 UT)

Fig. 3. Changes in microwave spectra of the solar bursts.

3. Discussion

The high resolution studies of the intense hard X-ray bursts of June 1980 indicate the occurrence of regular pulse trains of hard X-ray spikes superposed over the impulsive phase. These pulse train phenomena are repeated at four intervals during the time of 7 June events, whereas they were not observed repeatedly near the 4 June flare.

The evolutionary changes of the radio spectra of these two events are found to be different. The 'U' type spectrum occurred only for the 7 June event, which also produced high-energy y-ray bursts. These spectra, therefore, indicate a progressive increase of energy of the trapped X-ray emitting electrons, rather than a simultaneous process.

8 B. LOKANADHAM ET AL.

The works of Vorpahl (1976) and Emslie (1981), suggest that the pulse trains simply represent a successive firing process of the loops. It was also seen that the X-ray emission occurred in an arcade ofloops rather than in a single loop, suggesting that the loops fired sequentially as if triggered by a progressing disturbance. Emslie (1981) has developed a detailed model of sequentially firing loops, based on an important premise, that the free energy of the flare is stored in the poloidal component of the magnetic fields of twisted loops. and only a portion of this free energy is released during a flare.

Examination of the hard X-ray data, in conjunction with radio and i-ray observations, showed that the X-ray emission is simultaneous with microwave and y-ray bursts. Studies of their temporal and spectral properties indicate that a sequential firing loop mechanism may be responsible for the manifestation of the observed events associated with flares of 4 and 7 June, 1980.

References

Emslie, A. G.: 1981, Astrophys. Letters 22, 171. Kiplinger, A. 1., Dennis, B. R., Frost, K. J., and Orwig, 1. E.: 1983, Astrophys. J. 273, 783. Orwig, 1. E., Frost, K. J., and Dennis, B. R.: 1980, Solar Phys. 65,25. Tsuneta, S.: 1983, in Proc. Japan-France Seminar, 'Active Phenomena in Outer Atmosphere of Sun and

Stars' held at Paris, during 3 - 7 October. Vorpahl, J. A.: 1976, Astrophys. J. 205, 868.

CORONAL STRUCTURE OBSERVED AT THE TOTAL SOLAR

ECLIPSE OF 11 JUNE, 1983 IN INDONESIA*

E. HIEI, Y. SHIMIZU, H. MIYAZAKI, H. IMAI

Tokyo Astronomical Observatory, Mitaka. Japan

K. SAro, S. KUJI

International Latitude Observatory, Mizusawa, Iwate-Ken, Japan

and

W. SINAMBELA

Indonesian National Institute of Aeronautics and Space, Bandung, Indonesia

(Received 22 March, \985)

Abstract. From the photographs taken at the total solar eclipse of 11 June 1983, we derived the electron density for the north polar rays and for the thread-like fine structures above the active region, which are 108 at 1.4 solar radii and 3 x 109 at 1.15 solar radii, respectively. The brightness distributions of the corona at the polar region and above the active region, and the flattening index were also derived.

1. Introduction

The corona has thread-like fine structures, which presumably follow the coronal magnetic fields closely. Some structures extend radially and some show loops, surrounding the prominences. Coronal heating is probably related to the magnetic field and, therefore, the physical conditions of the thread-like fine structures in the corona would be important for considering the coronal heating.

For the purpose of obtaining details on fine structures of the corona, coronal observations at the total solar eclipse of 11 June, 1983 were carried out at Cepu and Mojokerto in Java island in Indonesia. The weather on the eclipse day was good at Mojokerto, but cloudy at Cepu.

2. Observing Instruments

A horizontal telescope of a doublet lens (</> = 20 cm, f = 11 m) fed by a 30 cm aperture Coelostat was used for observing the K corona by using an 0-57 sharp cut filter with



10 E. HIEI ET AL.

a large aerial camera (WILD made in Swiss) at mid-totality. A part of the green line corona, observed with an interference filter of 5303 A (bandwidth; 3.7 A), and a part of the K corona, observed with an interference filter of 5000 A (bandwidth; 450 A), were both photographed with four 35 m/m Nikon motor drive cameras just after the second contact and before the third contact. The films used were Kodak Plus-X aerographic film 2402 for the large camera, and Kodak Tri-X for 35 m/m cameras. A 20 em equatorial telescope with a doublet lens (f = 225 em) was used for taking the K corona and green line corona by using interference filters of 5780 A (bandwidths ;400 A) and 5303 A (bandwidth; 3.7 A), and their degree of polarization was measured with a linear polarizer. Kodak Tri-X 2B film was used for this purpose.

The K corona was also observed with a Celestron 5 (¢ = 12.7 em, f = 127 em) and Celestron 8 (¢ = 20 em, f = 2 m) using Kodak 2415 film.

Fig. I. Photograph taken with a 10 cm equatorial telescope (f = 110 cm) at Mojokerto. Effective wavelength: 6270 A, film: Kodak 2415, and exposure time: 1 s.

CORONAL STRUCTURE OBSERVED AT TOTAL SOLAR ECLIPSE 11

The former two instruments were operated at Cepu by the team of the Tokyo Astronomical Observatory, and the two Celestrons were operated by the team of LAPAN (Indonesian National Institute of Aeronautics and Space).

The team of the International Latitude Observatory took the fine K corona at Mojokerto with a 10 cm equatorial telescope (f = 110 cm) at an effective wavelength 6271 A by using an interference filter (bandwidth; 98 A).

-5

Brightness

X Koutchmy

~ our observation -6 - X

.\ e·--. Allen

'~ lC .2 , \9 , ~ , ®

lC , .. , Ii ., 0

, ® ....1 , (j , lC .. ,

-7 r-, ,

... ... ... ... ... , , ... ... , "- , ... ... ...

... ... -8 I-

... ... - 9 ... ' ... .,

Z .. • 0 • . - electron density ....1 0 • • - • - • •

• • .. • • ours 0 • 8 -9 - • • • •• 0 • 0 Saito •

0 • 0

0

I I I ,.., I 7

1.0 1.2 1.4 1.6 1.8 r / R0

Fig. 2. Brightness distribution of the corona at the north polar region (above), and derived electron density (down) with height in units of the solar radius. The left ordinate is expressed in units of the continuum brightness at the disk center at 6270 A. The cross represents brightness measurements by Koutchmy and Nitschelm (1984), and 'Allen' means the smoothed coronal brightness at the pole, at minimum phase, in

the K corona (Allen, 1973). The circle represents the electron density derived by Saito (1965).

12 E. HIEI ET AL.

3. Observations

The geodesic positions of the observing sites at Cepu and Mojokerto were determined by Doppler observations of the NNSS satellite. The positions are at longitude = E 111 ° 35' 25': 909; latitude = S 7 ° 7' 52 ': 350; h (height from sea level) = 92.07 mat Cepu, and at E 112 °26' 39': 540; S 7°27'1': 355; h = 77.53 m at Mojokerto.

The eclipse observations at Cepu were carried out under a cloud, though the films taken with longer exposure times of 30 s show some coronal features. At Mojokerto, however, fine coronal photographs were obtained at an exposure time of 1 s as shown in Figure 1.

... I

0 .30

0 .20

0.10

0.00

c = a+b(Req / Re -1)

a+b / ----- ----- --1: i ' x* iXx

/

/' '\ ~ x x

I

/ I ,

I

/ a-b

11 d X

• • •

x

2

X Ko utch my

o Ou rs Mojokerto)

• Ours ( Cepu)

3 4 5 r=Req / Re

Fig. 3. Flattening index versus height. The crosses denotes the results of Koutchmy and Nitschelm (1984); the circles at Mojokerto; and points, those at Cepu, LAPAN.


4. Analysis

The films taken at Mojokerto and Cepu were traced with a microphotometer at the Tokyo Astronomical Observatory.

The brightness distribution of the corona was derived from the film taken at Mojokerto. The solar disk, reduced by neutral filters, was taken before and after the eclipse for an absolute calibration. The brightness distribution with height at the north polar region is shown in Figure 2, which is in good agreement with Koutchmy and Nitschelm (1984) result.

The intensity and width of a north polar ray were measured along its length. The intensity around the ray was assumed to be as a background and a total width at half intensity was measured at different heights. This width, on average, is about 10 arc sec, which is almost the same as the measurements by van de Hulst (1950).

The electron density for the ray is derived as shown in Figure 2, under the assumption that the length in line-of-sight of the ray is the same as its width. The deduced electron density is about five times larger in this ray than Saito's (1965) result.

The flattening index, defined by H. Ludendorff (van de Hulst, 1953), was computed by using the iso-intensity curves derived from the film taken at Mojokerto. The film taken by the LAP AN team at Cepu, which might be affected by cloud, also gives the flattening index near the solar limb. The index values at Mojokerto are in agreement with Koutchmy and Nitschelm (1984) result, as shown in Figure 3.

The thread-like fine structures above the active region at the west limb were measured on the film taken with the horizontal telescope at Cepu. Iso-intensity curves indicating

2 . 5 X 1 0 '<1

B A

---------------------Fig. 4. Iso-intensity curves, and positions, of the thread-like fine structures derived from the film at

Cepu.

14 E. HIEI ET AL.

the positions of the fine structures are shown in Figure 4. The absolute intensity has here been calibrated in such a way that the brightness above the equator at the west limb becomes equal to that derived from the Mojokerto data. The widths of the fine structures are about 10 arc sec on the average. The electron densities for these structures have been derived, as shown in Figure 5, under the same assumption of cylindrical shape of the structures. The widths of the thread-like structures above the active region, and the polar ray, are about the same. If the electron density above the active region decreases with height in the same way as Newkirk's (1967) model, then the electron densities above the active region at 1.4 solar radii are larger by 10 times than at the polar ray.

12

11 f-

10

'" F ~ Z E C

bJ) B 'e D

0 H ...:l

A 0 0 G

9

Newkirk

7

1.0 1.2 1.4 1.6 1.8

r / R0

Fig. 5. Electron density of the fine structures with height. The dotted line is a model corona at maximum phase (Newkirk, 1967). A, B, ... , H are the electron density values in each fine structure.


Acknowledgements

We would like to express out hearty thanks to the National Committee for the 1983 Solar Eclipse in the Indonesian Institute of Sciences CUPI) for giving us information and taking care of the customs arrangements for the eclipse, and to the Indonesian National Institute of Aeronautics and Space (LAP AN) for arranging the observing sites and sending the staffs to help our observations. The research of the eclipse observation was carried out with the support of the Overseas Scientific Research, Ministry of Education, Science, and Culture, Japan.

References

Allen, C. W.: 1973, Astrophysical Quantities, third ed., The Ath10ne Press, London, p. 176. Koutchmy, S. and Nitschelm, c.: 1984, preprint No. 49, Institut d'Astrophysique de Paris. Newkirk, G., Jf.: 1967, Ann. Rev. Astron. Astrophys. 5. Saito, K.: 1965, Pub{. Astron. Soc. Japan 17, 1. Van de Hulst, H. c.: 1950, Bull. Astron. Inst. Neth. 11, 150. Van de Hulst, H. c.: 1953, in G. P. Kuiper (ed.), The Sun, The University of Chicago Press, p. 285.

CONTINUUM ABSORPTION IN THE SOLAR EUV SPECTRA*

TAKARA NISHIKAWA

Takayama Junior College, Takayama, Gifu, Japan

(Received 7 October, 1985)

It has been shown from ground-based and space observations that the lower corona of the Sun contains a significant amount of cool chromo spheric material in highly inhomogeneous structures, such as spicules, dark mottles, and fibrils. Therefore, some interactions between the cool and the hot material have been found in optical and ultraviolet observations. One of such phenomena is the weakening of solar EUV line emission originating from the chromosphere-corona transition region (H I weakening) in the cool chromo spheric material above the EUV emitting region, as suggested by Kanno (1979) and Schmahl and Orrall (1979). The remarkable nature of the weakening is that it is found even at the disc center of the quiet Sun.

Here we calculated the weakening of 11 ions by solving the rate equations (Dufton, 1977) in order to examine the wavelength-dependence of the weakening, because some authors did not find it (e.g., Doschek and Feldman, 1982).

Four points of this work are superior to other works up to now. (1) The steady-state rate equations of multilevel atoms were solved. Then we

calculated the predicted intensities of a number of lines of 11 ions by using Dufton's (1977) code. This code includes the spontaneous transitions, the collisional excitations by electron and proton impact, and the collisional de-excitations.

(2) New atomic data were used. (3) In calculating the weakening we used only lines belonging to the common ion,

which exclude the systematic errors due to an abundance, an ionization calculation, and various atomic data as well as due to the adopted values of the pressure and the temperature gradient of the model.

(4) We convolved the intensities predicted from multilevel calculations over an instrumental profile of the observation, because all members of a multiplet were not always contained in the bandpass (1.6 A) of the Harvard spectrometer on Skylab.

The equivalent optical thickness 'L"H was used as the parameter representing the degree of the weakening. 'L"H is defined by

IObs/lpr = k exp [ - (}c/ AH)3 'L"H] ,

where lobs and lpr are the observed and predicted intensities, respectively, A is the

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan. between 30 September-6 October, 1984.


18 T. NISHIKAWA

I I I~ 1.4

X

0 Q ~

o 19

6l! 41 It tSI 'i'

III .4 ~ C. 0

"-~

.c -1 & ~

0 ~

:2 I ..l xI

I -2 I

I I I

0 0 .5 3 5

(A / AH )3

Fig. I. The normalized weakening In(Iobs/k1pc) vs (A/AH)3 for the quiet Sun. x: Cu, L: Nu,.It.: NIII, L: N IV, .: 0 III, 0: 0 IV, 0: 0 v, and 0: S IV. The points with arrows are the upper limit estimations

due to blends.

4

o ... 'l: 2

o . ---

4.2

°t t f

o as HI o AR

... as He I t;. AR

--- - --- -_. --- -- -;.- .. -.. --- ...... ~

4.6 5.0 5.4 5.S 6.2 LO G T

Fig. 2. The equivalent optical thicknesses 'H and 'He as a function of temperature. The error bars show the standard deviations for each ions.

wavelength of the line, and AH = 912 A. 'H is the optical thickness at the Lyman continuum head, when the absorbing cool chromo spheric material is assumed to be located above the EUV emitting region, and k is a normalization factor showing the systematic errors mentioned above.

CONTINUUM ABSORPTION 19

Furthermore, we calculated the weakening due to neutral helium continuum absorption (He I weakening), which may be appear in lines shortward of 504 A. The data used were from Vernazza and Reeves (1978) and Doschek and Feldman (1982).

The results were shown in Figures 1 and 2. Figure 1 clearly indicates that the weakening increases as the wavelength increases in the range of A < 912 A. It seems that the points of the quiet Sun concentrates on a straight line in A < 912 A. This linearity of the weakening justifies the cloud model, as concluded by Kanno and Suematsu (1982) and Nishikawa (1983).

We summarized the equivalent optical thickness !H calculated for each ions in Figure 2. This figure also includes those due to He I weakening. The abscissa is the temperature of the maximum ion concentration (Jordan, 1969). !H s of the quiet Sun show a good agreement among the various ions formed in the transition region (4.3 < log T < 5.4). This agreement also justifies that the weakening should be surely due to Lyman continuum absorption.

The ratio of both optical thickness must be a good diagnostics of the temperature, since the neutral hydrogen can be ionized at lower temperature than the neutral helium. We can estimate the temperature of the weakening cloud using the two equivalent optical thicknesses.

We calculated the ratio R = !H/!He as a function of the temperature using the model C ofVernazza et al. (1981 ). We estimated R > 9 from the H I and He I weakenings in the quiet Sun. We conclude that the temperature of the weakening cloud is less than 7000 K. In consideration of the error of the calculation of R, the upper limit of temperature will be at most 9000 K.

References

Doschek, G. A. and Feldman, U.: 1982, Astrophys. J. 254, 371. Dufton, P. L.: 1977, Computer. Phys. Comm. 13,26. Jordan, c.: 1969, Monthly Notices Roy. Astron. Soc. 142, 501. Kanno, M.: 1979, Publ. Astron. Soc. Japan 31, 115. Kanno, M. and Suematsu, Y.: 1982, Publ. Astron. Soc. Japan 34,449. Nishikawa, T.: 1983, Solar Phys. 85, 65. Schmahl, E. J. and Orran, F. Q.: 1979, Astrophys. J. 231, L41. Vernazza. J. E. and Reeves, E. M.: 1978, Astrophys. J. Suppl. 37,485. Vernazza. J. E., Avrett, E. R .• and Loeser, R.: 1981, Astrophys. J. Suppl. 45,635.

HEIGHT MEASUREMENTS OF S-COMPONENTS*

KlYOTO SHlBASAKl

Research Institute of Atmospherics, Nagoya University, Toyokawa, Japan


Abstract. The direct measurement of the height of the radio source above a solar active region was done by the Westerbork Synthesis Radio Telescope when the source crossed the west limb. The height of the brightest part was 12000 km above the limb. The result of the disk observation is also presented and the emission mechanisms of the observed sources are discussed.

1. Introduction

The height of radio sources above solar active regions (S-components) provides very important information for interpretation of radio emission mechanisms and for the study of physical conditions above active regions. There are many methods to measure the heights of S-components. These methods are based on the fact that the radio sources at higher altitudes shift limbward relative to the photospheric or chromo spheric features when they are away from the solar disk center and are projected on the disk. In these methods, it is assumed that the radio sources are just above the optical features, such as sunspots and plages, and that radio sources co-rotate with these optical features. These methods are used to compensate low resolution observations and correct inaccuracies in position of radio sources and optical features. The results of height measurements at various frequencies by various authors have been summarized by Graf and Bracewell (1973).

Large synthesis radio telescopes such as the Westerbork Synthesis Radio Telescope (WSRT) and Very Large Array (VLA) have high spatial resolution and high positional accuracy. Observations using these telescopes make the measurement of radio source heights more reliable if the positional accuracy of the corresponding optical picture is sufficient. Felli et al. (1981) used VLA radio maps and Sacramento Peak optical pictures and found the sunspot associated source height of2 x 104 km at 6 em wavelength. The accuracy of the measured height depends on the accuracy of the position of the optical picture, Akhmedov et al. (1982) observed an S-component at the extreme limb by the RATAN 600 radio telescope. Their one-dimensional multi-frequency observation shows that the circularly polarized component of the S-component coincides with the optical spot to within ± 1500 km at 3.2 and 4.0 em, while the intensity peak is at a much higher altitude.

* Paper presented at the lAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984.


22 K. SHIBASAKI

In the following, two measurements of S-components are presented, using the synthesis observation by WSRT. One is a direct measurement of an S-component on the solar limb. The other is a measurement on the solar disk using the limbward shift of radio sources relative to the optical features. Very accurate positioning of the optical picture is obtained.

2. Limb Observation

The height of an S-component can be measured directly when the active regions cross the solar limb. We synthesized the radio map of AR3080 (Hale Region 17620) on 12 May, 1981 when it crossed the west limb, by use of the Westerbork Synthesis Radio Telescope (WSRT).

WSRT consists of 14 dishes of 25 m diameter, and the longest baseline is 3 km in the EW direction. The observation was done at 6 cm wavelength and the synthesized beam was 3.5" (EW) x 13" (NS). It took 12 hr to synthesize a two-dimensional map using the Earth's rotation. AR3080 crossed the west limb of the Sun in the middle of the observation. The relative motion of the radio source due to solar rotation with respect to the solar disk at the extreme limb can be ignored. The fringe stopping center was fixed to the west limb at 16 deg north.

Figure 1 is the synthesized intensity map. The contour interval represents a brightness temperature of 105 K. An extended source above the west limb is associated with AR3080 and the peak brightness temperature is about 3.5 x 105 K. The height of the brightest part of the extended source is 12000 km above the photosphere. No circularly polarized component was detected for this source. The activity of AR3080 was at maximum on 5 May and produced a 3B flare. After that, it declined, and the activity during the observation was low. A compact V-shaped source at the lower left comer has been deformed somewhat by the relative motion due to solar rotation during 12 hr observation.

3. Disk Observation

On the solar disk, the height of an S-component is measured by the limbward shift of the radio source relative to the corresponding optical feature. We observed the Hale Region 16898 on 13-16 June, 1980, and overlayed the radio maps on the optical pictures.

The radio observations were done by WSRT. Detailed observations and results are in Shibasaki et al. (1983). An accurate overlay of the radio map on the optical picture was done in the following way. We used the full-disk white-light picture, which is exposed twice during a few minutes interval, to measure the east-west drift direction accurately. After drawing a fine mesh on the picture, we expanded that part which includes HR 16898 up to the same scale as the radio map. We plotted the fringe stopping center of the WSRT observation on the enlarged optical picture and overlayed the radio map on it. We selected the data of 16 June to determine the height of radio sources

HEIGHT MEASUREMENT OF S-COMPONENTS 23

ilEA ..

e

Fig. I. Synthesized intensity map of AR 3080 on the West limb on 12 May, 1981. The contour interval is 105 K. The latitude lines are 10 and 20 deg north and the interval of longitude lines is 10 deg.

o

1 erc min.

Fig. 2. Overlay of the radio intensity profile and the corresponding white-light features. The contour level is 4 x 105 K. Sunspots are shaded. The dotted lines are the boundaries of sunspots shifted limbward corresponding to a radial height correction of 6000 km (alternatively one could shift the radio contours

toward the center).

24 K. SHIBASAKI

because the activity was low, and the spots were stable compared with the other days .. In Figure 2, the low brightness temperature contour of the radio intensity (T = 4 x 105 K) and the sunspots (shaded areas) are overlayed. The dotted lines are the boundaries of the sunspots shifted limbward for a radial height correction of 6000 km (instead of shifting the radio contours toward the center). It is clear from the coincidence between the radio contours and the shifted sunspot boundaries that the weak and small radio sources are systematically shifted toward the solar limb with respect to the small spots. But the strong and large radio source above the leading spot does not show any shift.

Ifwe assume that the radio sources are radially located above the sunspots we deduce a height of 6000 ± 3000 km above the photosphere. (The error is the maximum uncertainty of the overlay.) This assumption is supported by the systematic shift between radio and optical features. As already mentioned the low brightness contours of the large and strong radio source above the leading spot does not show shift. This means that the height of the low brightness region, surrounding the strong source, is very low (less than 3000 km).

There is another source which is extended, and connects the leading large sunspot and the following part. The height of this source cannot be determined, because there is no clear optical counterpart.

4. Interpretation and Discussion

In the above observations three height values are obtained of S-components associated with different kind of optical features. The first one is 12000 km above the solar limb. This source was extended in structure and no circular polarization was detected. The brightness temperature was 3.5 x 105 K. The radio source on 16 June, 1980, which connects the leading sunspot and the following part, had an extended structure, and the brightness temperature was 5-10 x 105 K. These sources are interpreted as due to the free-free mechanism acting in a high density plasma, trapped by the magnetic field which connects the leading and the following sunspots. Ifwe assume uniform temperature (T) and density (N) within the source, the brightness temperature (Tb ) can be calculated in this way:

where "[ is the optical depth, L, thickness of emitting region (cm); and f, observing frequency (Hz).

The thickness of the emitting region can be assumed from the observed source size. From these equations and the observed brightness, we can find the density if the temperature is known. Ifwe assume a coronal temperature of 106 K, the density is about 1010 cm - 3. The calculated density is insensitive to the temperature.

The second height is 6000 ± 3000 km, corresponding to small sunspots. Figure 2 shows the weak compact radio source associated with the small sunpots. These sources

HEIGHT MEASUREMENT OF S-COMPONENTS 25

are interpreted as free-free emission from the legs of magnetic loops, such as are often observed in EUV pictures. Weak circular polarization was detected.

The last one is the source associated with a large sunspot. No radial shift was detected due to projection effects. The emission mechanism associated with the large sunspot is gyroresonance. The outer boundary of the source corresponds to the outer boundary of the third harmonic layer, where the magnetic field strength is ~ 600 G. This boundary coincides with the large sunspot. As the maximum magnetic field strength of the sunspot was 3000 G (Crimean Observatory), the photospheric magnetic field strength of the sunspot decreases to 20 % from the center of the sunspot to the outer edge of the

penumbra.

5. Summary

The heights of S-components of solar radio emission above the photosphere was measured using high resolution radio maps of active regions on the solar limb and on the solar disk. On the extreme limb, the height of radio sources can be measured directly. The observed S-component was extended in structure, and the brightest part was 12000 km above the photosphere. This source is explained as being due to free-free emission from a high density plasma trapped by magnetic loops connecting the leading and following sunspots.

On the solar disk, heights can also be measured from the radial shifts of the radio sources relative to the optical features. We determined the position of an optical map very accurately. The height of radio sources associated with certain small sunspots was found to be 6000 km. The emission was due to a free-free process from the legs of magnetic loops, such as are observed in EUV pictures.

A large and strong radio source associated with a large sunspot does not show any shift relative to the sunspot. The emission is due to gyroresonance, and the outer boundary of the third harmonic layer (600 G) coincides with the outer boundary of the sunspot penumbra. The magnetic field strength decreases to 20% from the center of the sunspot to the outer edge of the penumbra.

References

Akhmedov, Sh. B., Gelfreikh, G. B., Bogod, V. M., and Korzhavin, A. N.: 1982, Solar Phys. 79, 41. Felli, M., Lang, K. R., and Wilson, R. F.: 1981, Astrophys. J. 28, 325. Graf, W. and Bracewell, R. N.: 1973, Solar Phys. 28,425. Shibasaki, K., Chiuderi-Drago, F., Melozzi, M., Slottje, c., and Antonucci, E.: 1983, Solar Phys. 89,307.

V ARIATIONS IN QUIET SUN RADIATION AT CENTIMETRE

WAVELENGTHS DURING SOLAR MAXIMUM PERIOD*

B. LOKANADHAM and P. K. SUBRAMANIAN

Centre of Advanced Study in Astronomy, Osmania University, Hyderabad, India


Abstract. Observations of solar radio emission at 3 cm wavelength have been made at Japal-Rangapur Observatory for 1980-1981, the solar maximum year using the 3 m radio telescope. The correlation between microwave solar emissions and the sunspot activity on monthly basis has been found to be high during the maximum phase and in the high cm wavelength band. The basic component has been estimated statistically for successive solar rotations using the data obtained at Japal-Rangapur Observatory. Further, this was compared with the data obtained at other em wavelengths during 1980-1981 and the solar minimum period 1975-1976 of the 21 st cycle. The comparison showed pronounced dips in flux levels at different wavelengths during the summer months of the solar maximum year which may be attributed to the presence of coronal holes in the various levels of the solar atmosphere. The computed basic component values showed pronounced variation at high cm wavelengths for the solar maximum period with dissimilar variations at different wavelengths. During the solar minimum period the variations were negligibly small and showed more or less constant level of activity.

1. Introduction

The quiet Sun radiation represents the radiation of the undisturbed static solar atmosphere. The undisturbed component has been observed to vary markedly during a solar cycle (Van de Hulst, 1949; Pawsey and Yabsley, 1949; Christiansen and Hindmann, 1951; Das Gupta and Basu, 1965; Xanthakis, 1969; Kruger and Olmr, 1973; Zieba and Gula, 1976). Recent observations with high-spatial resolutions (Kundu and Velusamy, 1974; Zirin et al., 1978) have shown the existence of chromo spheric fine structure mainly influencing the centimetre and millimetre wavelength radiations showing the importance of radio observations at these wavelengths to explain the variation of the quiet Sun radiation at centimetre wavelengths.

2. Observations and Analysis

The present paper gives a study of the quiet component of the solar radio emission during the solar maximum period, 1980-1981 at 3 cm derived from the radio observations of the Sun carried out at J apal-Rangapur Observatory, Osmania University with the 10 foot radio telescope operating in Dicke mode having the following characteristics:

Frequency (GHz) 10 Radiometer sensitivity (K) 0.5 Integration time (second) 1 Total receiver noise figure (dB) 7 Antenna dish diameter (m) 3 Effective beamwidth (deg) 0.8

* Paper presented at the lAD Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984.


28 B. LOKANADHAM AND P. K. SUBRAMANIAN

The daily mean solar flux values are determined from the regular observations at 10 GHz carried out during the period February 1980 to June 1981.

The quiet component of the solar radiation at 3 cm wavelength during each 27 -day rotation period is determined from the plots of the daily flux values against the sunspot number and by drawing a least square best-fit line assuming the equation

where

Bo = observed daily mean flux,

Bo = the basic component corresponding to 'zero' sunspot number,

k = a constant which corresponds to slope, and

R = Zurich sunspot number.

The quiet Sun levels thus obtained from 3 cm wavelength radio observations during solar maximum period are given in Figure 1. The values of the basic component at other

r-~--~--~-'--~--'---r-~---r--~--r-~---r--~-'r-~--,Rz

;:, u:

1)0

90

140

iii 100

12

10

J to

10·2 em

]·Oem

..... .' .....

/ , .

""'-"-.. / ;.-.-........ . / ...... ......-. - ...... . ...... .'

"

.-f

f

A o NOM A M J ---------------*~f~------1981 ~

Fig.!. Variation of B-component at various wavelengths for 1980-1981.

180

11,0

::> u: VI

r:

r: a/ r: o Q.

90

80

70

115

10S

E 280 o u V

11\ o

CD 260

21.0

525

505

16

8

VARIATIONS IN QUIET SUN RADIATION

• 1\

\ J', ..... ' --,I

,", _ ... I '..... ..... ... "

I \ I \

I \ ,

Sunspot actiVity

10·2 em

,., 3·1gem

,.'/ ".--- ........... - -. --... - -.- ... ~ ,'.- - .... ' \

\

I •

, , •

" . /

..... -._-.,. ........ ., .. ., ...... ' .......

/ '. , \.

1·gem ,

" ..... ......

" \ / ". \ "

\_.-- ................

, ., Mean Ap index

30

10

SON 0 J F M A M J J A SON 0 1975 -I- 1976 ~

Fig. 2. Variation ofB-component at various wavelengths for 1975-1976.

29

wavelengths using the solar flux data taken from 'Solar Geophysical Data' volumes are also given in the same figure for comparison. The quiet Sun component at these wavelengths during the solar minimum period 1975-1976 are also evaluated and presented in Figure 2. From Figures 1 and 2 it is seen that the variations of the basic


::i u.: vi c:

-r::: .. r::: 0 0..

E 0

u , OJ

5LO

SOO -

L60 -

L20 r-

380 r-

3LO .-

300 ~

260 r-

220 f-

180 -

140 -

100 ~

60 I

"-• ......

I I I 3 5 7

I I

/

I

/ ,

/ "

/

I I

I I

-x-x - Min i mum Period

__ Maximum Period

• I

,

- - - -e

-- x I I 9 1 1

Wavelengt h I n ems

Fig. 3. Variation of B-component and apparent temperature with wavelength.

- 64

- 56

~ - 48 ""8

~

Q ~ -.... ..

- LO 3 ..., II> ~

Q

c: - 32 ...

II>

x 1 03 K

- 2L

- 16

- 8

component at all cm wavelengths are dissimilar. It remained more or less constant during solar minimum period, whereas there are considerable variations during the maximum perio'd.

The apparent disk temperatures at different wavelengths have been obtained from the estimated values of the basic component and are plotted in Figure 3. It is seen from the figure that the basic component decreases with increase in wavelength, whereas the

VARIATIONS IN QUIET SUN RADIATION 31

apparent disk temperature (Td) increases. This shows clearly the thermal nature of the quiet Sun component at cm wavelengths.

3. Discussion

The dissimilar variations of the B-component at different cm wavelengths as is evident from the present investigation may be explained due to radiations from various active centres occuring simultaneously at different levels of the solar atmosphere. Due to these time-varying active centres at different levels, the electron temperature which is the cause of thermal emission from the solar atmosphere can vary irregularly and contribute to the observed quiet Sun flux variations. During the maximum phase, the active-centres associated with magnetic fields would be more in the solar atmosphere than during the minimum phase causing more fluctuations in the B-component. The pronounced diminutions in the flux levels of the B-component at different wavelengths as seen in Figure 2 during summer months of the Solar Maximum year suggest the intrinsic reduction of radio emissions due to the presence of coronal holes in the upper chromosphere-corona transition region, as explained by Covington (1977). This is evident by the presence of the peak Ap index during this period, since coronal holes are believed to be associated with the occurrence of magnetic storms (Bohlin, 1977).

4. Conclusion

The quiet Sun radiations at cm wavelengths are found to vary considerably during solar maximum period and are mainly influenced by the various time-varying active centres present at the upper chromosphere-corona transition region, revealing the inhomogeneous structure of the transition and upper chromo spheric levels of the solar atmosphere.

Acknowledgements

One of the authors (P. K. Subramanian) gratefully acknowledge the Osmania University authorities and the University Grants Commission, New Delhi, for the award of teacher fellowship.

This work has been supported by University Grants Commission, New Delhi, through the Research Project No. F-23-1189/79 (SRII/III).

References

Bohlin, J. D.: 1977, Solar Phys. 51, 377. Christiansen, W. N. and Hindmann, J. V.: 1951, Nature 167, 635. Covington, A. E.: 1977, Solar Phys. 54, 393. Das Gupta, M. K. and Basu, D.: 1965, Nature 208, 739. Kruger, J. L. and Olmr, T.: 1973, Bull. Inst. Czech. 24,202. Kundu, M. R. and Velusamy, T.: 1974, Solar Phys. 34, 125.


Pawsey, J. L. and Yabsley, D. E.: 1949, Australian J. Sci. Res. A2, 198. Van de Hulst, H. c.: 1949, Nature 163, 24. Xanthakis, J.: 1969, Solar Phys. 10, 168. Zieba, S. and Gula, R.: 1976, Acta Astron. 26, No.1, 53. Zirin, H., Hurford, G. J., and Marsh, K. A.: 1978, Astrophys. J. 224, 1043.

ANALYSIS OF A MAGNETOHYDRODYNAMIC STELLAR

WIND*

YASUMICHI SAITO

Physics Department, Faculty of Education, Iwate University, Morioka, Japan

and

MAMORU SAITO

Department of Astronomy, Faculty of Science, Kyoto University, Kyoto, Japan

(Received 13 June, 1985)

Abstract. Characteristic features of solutions are analysed around the Alfvenic point. There are three types of solutions through the point.

According to Weber and Davis (1967), the radial motion of a steady stellar wind is expressed by a nonlinear ordinary differential equation of first order and first degree. The topology of the solutions shows two critical points and one node. The critical points, which are concerned with the slow and fast modes of magneto-acoustic waves, are simple X-type singularities. The node is known as the Alfvenic point. The characteristic features of solutions around the Alfvenic point have not been well clarified. Here we analyse solutions around the point by functional series expansions through the method of undetermined coefficients.

The radial velocity v~ is expressed around the Alfvenic point ~A as

co

V~/V~A = 1 + L (Xi(~A - ~r;, i= 1

where ~ is the radial distance measured in units of the stellar radius, (Xi is a function of the physical quantities and not zero, and m i is a positive numerical value, A refers to the Alfvenic point. We consider Alfvenic Mach numbers for radial and azimuthal components and denote them as MA~ and M Arp, respectively. M;,,~ and M;"rp represent the ratios of kinetic energy of gaseous motion to magnetic energy for each component. The radius and radial velocity at the Alfvenic point are expressed by using the Alfvenic Mach numbers at the stellar equatiorial surface M A~, 0 and M Arp, 0 as ~A = {(I + (MA~,oMArp,o)-I)/(l + MA~,o/MArp,oW/2 and V~A = v~o/(~AMA~,O)2. We pay attention to the case of strong radial magnetic field, i.e., M M,O < 1 and ~A > 1. The stellar wind for ~A < 1 has been studied by Saito (1974).

There are three types of curves passing through the Alfvenic point on the ~ - v~ plane.



34 Y. SAITO AND M. SAITO

(I) Cuspidal curve about the Alfvenic point:

This solution has m; = (i + 1 )/3 and

IXI = [2Ad(Az - A3)P/3

with

and

Al = (1 + MAl;, o/MA</>, o)Z,

Az = (cso/V</>o)Z MJ",CZ,o I) ,

A3 = (VI;O/V</>O)Z/( (A MAl;, ot ,

where v</> is the rotation velocity, Cs is the sound speed, and y is the polytropic index. The curve separates into two branches across the Alfvenic point. The tangential line of the branches is (= (A' It is difficult to obtain a general recursion relation among coefficients for higher order terms because of the nonlinearity of the expansion equation.

The value of IX; usually becomes larger as i increases, and v,; may be convergent for I(A - (I ~ 1. We consider, for example, a rapidly rotating star with strong radial magnetic field, i.e.,

vesc,o/v</>o = 1.2 and MAl; = 0.1 ,

where Vesc is the escape velocity. If values of other parameters are taken as vI;O/v</>O = 0.01, cso/v</>o = 0.02, MA</>,o = 1.0, and y = 1.1, we obtain

(A = 101/Z and V,;A = 0.1 V</>o ,

and also IXI = - 7.02, IXz = 179, and 1X3 = - 457. Thus the radius of convergence is less than 10 - 5. For slowly rotating stars, Az and A3 are both not so small, and thus radius of convergence is greater than 10 - 5.

The leading term of the solution is concerned with the kinetic energy of gas, the gas pressure, and the magnetic energy, but not concerned with the gravitational energy. Along the branches of the solution, the magnetic strength B</> changes sign across the Alvenic point.

(II) Rectilinear curves about the Alfvenic point:

This solution has m; = i, and IXI an arbitrary non-zero constant. The solutions have been studied by Limber (1974). For various values of M A</>, 0' we can obtain the solutions which do not pass through the X-type critical points and approach non-zero radial velocities at (--+ w (Limber, 1974; SaitO, 1974).

The leading term of the solution is concerned with the magnetic energy only. Across the point all the physical quantities continuously change with non-zero values.

(III) Parabolic curve about the Alfvenic point:

This solution has m; = i + 1 and IXI = 2(A4 - 2Az)/(A I (!J with A4 =

ANALYSIS OF A MAGNETOHYDRODYNAMIC STELLAR WIND 35

= (Vesc , o/vrpo)2/(2c,A)' The curve is an even function and the tangential line is v~ = V~A' The numerical values of coefficients are !Xl = 3.67 x 10 - 3, !X2 = 2.90 x 10 - 3, and 1X3 = - 4.13 x 10- 3 for the same values of parameters given for the solution (I).

The leading term of the solution is concerned with the gas pressure, the gravitational energy, and the magnetic energy. Along the parabola, vrp is proportional to 1X11 C,A - c, I and changes sign across the Alvenic point.

References

Limber, D. N.: 1974, Astrophys. J. 192,429. Saito, M.: 1974, Publ. Astron. Soc. Japan 26, 103. Weber, E. J. and Davis, L. Jr.: 1967, Astrophys. J. 148,217.

STUDY OF TIME-EVOLVING HYDRODYNAMIC CEPHEID

MODELS*

MINE TAKEUTI

Astronomical Institute, T8hoku University, Sendai, Japan

(Received 15 May, 1985)

Abstract. For studying modal coupling, we ran the hydrodynamic models of cepheids and observed the growth and disappearance of various modes in their pulsation. The existence of modal coupling has been confirmed.

1

Some recent analytical studies on stellar pulsation are based on the assumption that the time-evolving behaviour of pulsation is mostly controlled by modal coupling (see Aikawa, 1983, 1984; Dziembowski and Kovacs, 1984; Takeuti, 1985). A review paper has been presented by Takeuti (1984). For studying modal coupling, it should be necessary to run hydrodynamic models and to observe the growth and disappearance of various modes in their pulsation. Simon et al. (1980) studied hydrodynamic models and presented a two-amplitudes diagram which denied the idea of three-mode resonance. We shall demonstrate here some properties of our hydrodynamic simulation. We have had an indication that the time-evolving behaviour of pulsation is not a simple process in which the higher modes are weakened by dissipation. The existence of modal coupling has been confirmed in our study.

2

Keeping the hope to investigate the nature of double-mode cepheids in mind, we constructed two models near the blue edge of the cepheid instability strip, where double-mode cepheids are found observationally. The properties of models are tabulated in Table I. Model A has the mass usually predicted by the stellar evolution theory and Model B has a reduced mass. Pulsation periods and growth rates were calculated by the Castor code directly derived from the DYN-code, the hydrodynamic code we used. Three modes are pulsationally unstable in Model A and two in Model B. A part of the result for hydrodynamic simulation of Model B is illustrated in Aikawa et al. (1984). These results were analysed by the maximum entropy method (MEM), and the amplitudes of components were determined by least-square fitting for the obtained


Astrophysics and Space Science 119 (1986) 37-40. ©1986 by D. Reidel Publishing Company

38 M. TAKEUTI

TABLE I

Properties of model-cepheids

Model A B

Mass (in solar units) 6.714 5.039 Luminosity (in solar units) 2280 2280 Effective temperature (deg K) 5850 5850

Periods (in days) F 4.460 5.374

10 3.434 3.967 20 2.820 3.122 30 2.302 3.532

Growth rates F 0.006 0.017 10 0.024 0.045 20 O.oz8 - 0.030 30 -0.030 -0.174

periods. The periods and amplitudes for each mode will be published in future. In the present note, we describe only some of the more remarkable properties of the results.

3

First, we describe the pulsation of Model A. For the first case, Case 1, the initial radial velocity distribution imposed upon Model A is the fundamental mode (F-mode) with an amplitude of 10 km s - 1 at the surface. The initial condition for Case 2 is the F-mode with the amplitude corresponding to that of the limit-cycle, 19 km s - 1. Case 3 is started from the imposed first overtone (J O-mode) with the amplitude of 20 km s - 1 near the limit-cycle of this mode. These limit-cycles refer to the limiting oscillations when we drive a pure mode without any disturbance. In Case 1, although we imposed a pure F-mode, the second overtone (2 O-mode) became enhanced first, and then the lO-mode was enhanced, accompanied by a decrease in amplitude of the 20-mode. After the disappearance of the 20-mode, the lO-mode increased quite quickly and the amplitude of the F-mode decreased slowly, with a certain connecting relationship. In Case 2, the enhancement of a 20-mode never appeared, and the enhancement of the lO-mode began just after the start of simulation. The ratio of amplitudes of F-mode and 10-mode approached that of Case 1. We have calculated the simulation over a few hundred thousand steps for Case 1 and Case 2, corresponding to seven years and more, but did not find any stable limit-cycle yet. Model A had been moving to the pure lO-mode though the F-mode is still found. In Case 3, the amplitude of the F-mode evidently did not increase. Because we have not completed the calculation until the oscillation converges to the limit-cycle, the final state is still unclear. We can see, however, the behaviour of each mode seems to be determined from the position on the amplitudes diagram. The difference between Case 1 and Case 2 indicates the temporal appearance

TIME-EVOLVING CEPHEID MODELS 39

of the 20-mode is the result of insufficient suppression caused from the smallness of amplitudes both in the F- and lO-modes.

In Model B, the lO-mode increased with time first, and then reached a maximum value. The amplitude of the lO-mode decreases with enhancement of the F-mode, and finally the lO-mode was completely suppressed. No enhancement of 20-mode was found. The important difference of the properties of Model B from Model A is that the 20-mode is pulsation ally stable and the growth rate of the F-mode is greater than that in ModelA. The absence of the 20-mode and suppression of the lO-mode in Model B are probably connected with these properties. The temporal enhancement of the lO-mode indicates the coupling of these modes, and the existence of a threshold amplitude for suppressing the other mode. This seems also to be evidence for the modal coupling theory.

Because the DYN-code, which we used here, runs very smoothly with a small artificial viscosity, we succeeded in observing the behaviour of each mode in detail.

One of the most interesting results in the present study is the fact that the pulsation period-ratio found for Model B was a little small compared with that of the linear approximation during the phase when the 1 O-mode was enhanced. It is well-known that the observed period-ratio is certainly smaller than that calculated from the standard evolutionary stellar model for double-mode cepheids. So it is interesting that the period-ratio decreases when two modes are enhanced simultaneously. This property is not clear in Model A. We shall analyse carefully the results of our hydrodynamic simulation.

4

Through our hydrodynamic simulation we may believe that the convergence to the limit-cycle is the consequence of suppression of inferior modes by the strongest mode, not the result of a simple dissipative process on higher overtones. This modal coupling seems useful to investigate multi-modal phenomena in stellar oscillations. Vibrational instability is not sufficient for the stable limiting oscillation. The stable long-living pulsation may be established as a result of competition in various unstable modes.

Based on modal coupling theory, Takeuti (1985) proposed that the single-mode cepheid is produced from a star which has pulsation ally unstable modes, as a result of the suppression of inferior modes by the strongest mode. He also showed that the suppression of the lO-mode by the F-mode seems marginal in actual cepheids. By this theory double-mode cepheids are those cepheids for which the strongest mode cannot suppress the second strongest mode. Since the effectiveness of modal coupling is confirmed, double-mode cepheids will be reproduced from a suitable model which has two pulsation ally unstable modes without very strong coupling. The problem of the period-ratio remains still open, although we may suppose that the period-ratio would be reduced for a model which pulsates in a double-periodic way. We should try to construct a stellar model which shows long-life double periodicity.

40 M. TAKEUTI

Acknowledgements

I wish to express my thanks to Drs T. Aikawa and G. Kovacs for their useful discussions and to Mr K. Uji-iye for showing me his unpublished results.

References

Aikawa, T.: 1983, Monthly Notices Roy. Astron. Soc. 204, 1193. Aikawa, T.: 1984, Monthly Notices Roy. Astron. Soc. 206, 833. Aikawa, T., Takeuti, M., and Uji-iye, K.: 1984, Sendai Astronomiaj Raportoj 264,23. Dziembowski, W. and Kovacs, G.: 1984, Monthly Notices Roy. Astron. Soc. 206,497. Simon, N. R., Cox, A. N., and Hodson, S. W.: 1980, Astrophys. J. 237, 550. Takeuti, M.: 1984, Sendai Astronomiaj Raportoj 265, 1. Takeuti, M.: 1985, Astrophys. Space Sci. 109,99.

UNUSUAL VARIABLE STARS IN THE GLOBULAR

CLUSTER M4*

BAO-AN YAO

Shanghai Observatory, China


1. Introduction

With the development of observational techniques, at an accuracy of 0":'001 or higher, most stars have appeared to be variable and some have already been proposed to compile a non-variable star catalogue. We would not regard microvariability as unusual. The variable stars which we refer to as unusual in this paper are such stars whose amplitudes are moderately small in the classical meaning (0':'2 or so, much larger than that 0":'001), their photometric characteristics are not unlike those of D Sct stars, with large amplitude of certain stars of the RRs-type. Their positions on the C-M diagram are quite remarkable - where no such stars have been reported in literature as yet - and who people believe in their existence are few, at present.

There is a cooperative group in China consisting of members from Shanghai, Beijing, and Purple Mountain Observatories searching for new flare stars and variable stars in a series of dark cloud regions. While searching for such stars in the Sco-Oph region, a group of unusual suspected variable stars in the globular cluster M4 were found as a by-product in 1975 (1979). At first, we took them to be ordinary RR stars or long period red variable stars. On plotting them on the C-M diagram, and obtaining their light curves, we soon found their potential importance. If the discovery is true, it will be significant for the theory of variable stars and cosmogony, for it is not comprehensible to ordinary pulsation theory of variable stars. Though the declination of this globular cluster is - 26 0 26' and more suitable for the southern hemisphere, we, as northern hemisphere observers, still pay close attention to it. Owing to the fact that we have been working under unfavourable observational conditions, we can not say that all of these suspected stars are definitely variable and in order to solve the problem thoroughly we still have a long way to go. Although the progress made so far is not great, some exciting results have already been obtained.

2. Are There Any Variable Stars in the Middle Part of the Red Giant Branch of Globular Clusters?

F or the reason mentioned below only two of these suspected variable stars are dealt with in this paper, i.e., G265 and G266. According to Eggen (1972), G265: V = 12.99,



42 BAO-AN YAO

B - V = 1.35, U - B = 0.83; G266: V = 13.04, B - V = 1.36, U - B = 0.89. According to Alcaino (1975), however, G265: V = 12.87, B - V = 1.34; G266: V = 12.92, B - V = 1.37; but then according to Lee (1977), G265: V = 12.89, B - V = 1.30; G266: V = 12.95, B - V = 1.30 (photographic values). The angular distance between these stars is about 14", and their distance from the center of the cluster is about 3: 3, so their apparent positions on the C-M diagram are nearly the same, slightly below the middle part of the red giant branch. We have already shown the evidence that both G265 and G266 are variable (1979), but some people still have a little doubt about the truth of these variations for the simple reason that we observed at the rather large zenith distance and used mainly photographic methods. In order to clarify the problem we give further evidence here. In this paper we only discuss one question: are there any variable stars in the middle part of the RGB? Let us note that differential photometry should be more accurate, especially in the case where two stars have nearly the same colour and magnitude. Hence, we still present the values of 11m = G266-G265 (the difference between two light curves) instead of individual light levels. This is quite enough because they are both located almost at the same place on the C-M diagram. Whether one or both of them are variable, after the problem of membership has been settled, the argument that there are indeed variable stars in the middle part of the RGB will be proved.

All the figures given here are self-explanatory. As you can see, sometimes the light curve is relatively quiescent (Figure 1) and sometimes not. Even though certain errors can be admitted to be superimposed on the light curves, we cannot explain all the light curves as erroneous!

Though we take the light variation problem to be solved, there is still a membership question. While making the abstract of our paper (1979), the editor of the Astron. Astrophys. Abstracts, Vol. 29, literature 1981, part 1, added: 'It seems likely to consider all these variables as field stars' (1981), we only said: 'It seems hardly likely to consider all these variables as field stars if one thinks in terms of stellar statistics' (1979). Obviously, the editor's addition represents the conventional opinion: no variables exist in these parts. Fortunately, Norris investigated the cyanogen distribution of M4. He selected a number of red giant stars including G265 and G266 as samples and

G266-G265 0.05 •

• 0.0

~ <l

•

-0.05

13"0'" 13h30'" 14ho01 1979.8.25 UT

Fig. I. Yunan Observatory 1 m reflector 1 03a - 0 + GG 13, photographic photometry.

0. 10 l ~ 0.05

015

0.10

0.05 ~

0.00

-0.05

..

1~30m

UNUSUAL VARIABLE STARS IN THE GLOBULAR CLUSER M4

G266-G265

2~30n\

198 1.5. 1 T

•

43

..

Fig.2. (a) (upper) Difference of two comparison stars. (b) (lower) Measured on the same plates as (a), I03a - 0 + GG 13, I m reflector, Yunan Observatory.

G266-G265 c

0.20

.. 0. 15

::.. .. .. 0. 10 <l

.. • • .. .. • 0.05 • ..

0.00 .. .. - 0.05

16"om 16h30'" 1 7~0'" 17"30m

1979.5.28 T

Fig. 3. I 03a - D + GG II, photographic photometry Schmidt telescope of Beijing Observatory.

determined their radial velocities (Norris, 1981). The Vy of G265 is 62 km s - 1, it is a CN weak star (S3839 = 0.14), and G266's Vy = 60 km s - 1, its S3839 = 0.62, a CN strong star. The cluster's Vy is 65 km s - 1, so the conclusion seems inevitable: there are definitely variable stars in the central part of the RGB of M4.

0.15

0.10

0.05

0.00

44

•

..

"

BAO-AN YAO

G266-G265

c

..

18h 30m

1982.4.28 UT.

" c

19"0'"

Fig.4. Photoelectric photometry I m reflector of Yunan Observatory.

c

19"30"'

3. Is There Any Periodicity in the Light Curves of These Stars?

"

We have already tried to analyse the light curves with Deeming's Fourier analysis of unequally spaced data (Deeming, 1975). Maybe there exists some kind of periodicity, but it is too early to say any more about it because of our insufficient data.

4. Conclusion

For the first time new unusual variable stars have been found in the central part of the red giant branch of the globular cluster M4.

This is a challenge to the theory of variable stars and cosmogony.

References

Alcaino, G.: 1975, Astron. Astrophys. Suppl. 21 , I. Deeming, T. J.: 1975, Astrophys. Space Sci. 36, 137. Eggen, O. J.: 1972, Astrophys. J. 172, 645. Lee, S. W.: 1977, Astron. Astrophys. Suppl. 27,367. Norris, J.: 1981, Astrophys. J. 248, 177. 1979, Chinese Astron. Ore., No.5. 1979, Publ. of the Beijing Astron. Obs., No.4. 1981, Astron. Astrophys. Abstracts, Vol. 29, literature 1981, part 1, p. 581.

THE PHASE TRANSITIONS OF SUPERDENSE MATTER AND

SUPERNOVA EXPLOSIONS*

MARIKO TAKAHARA

Department of Astronomy, Faculty of Science, University of Tokyo, Japan

and

KATSUHIKO SATO

Department of Physics, Faculty of Science, University of Tokyo, Japan


Abstract. Effects of the phase transitions of superdense matter on supernova explosions are investigated with the aid of an idealized equation of state on the assumptions of adiabatic collapse. It is found that in the case of strong phase transitions explosions become weaker, while in the case of weak phase transitions explosions become stronger. However, the increment of the ejected energy is not so large as suggested by Migdal et al. (1979).

1. Introduction

In theories of type-II supernovae, the collapsing stellar core is considered to 'bounce' when the central density Pc exceeds the nuclear density Pn' because at such high density the equation of state (EOS) becomes 'stiff' due to the nuclear force. However, it has been suggested that at that density there could occur phase transitions to the pion condensed state, and to quark matter. If such transitions occur, what happens in the collapsing core? Migdal et al. (1979) suggested that the release of a great amount of the gravitational energy may result in a violent explosion. This is very important, because it will be a new mechanism for the formation of neutron stars, and because the formation of neutron stars from massive stars (M> 10 M 0) is difficult to achieve in current theories of supernova explosions. In order to make clear the effects of the phase transitions on supernova explosions, we performed simulations of the collapsing stellar cores.

2. Model of Equation of State with Phase Transitions

In order to treat phase transitions in a general form, we adopted the following idealized EOS. The total pressure P is assumed to be the sum of the cold pressure P Co which originates from degenerate leptons and the nuclear force, and the thermal pressure P T'



46 M. TAKAHARA AND K. SATO

N I

E

36

U 35 Ql

~ ::?.

o...U OJ

E 34 I , I , I , ,

33~~~ __ ~~' __ ~ 14 15 :

p" p" Ph logp (g em - J)

Fig. 1. Equation of state (EOS) of cold matter. The upper solid line represents the normal EOS (Model I of Bethe and Johnson), and the lower solid lines the EOS with phase transitions which start at Pc> and

terminate at Ph' The nuclear density is shown by Pn'

~ Case B 5/3

1

- - - - - - - - -I c," A

4/3t------f---'----, I

14 p ..

logp (g em - 3)

Fig. 2. Thermal stiffness YT' In Case A, YT remains at 1, while in Case S, it increases with density to ~ (P> Pn; nuclear density).

where P and eT describe the density and the specific thermal energy, respectively. We assumed that Pc changes as shown in Figure 1; the critical density Per and Ph at which phase transitions terminate are treated as parameters, because they are not yet confirmed. As for the EOS at a density lower than Pn' we adopted the idealized one described by Tahakara and Sato (1984).

After the core bounce, the shock dissipation significantly increases P T which is connected to eT by the equation

where YT is the thermal stiffness, for which we considered two cases as shown in

.... , V>

E u

O"l 0

::J

SUPERDENSE MATIER AND SUPERNOVA EXPLOSIONS 47

6. 0

4. 0 (a)

? 0

O. 0

2. 0

. ('

! •

, ..

6. 0

Ij·O (b)

? 0

T T

I ~!1

":!d,,.. .... I· ' '~ ",

/ J'l/~ 1

3,/ \w, 7 41.)( 0' ' 6

~ l. 5

1 . M fMC') (a)

T 1 I r r

, "

.. ' 8 ,

~\~l-I,- ,J { ~ G.O

\ , 6

3~ t/1/5 \~ f-.O

i J. 0

12. ( l l

J. 0 1 • ~ (b)

Fig.3(a)-(b). Snap-shots of velocity profiles for several stages. The numbers in each figure show the evolutionary sequences. Figure 3(a) shows a typical case (Case A with Pcr = 4.0 X 1014 g cm - 3 and Ph = 1.4 X 1015 g cm - 3) and should be compared with the one calculated neglecting the phase transitions shown in Figure 3(b), Due to the phase transitions, there appears a minimum of the velocity in the interior

as is shown in Figure 3(a).

Figure 2. In Case A, YT remains at ~, while in Case B, it increases with density to ~; Cases A and B would correspond to the phase transitions to quark matter and to the pion condensed state, respectively, according to the particles which most contribute to the specific heat.

48 M. TAKAHARA AND K. SATO

15 50 15 3x10 //1//

'l /11 // /

"? / ;II /// /

tI;/ M ////;1 E , <..l I E

1 x 1051 0110 51 / <..l 1O 1x 10 / 01 '<t '<t .

'-0 /J ""'0 / !: " ~ / 0:;:

" 5

3 4 5 6 7 3 4 5 6 7

.Per ( 1014 gcm-3 ) ?er ( 1014 9 cm-3)

(a) (b)

Fig.4(a)-(b). Iso-contours of the ejected energy in parameter plane. Figures 4(a) and (4b) show Cases A and B, respectively. The left and lower shaded regions are not considered in our calculations because we assumed Per ~ Pn and Ph> Per' The right shaded-region corresponds to the case in which the central density never exceeds the critical density, hence, the phase transitions never affect the dynamics of the Fe-cores. The contours of the ejected energy in these diagrams show the strength of the explosion. The dotted regions

show the cases in which explosions become stronger than the case neglecting the phase transitions.

We simulated the collapse of an Fe-core of 1.4 M 0' considering the effects of general relativity on the assumption of adiabatic collapse. This assumption is based on the neutrino trapping phenomenon and is a good approximation before neutrinos diffuse out from the core. As for the trapped lepton fraction Yv we adopted the value 0.39.

3. Results

The typical change of the dynamics of the Fe-core is shown in Figure 3, and results are summarized in Figure 4.

Due to the effect of phase transitions, there appears a minimum of the velocity in the interior, as is shown in Figure 3(a).

Figure 4 shows that only the case of phase transitions for which Pcr < < 6.5 X 1014 g cm - 3 can affect the dynamics of the Fe-cores. It is most important that there exist parameter regions in which explosions become stronger than that in the case of complete neglect of the phase transitions (see Figure 4). However, the increment of ejected energy is at most 18 % in Case A and 26 % in Case B, respectively.

SUPERDENSE MATTER AND SUPERNOVA EXPLOSIONS 49

4. Summary and Discussion

Only phase transitions of Pcr < 6.5 X 1014 g cm - 3 can affect the dynamics of Fe-cores.

Strong phase transitions make the explosions weaker, while weak transitions make them stronger. However, the increment of ejected energy is not so large as suggested by Migdal et al. (1979). Especially in the case of strong phase transitions the collapsing core is difficult to explode, which is in contrast to the suggestion by Migdal et al. (1979). The difficulty of explosion cannot be solved by the phase transitions of superdense matter.

Since strong phase transitions suppress the supernova explosions, it is very important to research the EOS of hot superdense matter. Such research might be carried out by the study of heavy ion collisions.

References

Migdal, A. B., Cherenoutsan, A. I., and Mishustin, I. N.: 1979, Phys. Letters 83B, 158. Takahara, M. and Sato, K.: 1984, Prog. Theor. Phys. 71, 524.

SUPERCRITICAL WINDS FROM COOL 'CANONICAL' STARS

CAUSED BY EVOLUTION ON THE MAIN SEQUENCE*

P. VENKATAKRISHNAN

Indian Institute of Astrophysics, Bangaiore, India


Abstract. Even the very slow expansion of a star's radius due to evolution on the Main Sequence is shown to be supercritical for cool stars without coronae. Since steady sphericaily-symmetric supercritical solutions are theoretically impossible, unsteady supercritical solutions are studied. It is seen that smooth sonic transitions are possible in the unsteady case, but are accompanied by enhancement of pressure over the critical values.

1. Introduction

Stellar winds are driven by gradients of pressure between the atmosphere and the interstellar medium. Conventional sources of pressure heads are (1) thermal energy of hot coronae (significant for cool stars) and (2) radiation pressure (significant for hot stars). A possible third source is thermonuclear energy generated in stellar cores. This energy is known to increase the star's radius on the Main Sequence at a rate of ~ 10 - 7 cm s - 1 (Stromgren, 1965). Even this apparently negligible expansion becomes supercritical for cool stars without coronae. This paper is a preliminary effort to understand the dynamics of the star's environment in the presence of such an evolutionary expansion.

2. The Magnitude of Supercriticality

Isothermal wind solutions suffice for a simple estimation of supercriticality. The parameter representing the critical isothermal wind is relr * where rc = GM * /2S; is the sonic point, r *' M *' and S * being, respectively, the star's radius, mass, and isothermal sound speed of its atmosphere. From the well-known solution of an isothermal wind, one obtains

(1)

where V * is the wind speed at the stellar surface. In Table I we can see the values of V * / S * corresponding to various values of relr * .



52 P. VENKATAKRISHNAN

TABLE I

Values of critical surface Mach numbers V * IS * for various values of

relY *

relr * V*IS*

0.5 0.45 1.0 1.00 5.0 5 X 10- 3

10.0 9 X 10- 7

100.0 6 X 10- 83

1000.0 0

A typical 'canonical' cool star (T * = 6000 K) without a hot corona would have relr * ~ 100,for which V * IS * = 6 x 10 - 83! Thus we see that any non-static behaviour of the stellar surface would lead to extreme supercriticality. It is also interesting to ponder over the fact that evolutionary expansion velocities of 10- 7 cm s - I are critical

only at T * ~ 105 K for a star with solar mass and radius.

3. Impossibility of Steady Spherically-Symmetric Supercritical Expansion

Wolfson and Holzer (1975) have shown that steady supercritical solutions are not theoretically possible. This is because the transition near the singularity V = S * would make the solution jump from a branch of higher entropy to one of lower entropy. Wolfson and Holzer, however, do not explicitly answer the question as to what could be a result of imposing a supercritical mass flux on a steady critical wind. They suggest either breakdown of the steady condition or the adjustment of surface conditions to the new value of the mass flux. In this paper we numerically examine unsteady supercritical solutions.

4. The Unsteady Solutions

The following equations for 'isothermal' unsteady flow in a gravitational field were integrated in time using the method of characteristics (Zucrow and Hoffman, 1976):

o 10(2) - p+- - rpv =0, at r2 or (2)

ov av 1 0 GM -+v-+--p+-=O, ot or p or r2

(3)

p = S;p. (4)

At t = 0, a supercritical base velocity Vbase was imposed on the steady critical solution and the resulting response was followed numerically in time. Figures 1 and 2 show the

N ,

SUPERCRITICAL WINDS FROM COOL STARS

1·0

I

I I

I I

I I

I I

10

~ 0.5 I- / I

I ..... >

u a. "Q.

Co -

I I

/ 40

/~/--.... ·-23 ".. / / "

,' " ." ./ ' ,,' ... ., ~/ . 5 0.0 L..;;;;;;;;;:= .... ::: .. ::::.d=·L .... ..:.. " 0;.;." :.;,,;' "~".:.:." .:.:.:, .. _ ... J.. .. , ':""'....J

1.0 2.0

(I a)

0·07 -~ ____ _ 40

0 .061-

0.051-

0·01 ~.----.-._. __ . kO .. ': !

0.00 ""' .. _ .. _._ .. _,,_ .. _. · ____ ~ .... 5...1, ................. }_ ............. J"'__~ 1·0 1·5 2.0

R/Re (lb)

53

Fig.1. Spatial profile of (a) velocity and (b) InP/Pcritical at different instants of time for T * = 106 K, r * = 1 Ro, M * = 1 Mo, and for Vb.,e/V * = 3 X 103•

54

t >

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 1.0

P. VENKATAKRISHNAN

1.5

R IR e -(2a)

2.0

6 V base / V • = 3 X 10

10.0 f-

r-._._._._._._._ ........ _._._._._

5.0 r-

~----------------~ ----------l

o 1.0

I I I I I

2.0

Fig. 2. Same as in Figure 1 but for Vbase/V * = 3 X 106.

SUPERCRITICAL WINDS FROM COOL STARS 55

velocity and pressure profiles for two values of the base velocity (VbaSe/ V * = ( a) 3 x 103

and (b) 3 x 106 ) for a million degree isothermal flow. The high value of T * was chosen for computational convenience. We can see that in case (a) the solutions remain unsteady even after ::::; 40 free-fall times while for (b) an asymptotic steady state for the velocity is approached. In both the cases pressure enhancements commensurate with

the magnitude of supercriticality are seen, without approaching any asymptotic state for pressure.

5. Summary and Conclusions

The evolutionary expansion of a star's radius on the Main Sequence results in a supercritical wind for cool stars without coronae. Steady solutions are theoretically impossible. The present limited numerical study for unsteady supercritical winds from a million degree atmosphere points out the possibility of a smooth sonic transition. The price to be paid, however, is to tolerate an increase in the pressure (or density, in this

isothermal case) commensurate with the amount of supercriticality. The implications for actual situations in stars with T * ::::; 6000 K will be seen after further calculations.

References

Stromgren, B.: 1965, in L. H. Aller and D. B. McLaughlin (eds.), Stellar Structure, University of Chicago Press, Chicago, p. 269.

Wolfson, R. L. and Holzer, T. E.: 1975, Astrophys. J. 225, 610. Zucrow, M. J. and Hoffman, H. D.: 1976, Gas Dynamics, Vol. I, John Wiley, New York.

STEADY MASS-LOSS FROM SUPERMASSIVE ST ARS*

MARIKO KATO

Department of Astronomy, Faculty of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan


Abstract. Structures of Newtonian super-massive stars are calculated with the opacity for Compton effect Ko/(l + IXT), where Ko = 0.2(1 + X) and IX = 2.2 x 10 - 9 K - 1. The track of the Main-Sequence is turned right in the upper part of the HR diagram. Mass loss will occur in a Main-Sequence stage for a star with mass larger than a critical mass. The cause of mass loss and the expansion of the radius is continuum radiation pressure. The critical mass for mass loss is 1.02 X 106 Mo for a Population I star, and 1.23 x 105 M 0 for Population III star. Mass loss rates expected in these stars are 3.3 x 10 - 3 and 4.0 x 10- 3 Mo yr-!, respectively.

1. Introduction

Some authors have suggested that mass loss does not occur for very massive stars. Appenzeller and Fricke (1971) obtained static Main-Sequence solutions with no mass-loss for masses in the range 5 x 105-5 X 107 Mo. Nomoto and Sugimoto (1974) examined the surface boundary condition, and found a static solution for a 103 M 0 star. They concluded that no steady mass-loss would occur in such a star.

However, the possibility of steady mass-loss cannot be discussed from their solutions. In both these works the opacity is assumed to be constant. The change of opacity is essential for the acceleration of matter.

The present paper shows the solutions for super-massive stars with a Compton opacity. These solutions indicate steady mass-loss occurs even in the Main-Sequence stages.

2. Numerical Results

Stellar structure is obtained from simultaneous numerical integration of the equations of hydrostatic balance, mass continuity, energy transfer and energy conservation. The boundary conditions and method of numerical calculation is same as that described in Kato (1984). We use the opacity formula for Compton scattering

KO K=---

1 + rxT (1)

where rx = 2.2 x 10 - 9 K - 1 and Ko = 0.2(1 + X). The chemical abundance of hydrogen, helium, and heavy elements are assumed to be X = 0.8, Z = 0.02 for Population I stars, X = 0.8, Z = 10 - 7 for Population III stars.



58 M. KATO

6 6.03 <;)

--1 10 ----1 5.09

en 0

2

5 Pop.III

5.0 4.5 4.0 109 T ph ( K )

Fig. 1. Tracks of Main Sequences in the HR diagram. Numbers attached to each point denote the logarithmic values of stellar mass. The crosses correspond to the critical mass stars. Stars in the right side

of the crosses have steady mass outflow.

Figure 1 shows the locus of the Main Sequence for both populations. The upper parts of the curves turn to the right, because the surface region is very extended in such stars. The crosses denote the critical mass for steady mass-loss. More massive stars must have mass outflow.

The mass loss and expansion of the surface region of the stars is caused by a radiation pressure gradient. In these stars, the luminosity is very close to the Eddington luminosity 4ncGM/ K which decreases outward. Therefore, some amount of photon flux is blocked in the outer regions of the stars, which causes matter to be pushed upward (for interior structure of such stars, see Kato, 1985b).

In the stars of critical mass (the crosses in Figure 1) the thermal energy at the surface region is comparable to the gravitational energy. We should expect that a steady mass-loss will occur in the stars to the right side of the crosses.

The mass-loss rate in stars very near to the critical mass is estimated as follows. When a steady mass-loss has just occurred, the structure is almost the same as that of the static solution, just as the critical point of a solar-wind-type solution is very close to the photosphere (cf. Kato, 1985a). Therefore, the mass-loss rate is calculated from

• _ 2 _ 2 JkTph M - 4nrph Pph Vph - 4nrph Pph --,

Jlrna

where Jl and rna are the mean molecular weight and atomic mass unit, respectively. The mass loss rate is 3.3 x 10 - 3 M 0 yr - 1 for Population I stars, and 4.0 x 10 - 3 M 0 yr - 1

for Population III stars.

STEADY MASS-LOSS FROM SUPERMASSIVE STARS

References

Appenzeller,!. and Fricke, K.: 1971, Astron. Astrophys. 12,488. Kato, M.: 1985a, Publ. Astron. Soc. Japan 37, 19. Kato, M.: 1985b, Publ. Astron. Soc. Japan 37, 311. Nomoto, K. and Sugimoto, D.: 1974, Publ. Astron. Soc. Japan 26,9.

59

EFFECTIVE TEMPERATURES, RADII, AND LUMINOSITIES OF

o EMISSION, Be AND Ae ST ARS*

JONG-OK woo Department of Earth Science, Pusan National University, Pusan, Korea


Abstract. Our de-reddened fluxes, together with the ultraviolet measurements of Thompson et al. (1978), have been compared with those of Kurucz's (1979) model atmospheres to derive effective temperatures of some 0 emission, Be and Ae stars. With the measured monochromatic fluxes we determined their angular diameters and luminosities. It is found that the majority of the stars are cooler than the Zero-Age Main Sequence (ZAMS), suggesting that they are slightly more evolved than ZAMS stars.

1. Introduction

Our purpose has been to measure very carefully the absolute fluxes in the optical range for some 0, B, and A stars with emission lines by means of a two-channel scanner, and to derive effective temperatures and log L*/ Lo .

2. Observations and Results

We obtained the absolute measurements offlux in the continuum for fourteen early-type stars with emission lines (HIX and/or HP) observed by the two-channel spectrometer (Nguyen-Do an et al., 1977), at the Observatoire de Haute Provence (1.93 cm telescope) and at La Silla (ESO Chile, 1.50 m telescope).

Balmer discontinuities are estimated by the method of Chalonge and Divan (1952) from the energy distribution measured, compared with those of normal stars. Among Be stars many have a smaller Balmer discontinuity than that exhibited by MainSequence stars of similar spectral type (see Table I). Using the E(B - V) obtained we derive the corrected fluxes from 10gFicorr) = 10gFiobs) + 0.434R AE(B - V) (Hayes, 1970; Hayes and Lathams, 1975).

3. Effective Temperatures and Luminosities

The de-reddened fluxes, connected to the ultraviolet measurements of the IUE, (Thompson et al., 1978) are compared to those of Kurucz's (1979) line-blanketed model atmospheres to derive effective temperatures of the stars. With the measured mono-

* Paper presented at the lAD Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. * The observations were made at the Observatoire de Haute Provence (France) and La Silla (E.S.O., Chile).


62 JONG-OK woo

Supergiants: 80 81 83 85 88 7

6 Carson

5

TAl\IIS ---------

4

• o emission stars 3 • Be stars

2 4,8 4,7 4,6 4,5 4,4 4,3 4,0

log Te"

Fig, I. The positions of emission stars in the H-R diagram with Stothers' (1976) theoretical evolution tracks. The majority of these stars are cooler than Zero-Age Main-Sequence stars.

chromatic fluxes we determined angular diameters and luminosities, and then located the positions of these stars in the H-R diagram, Table I summarizes the physical parameters for the program stars, and the H-R diagram (Figure 1) illustrates relative positions of the stars,

4. Conclusions

The determination of effective temperatures mainly depends on the comparison between observations and theoretical models over a large spectral interval, it is therefore advisable to include spacecraft UV measurements,

TABLE I

Angular diameters e, distances d, radii R, effective temperatures T eff, and Balmer discontinuities D of program stars

HD Sp. T. e d RjRo Teff log LjLo D D a

(0': 0001) (kpc) (measured)

46573 07.5((f) 0.82 2.940 25.96 35000 5.95 64315 06nne 0.28 5.920 17.69 38000 5.76 69464 07ne 0.43 5.060 23.32 37000 5.95 28497 BrVne 1.06 0.805 9.19 24000 4.39 0.05 0.12 (BCD) 29557 B8 0.52 0.683 3.80 16000 2.92 0.38 0.35 (BCD) 34959 B5p 1.11 0.391 4.66 15000 2.99 0.29 0.25 (BCD) 41511 A2p 9000 0.54 0.48 (BCD) 49992 BOne 0.26 2.390 6.54 33000 4.65 0.04 0.06 (BCD) 51480 B5 1.26 0.262 3.55 18000 3.07 0.05 0.25 (BCD) 61224 B9III 1.41 0.277 4.20 11500 2.44 0.36 0.43 (BCD) 75658 BIIVe 0.49 0.880 4.60 31000 4.24 0.03 0.12 (BCD) 92528 AIV 9700

174237 B2.5V 1.18 0.277 3.53 20000 3.25 218393 Bpe 1.67 1.166 2.98 14000 2.48 0.09

a Balmer discontinuities of Main-Sequence stars of corresponding types by Chalonge and Divan (1952).

o EMISSION, BE AND AE STARS 63

The majority of program stars are found to be cooler than Zero-Age Main Sequence (ZAMS), suggesting that they are slightly more evolved than ZAMS stars.

References

Chalonge, D. and Divan, L.: 1952, Ann. Astrophys. 15, 201. Hayes, D. S.: 1970, Astrophys. J. 149,317. Hayes, D. S. and Lathams, D. W.: 1975, Astrophys. J. 197, 596. Kurucz, R. L.: 1979, Astrophys. J. Suppl. Ser. 40, I. Nguyen-Doan, Dubet, D., Godon, R., Hua, C. T., and Rouxel, M.: 1977, 'Electrique et Application

Industrielies', and Societe des Editions Radio, No. 239, p. 50. Stothers, R.: 1976, Astrophys. J. 209, 800. Thompson, G. I., Nandy, K., Jamar, C., Monfils, A., Houziaux, L., Carnochan, D. J., and Wilson, R.: 1978,

Catalogue of Stellar Ultraviolet Fluxes, S.R.c., London Rept, pp. 23 + 449.

ABSOLUTE MAGNITUDES OF LATE-TYPE ST ARS*

TAKAO MIKAMI

Tokyo Astronomical Observatory, University of Tokyo, Mitaka, Tokyo, Japan


Abstract. The improved calibration of absolute magnitude versus spectral type and luminosity class is presented for carbon stars and for K- to M-type giants. It is based on the recent results estimated by applying the maximum-likelihood method and other statistical methods to the homogeneous kinematical data including the proper motions in the AGK3 system.

1. Introduction

The overall absolute magnitude calibration versus the spectral type and luminosity class by Blaauw (1963) was often used as a reference, It was based on earlier results derived from trigonometric and statistical parallaxes, as well as from Main-Sequence fittings. Later Blaauw (1973) accepted the improved values of absolute magnitude for late-type giants on the basis of Jung's (1970, 1971) and other results,

Trigonometric parallaxes constitute the most fundamental method for estimating absolute magnitudes. However their precision degrades dramatically beyond a few tens of parsecs from the Sun. In addition, most of the stars within such an immediate solar neighbourhood are late-type dwarfs. Therefore, reliable absolute magnitude estimates for other stars must be obtained by different methods. The statistical-parallax method is the most appropriate one for A- to early K-type dwarfs, and for G- to M-type giants, considering the precision of the kinematic data available now (Blaauw, 1973; Heck, 1978). Although it has often been used with various modified algorithms, the quality of the kinematic data, above all the proper motions, has a critical bearing on the quality of the final results. The AGK3 Catalogue (Heckmann et aI., 1975) offers proper motions in a uniform system, which seems to be the best, at present, for statistical analyses of a larger number of stars.

In the following, we present an improved calibration of absolute magnitude versus spectral type and luminosity class for late-type stars derived using measured radial velocities (Wilson, 1963) and AGK3 proper motions, as the refinement of the results presented previously by Ishida and Mikami (1978).



66 T. MIKAMI

2. Carbon Stars

Mikami (1975) estimated the mean visual absolute magnitudes for various groups of carbon stars subdivided according to the C classification. Data include the measured radial velocities and specified C-types for 321 carbon stars (Yamashita, 1972, 1975), of which 90 stars have AGK3 proper motions. Absolute magnitudes were estimated by applying a differential galactic rotation formula to the radial velocity data. The usual statistical parallax method was also applied to 90 stars with both measured radial velocities and AGK3 proper motions. To these data, application of our maximumlikelihood statistical parallax method has been tried recently, though the results are still preliminary. A part of the results are shown in Table 1. Mean absolute magnitudes

C-type

CO-3 C4-5 C6-7 CH

TABLE I

Visual absolute magnitudes for carbon stars

Galactic rotation Usual statistical formula parallax (Mikami, 1975) (Mikami, 1975)

N Mv m.e N Mv m.e.

45 - 1.3 ± 0.6 14 - 0.6 ± 1.5 131 -2.7±0.3 31 82 - 2.4 ± 0.6 23 - 1.6 ± 1.3 18 17a - 1.7 ± 1.0

Maximum-likelihood statistical parallax (Present values)

N Mv m.e.

14 - 0.6 ± 1.0 31 - 1.7 ± 0.6 23 - 1.5 ± 0.6 10 - 1.0 ± 0.8

a The high velocity stars, which are not still confirmed as CH stars, are included.

derived using the galactic rotation formula are about 0.8 mag. brighter than those from statistical parallaxes, though differences are within the ranges of mean errors. It indicates a dispersion of above 1 mag. in absolute magnitude, since it is likely that carbon stars with AGK3 proper motions are nearby stars, and include intrinsically faint stars preferentially. The results obtained from the maximum-likelihood statistical parallaxes agree with those from usual statistical parallaxes, and also suggest a dispersion of about 1 mag. in absolute magnitude.

CH stars are high-velocity carbon stars showing a great enhancement of the G band due to the CH molecule in their spectra, and do not follow the normal galactic rotation.

3. K- and M-Type Stars

Mean absolute magnitudes of K- and M-type giants in the solar neighbourhood are estimated most reliably by using statistical parllaxes. Mikami (1978a) derived the mean visual absolute magnitudes for various subspectral types by applying the statistical parallax method to 749 M-type stars with both measured radial velocities and AGK3 proper motions. Subsequently, Mikami (1978b) applied a similar method to 3574 F-,

ABSOLUTE MAGNITUDES OF LATE-TYPE STARS 67

G-, and K-type stars with both measured radial velocities and AGK3 proper motions for the calibration of absolute magnitude versus subspectral type and luminosity class. Afterwards Mikami and Heck (1982) reanalyzed almost the same data for F- to M-type stars by applying a maximum-likelihood statistical parallax method (Jung, 1970; Heck, 1977). These results for K- and M-type giants are shown in Table II with other previous results. Mikami (1978a, b) and Mikami and Heck (1982) agree with each other within the ranges of mean errors for each spectral type, except for M3 and M7 -8, for which the differences are likely to come from the treatment of high-velocity stars. Blaauw's (1963) values are considerably faint in comparison with our results, though they were often used as references. Blanco's (1965) values agree well with our results for M3-4. They are mainly based on the results from the Wilson-Bappu effect calibrated using the Sun and four giants in the Hyades with a distance modulus of 3.03 mag. Adopting 3.3 mag. as the distance modulus of the Hyades and using mean magnitudes for variable stars in later subspectral types, Blanco's (1965) values for other M-subspectral types agree better with our results. The agreement of our results with Ljunggren and Oja (1966) and Jung (1970) is generally satisfactory. The values of Mikami and Heck (1982) shown in Table II have been smoothed from the original results, and should be a reliable calibration of the visual absolute magnitude versus spectral type for K- and M-type giants. Our results are valid for late-type giants in the galactic disk, while late-type giants in the galactic bulge and in the Magellanic Clouds may have different values of absolute magnitude (Blanco and McCarthy, 1983; Blanco etal., 1984).

Absolute magnitudes ofK- and M-type dwarfs in the solar neighbourhood are usually estimated from trigonometric parallaxes. Mikami (1978a, b) and Mikami and Heck

TABLE II

Comparison of visual absolute magnitude calibrations for K- and M-type giants

Spectral Blaauw Blanco Ljunggren Jung Mikami Egret Mikami type (1963) (1965) and Oja (1970) (1978a, b) et al. and Heck

(1966y (1982) (1982)

KO + 0.8 + 0.3 + 0.1 + 0.1 -0.9

+0.4 I +0.8 + 0.1 +0.5 +0.4 +0.3 2 +0.8 - 0.1 +0.2 + 0.3

+ 0.1 +0.0

3 + 0.1 -OJ -OJ -0.4 -0.2 4 - 0.1 -0.8 - 0.8 -0.6 -0.5 5 -OJ -1.0 - 1.0 - 1.2

-0.8 -0.8

MO -0.4 - OJ -1.2 -0.4 -0.7 -0.5 -1.1

-1.4 - 1.0

2 -0.4 -0.8 -1.5 -1.5 -1.2 3 -1.1 -1.6 -1.1 4 - 0.5 -1.0 -1.7: -0.7 -1.0 5 -0.9: -0.9 -0.7 6 -0.9: + 0.1 -0.3 7 -0.9:

+0.5: +0.5:

8 + 1.5:

a The Malmquist correction of 0.5 mag. is applied to the original values.

68 T. MIKAMI

(1982) also derived mean absolute magnitudes for F- to early M-type dwarfs from radial velocities and AGK3 proper motions. Their results generally support Blaauw's (1963) results.

4. Concluding Remarks

The calibrations of absolute magnitudes versus photometric or spectroscopic indices can be effectively based on the results presented here, although direct calibrations are desirable when trigonometric parallaxes or kinematic data are available. In the studies of the space distribution of stars in our Galaxy (e.g., Mikami and Ishida, 1981), the values of absolute magnitude per unit volume can be estimated by applying the Malmquist correction, taking into account the magnitude dispersion, to the absolute magnitude per apparent magnitude presented here. The dispersion of absolute magnitude for each subspectral type is 0.7 mag. on average for K- and M-type giants, while carbon stars have above 1 mag. as magnitude dispersion.

References

Blaauw, A.: 1963, in K. Aa. Strand (ed.), Basic Astronomical Data, University of Chicago Press, Chicago, p.383.

Blaauw, A.: 1973, in B. Hauck and B. E. Westerlund (eds.), 'Problems of Calibration of Absolute Magnitudes and Temperature of Stars', IAU Symp. 5447.

Blanco, V. M.: 1965, in A. Blaauw and M. Schmidt (eds.), Galactic Structure, University of Chicago Press, Chicago, p. 241.

Blanco, V. M. and McCarthy, M. F.: 1983, Astron. J. 88, 1442. Blanco, V. M., McCarthy, M. E, and Blanco, B. M.: 1984, Astron. J. 89,636. Egret, D., Keenan, P.c., and Heck, A: 1982, Astron. Astrophys. 43, 175. Heck, A: 1977, Astron. Astrophys. 56,235. Heck, A: 1978, Vistas Astron. 22, 221. Heckmann, 0., Dieckvoss, W., Kox, H., Gunther, A, and Brosterhus, E.: 1975, AGK3 Star Catalogue oj

Positions and Proper Motions North oj - 2.5 Declination. DerivedJrom Photographic Plates Taken at Bergedoif and Bonn in the Years 1928-1932 and 1956-1963, Hamburger Sternwarte, Hamburg-Bergedorf, Vols 1-8.

Ishida, K. and Mikami, T.: 1978, in A. G. D. Philip and D. C. Hayes (eds.), The H-R Diagram', IAU Symp. 80,429.

Jung, J.: 1970, Astron. Astrophys. 4, 53. Jung, J.: 1971, Astron. Astrophys. 11,351. Ljunggren, B. and Oja, T: 1966, in K. Loden, L. O. Loden, and U. Sinnerstad (eds.), 'Spectral Classification

and Multicolour Photometry', IA U Symp. 24, 317. Mikami, T.: 1975, Publ. Astron. Soc. Japan 27, 445. Mikami, T: 1978a, Publ. Astron. Soc. Japan 30, 191. Mikami, T: 1978b, Pub!. Astron. Soc. Japan 30, 207. Mikami, T. and Ishida, K.: 1981, Pub!. Astron Soc. Japan 33, 135. Mikami, T and Heck, A.: 1982, Publ. Astron Soc. Japan 34, 529. Wilson, R. E.: 1963, General Catalogue oj Stellar Radial Velocities, Carnegie Institution of Washington,

Washington D.C. Yamashita, T: 1972, Ann. Tokyo Astron. Obs. 13, 169. Yamashita, T: 1975, Ann. Tokyo Astron. Obs. 15,47.

ACTIVE PHENOMENA OF THE Be STAR EW LAC

OBSERVED IN 1978-1982*

MASAKAZU SUZUKI

Kanazawa Institute of Technology. P.O. Kanazawa-South. Ishikawa. Japan

and

TOMOKAZU KOGURE

Department of Astronomy. University oj Kyoto. Sakyo-ku. Kyoto. Japan


Abstract. The long-term variations ofEW Lac in the H y and Hpline profiles are presented. The active phase observed in 1978-1982 is characterized by the strengthening of emission lines accompanied by variations of radial velocities and VIR asymmetries. A model of a rotating elliptic ring is proposed.

EW Lac (HD 217050, B2IlIpe-shell, V sin i = 350 km s - 1) has been known as a typical shell star for many decades. The long-term variability of emission lines (VIR variations) has been inspected and an anomalous variation was found in 1978-1982 (Kogure and Suzuki, 1984; Kogure et al., 1984). Po eckert (1980) also reported spectrum variation in the early phase of this period. In order to examine the variability for the period 1970-1982 more closely, a series of coude spectrograms obtained at the Okayama Astrophysical Observatory, with the dispersion of 10 A mm - 1 at H{3, has been measured by PDS microdensitometers at the Kwasan Observatory and Tokyo Astronomical Observatory. Data reduction is carried out at the computer centers in Kanazawa Institute of Technology and Kyoto University.

In this paper we show a part of our measurements for the long-term variation of the H}' and H{3 line profiles. First we consider the H y line which is characterized by double-peeked emission and a sharp central shell absorption feature, superimposed on a broad dish-shaped photospheric absorption. For the smoothed line profile the following quantities are defined and measured:

Vr and Vv, heliocentric radial velocities of the red and violet emission peaks, respectively; Ve, mean velocity of the two emission peaks; Va' heliocentric radial velocity of the center of the shell absorption component at its half depth; Ir and Iv, relative intensities of the red and violet emission peaks, respectively, corrected with respect to the broad photospheric absorption; and log(IvfIJ, logarithm of the ratio of Iv and Ir.

Figure 1 illustrates the time variations of these quantities, from which one may obtain the following conclusions:


Astrophysics and Space Science 119 (1986) 69-72. <D 1986 by D. Reidel Publishing Company

70

v r

v v

! r

, y

.~ u ~ " >

,[ c ~ c

• > u ~

~

loq ( '/'r'

100

50

-100

-150

0.5

0 . 5

0. 5

-0 . 5

M. SUZUKI AND T. KOGURE

1970 75 80 85

2441000 )000 5000 Julian day . .. . . , . : · .

• . • . . < "

, · · · .. < "

, Q . , ,

". " , · , · ... · "

, . . D , · · , · ,,"

. . " . , , . · , , , .'"

Fig. I.

(1) Before 1976 the line profile was stable and quite symmetric, and the envelope could be represented by a circular gaseous ring or disk.

(2) Since 1978, the change of radial velocities and line asymmetry is remarkable. According to Huang (1973, 1975), this type of variation could be attributable to a rotating elliptic gas ring.

Although the highly asymmetric shell line in the active phase suggests a complicated structure of the envelope, we will simply assume a single elliptic ring, as a zeroth approximation. We can then obtain the following ring parameters: orbital period of the ring P = 4.7 yr, the ring ellipticity e = 0.15, and the semi-major axis of the ring a = 9.5 R* ' where we adopted Poeckert's values of M * = 9 Mo and R * = 7 Ro for the central star.

ACTIVE PHENOMENA OF THE Be STAR EW Lac 71

1970 75 80 85

2" 1000 lOOO 5000 Jul ian day

V loa . < ~

~ ,

SO

Ve ~ 0 0 . '

V. ;:

• ~S 0

" ~ 1> • 0 •• Job > • 0

l<I • -so

- 100

... ".7',.. • . v ~ · .. :

v , . - 150

~ 1.0 . " ~ · • · . .

" e • • S ~ . 1.0 · ~ . , . .. , ~ . , · . .

v " .": " ..

0.5 . · . 109 11 11",1 0 , . · . . ' " -0.5

Fig. 2.

N ext we consider the variation of the Hf3line which is shown in Figure 2, where the definitions of all quantities are the same as in Figure 1. One may see essentially similar behaviour to the case of the H y line, but closer inspection allows the following remarks:

(1) The separation of the Hf3 emission peaks is a little bit smaller than that of H y. This suggests that the size of the region of the envelope contributing to the formation of Hf3 emission is larger than that for H y.

(2) The variability of Hf3 in the active phase reveals a delay with respect to that of H y. This would indicate that the semi-major axis of the 'outer' Hf3-ring rotates behind that of the 'inner' H y-ring, as suggested by Kogure et al. (1984).

(3) The values of P and e of the outer Hf3-ring are about the same as those of the inner H y-ring. This is partly because of the scatter of our measured data.

72 M. SUZUKI AND T. KOGURE

These conclusions from and remarks on Figures 1 and 2 suggest the systematic difference between the physical condition in the elliptic gas envelope of the inner and the outer regions. For further study of the structure of the rotating envelope, wider examinations, including the H:x and shell absorption lines, are highly desirable.

Acknowledgements

The authors express their indebtedness to the staff members of the Okayama Astrophysical Observatory. Thanks are also due to Dr Y. Nakai of Kwasan Observatory and to Mr T. Noguchi of the Tokyo Astronomical Observatory for the use of PDS microdensitometers.

Huang, S. S.: 1973, Astrophys. J. 183, 541. Huang, S. S.: 1975, Sky and Telesc. 49, 359.

References

Kogure, T. and Suzuki, M.: 1984, Pub/. Astron. Soc. Japan 36, 191. Kogure, T., Asada, Y., and Suzuki, M.: 1984, in B. Hidayat and M. W. Feast, (eds.), Proc. Second

Asian-Pacific Regional Meeting, held at Bandung, Indonesia, 1981, p. 504. Poeckert, R: 1980, Pub!. Dominion Astrophys. Obs. 15, 357.

PHOTOMETRIC BEHAVIOUR OF THE Be STAR

EW LACERT AE*t

JANG HAE JEONG

Chungbuk National University, Korea

CHANG WON SUH, and IL-SEONG NHA

Yonsei University Observatory, Seoul, Korea

(Received 2 July, 1985)

Abstract. The night-to-night and short-term variations in UBV light curves of EW Lac which were made during 1982-1984 at Y onsei University Observatory are discussed. The long-term variability in the photometric behaviour of the star is examined with our own data as well as those of Harmanec et al. (1980).

The well-known shell and Be star EW Lacertae (HD 217050, HR 3731) has been observed for almost 100 yr. The spectral type and projected rotating velocity of this star are B3III and 350 km s - I, respectively (Jaschek et at., 1980).

With their photoelectric observations, Walker (1953) and Lester (1975) detected short-term variability of EW Lac, on a time-scale of 0.7-0.8 days, while long-term variations, on the other hand, were examined by Harmanec et at. (1979, 1980) and Kogure (1984). To summarize this literature, the variability of EW Lac seems to be erratic rather than regular.

Some hypotheses were advanced to explain the photometric behaviour of EW Lac. Among them, Walker (1953) suggested the star-spot model, but Lester (1975) argued against this and proposed, instead, that the wavelength dependence of the photometric variability was caused by changes of temperature in the stellar atmosphere, but not in the shell. Recently, Kogure (1984) considered that the reddening in U - B, based on the data of Harmanec et at. and some of ours, may be due to an increase of average electron density in the envelope.

The main purpose of the present work is to present UBV photometric observations of EW Lac obtained during 1982-1984 at Yonsei University Observatory. The longterm variability in photometric behaviour is explained with the data available, and also the night-to-night and short-term variations and its colour dependence are considered.

UBV photoelectric observations ofEW Lac were made with the 61 cm and the 40 cm reflectors of Yonsei University Observatory over 42 nights during two seasons, September 1982-January 1983 and September 1983-January 1984. Instrumentation

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. t Yonsei University Observatory Contribution No. 23.


74 JANG HAE JEONG ET AL.

and observational techniques used for these observations were described by Nha et al. (1985) in detail. The comparison star observed for EW Lac is 5 And, which was recommended by Harmanec et al. (1981).

A total of 771 observations (321 in V, 321 in B, and 129 in U) have been obtained, and each data point was the result of one or more minutes of integrations traced on chart recorder paper. The variations of the daily average B magnitudes of Harmanec et al. (square) and of ourselves (dot), and the radial velocities Vr (HI5-H25) of Kogure (cross) of EW Lac, made during 1972-1983, were plotted in Figure 1. The remarkable variations on the Vr curve (bottom of Figure 1) in the period of 1978-1983, are sufficient to validate the proposition that an active phase of this star began in 1978, as mentioned by a number of authors.

1972

B 5 . 1~ 5 . 2

5 . 3

1976 1980

I

'- i/ '''''- ., .. '1 --"'~,_ - -, , .

YEAR 1984

-10 Ur -20

' ..... :/~ .---t __ t _ , 11--._ ........... / , -3e I' ' '''" ................ . .

2441e00 420ea 430a0 44eea 4S0ee JD Hel .

Fig. 1. Long-term variatin of EW Lacertae in 1971-1984. Square: B of Harmanec et al. (1980); dot: B of ourselves; cross: Vr of Kogure (1984).

By comparing their VIR values with MS8 observations of Alvarez and Schuster in the period of 1977-1980, Herbert-Delplace et al. (1982) suggested thatMs8 (i.e., magnitude of 5800 passband; Johnson and Mitchell, 1975) increased when the VIR increased. For the period 1982-1984, our photometric observations are compared with the spectroscopic data of Kogure (1983,1984) as shown in the right part of Figure 1, in which we could not find any relations between Vr and B. In addition it is difficult to check whether the suggestion of Herbert-Delplace et al. is still available or not, because the photoelectric observations in 1979-1981, the important period of time, are unfortunately absent, and because their VIR - MS8 comparison and our Vr - B comparison cannot be considered in the same sense.

EW Lac was brightest in 1982-1983, and then sharply declined towards its faintest recorded magnitude with a large scatter in 1983-1984. A light behaviour similar to this was also detected once in 1975-1976. These two peaks coincide in epoch with the beginning and ending of the shell activity described by Kogure and Suzuki (1981). We need keep our sights on this point in order to confirm whether the coincidence happened by chance or not.

We selected the nights in which observation periods (3 to 8 hr) were relatively long,

THE Be STAR EW LACERT AE 75

(I.) (1 ) (0 ( d ) ( e )

I i I i i I i I i I i I I

] "f u k ~ 4 . 7 0 . 2 da~

51~ ~ . - ::-: ...... , . ·.··w .'. 8 5 .2 " ...... -. ••• : .w, " .'. ... ....

. ..•... 5 . 3

.. : ......... ~. ' . ....

J . '. ,': ..... ', , 5'[ - ,.' .

U ., ' .. ,,-, ,'-"

5 .4 i I i I i i I i I i i I i I I I I i I i !

594 614 617 629 635 JO HU 244500e+

(r) ( 9) 0) (i) ( j ) ( k)

I i I'T' I i I I i I I i I I i

] "f .......... , ...... .. u k ~ 4 .7

0 2 di~

51 ! ~ ....... ... ... .. ... ~ ... :: ..•.... B 5 .2 ' ... ... ...... .' 5 . 3 ,- "

.......... -. .... .... ; ..•. ,' ..... ,' : ' . ] 5 .3 ,', .... .... .' U

. '. 5 . 4 .. . . "

I i L.......-L.... i I I i I I I I I I I I i

647 658 663 674 684 705 JO Hel 2445000+

Fig. 2. Selected UBV light curves of EW Lacertae for II nights, from (a) to (k).

and the light curves of these nights are shown in Figure 2 to investigate for any short-term light variation. Light variations of EW Lac are clearly found on every night except two nights (JD 2445658 and JD 2445684). The largest variations of about 0.15 and 0.12 mag. in V and B, respectively, were observed on JD 2445629. Observations made on the two nights, JD 2445594 and 2445663, are fainter than the average of those of the rest by about 0.1 mag. Although Walker (1953) and Lester (1975) reported a quasi-periodic short-term variability on a time-scale 0.7-0.8 hr, it is difficult to confirm this with the data made by the present investigators.

Finally, to examine the night-to-night variations of EW Lac the daily average UBV observations versus Heliocentric Julian day have been plotted in Figure 3. Three minima are apparent in the UBV light curves, with intervals between the minima of about 50-60 days in a quasi-periodic fashion. The depths of the minima, marked with arrows, are different each time, and they tend to become deeper with time in all UBV curves. These erratic light changes are considered to be related with the ending of the active phase of the shell, mentioned by Kogure and Suzuki (1984).

We intend to continue our monitoring of EW Lac at Y onsei University Observatory.

76

u

B

u

"~ 4. 7

5 . 2

5 . 3

;II •• I .' ". 'I, ' l

5 . ! ~

, J ~ "' ,/" '.' ''

'5 . 4 I

2445270

JANG HAE JEONG ET AL.

I . 1 /

",

,-- '

330 390 600

...... , , \ i

660 720

JD He! .

Fig. 3. Night-to-night variations in 1982-1984. Arrows indicate the deep minima.

References

Harmanec, P., Horn, 1., Koubsky, P., Zaarsky, F., and Kfiz, S.: 1979,Inf. Bull. Var. Stars, No. 155. Harmanec, P., Horn, 1., Koubsky, P., Zaarsky, F., Kfiz, S., and Pav1ovski, K.: 1980, Bull. Astron. Inst. Czech.

31, 144. Harmanec, P., Horn, 1., and Koubsky, P.: 1981 , Proc. Workshop on Pulsating B Stars, p. 397. Herbert-De1place, A. M., laschek, M., Herbert, H., and Chambon, M. Th.: 1982, in M. laschek and

H. G. Groth (eds.), 'Be Stars', IAU Symp. 98, 125. laschek, M., Herbert-Delplace, A. M. , Herbert, H., and laschek, c.: 1980, Astron. Astrophys. Suppl. 42, IOl lohnson, H. L. and Mitchell, R. T.: 1975, Rev. Mex. Astron. AstroJ 1, 229. Kogure, T: 1983, private communication. Kogure, T.: 1984, Proc. of Beijing Workshop on Stellar Activities and Observational Techniques. Kogure, T and Suzuki, M.: 1981, InJ Bull. Var. Stars, No. 1952. Kogure, T and Suzuki, M.: 1984, Publ. Astron. Soc. Japan 36, 191. Lester, D. F.: 1975, Publ. Astron. Soc. Pacific 87, 177. Nha, Il-Seong, Lee, Yong-Sam, Chun, Yang-Woo, Kim, Ho-Il, and Kim, Young-Sao: 1985, in press. Walker, M. F.: 1953, Astrophys. J. 118,481.

IRON K-EMISSION LINE FROM CYGNUS X-2*

T. HIRANO, S. HAY AKAW A, F. NAGASE, and Y. TAWARA

Department of Physics. Nagoya University. Furo-cho. Chikusa-ku. Nagoya. Japan


Abstract. The iron K-emission line of Cyg X-2 was detected from the TENMA observation. The centre energy, the equivalent width and the intrinsic line width are 6.7 keY, - 30 eV, and less than 0.6 keY, respectively. These properties indicate that the observed line is mostly due to helium-like iron and the electron scattering depth of the line emitting region is smaller than three.

1. Introduction

Cyg X-2 is a bright galactic X-ray source with the optical companion V 1341 Cyg (Giacconi et al., 1967). As V 1341 Cyg is an early F giant or subgiant, Cyg X-2 is one of the low-mass binary sources (Cowley et al., 1979). Cowley et al. (1979) suggested that the distance ofCyg X-2 is about 8 kpc, if the optical companion fills its Roche lobe. This implies that its X-ray luminosity is about 1038 erg s - I.

Most low-mass binary sources, including Cyg X-2, show a soft energy spectrum, which can be simulated by a thermal bremsstrahlung spectrum and erratic intensity variations. However, the high luminosity ofCyg X-2 argues against thermal bremsstrahlung, because the emissivity of thermal bremsstrahlung is too low to explain the high X-ray luminosity. X-ray emission from the low-mass binary source can be accounted for in terms of a combination of Comptonized black-body radiation from the surface of the neutron star and that from the accretion disk (Hayakawa et aI., 1984; Hirano et aI., 1984).

The X-ray observation with HEAO-l (Pravdo, 1983) suggested that the equivalent width of the iron K-emission line of Cyg X-2 is less than 200 eV. Equivalent widths of K-emission lines of ~40 eV have been found for several low-mass binary sources from TENMA observations (Suzuki et aI., 1984).

2. Observations and Results

Cyg X-2 was observed from 23 through to 30 September, 1983 with the gas scintillation proportional counters (GSPC's) on board TENMA. These detectors were characterized by a good energy resolution of 10% at 6 keY, which is twice as good as that of an ordinary proportional counter. During the observation period, we observed variations of both the X-ray intensity, in the energy range 2-10 keY, and the hardness ratio of X-ray



Iron

lin

e

Dat

a se

t E

nerg

y In

tens

ity

No.

(k

eV)

(cis

)

1 6.

59 ±

0.1

5 0.

8 ±

0.3

2 6.

77 ±

0.1

5 1.

1 ±

0.4

3 6.

84 ±

0.1

8 0.

8 ±

0.4

4 6.

77 ±

0.0

5 2.

0 ±

0.3

5 6.

79 ±

0.0

9 1.

3 ±

0.3

6 6.

78 ±

0.0

9 1.

2 ±

0.3

7 6.

77 ±

0.2

5 0.

5 ±

0.3

Not

e:

The

eff

ectiv

e ar

ea is

640

cm

2.

TA

BL

E I

Res

ults

of

the

spec

tral

fitt

ing

of C

yg X

-2

Con

tinu

um

E.W

. In

tens

ity

(2-9

ke V

) (e

V)

(cis

)

18 ±

8

460.

8 ±

1.7

22 ±

8

526.

7 ±

2.1

14 ±

7

585.

7 ±

1.8

43 ±

6

562.

1 ±

1.3

26 ±

6

560.

2 ±

1.5

24 ±

6

561.

3 ±

1.3

9±

6

572.

2 ±

1.4

Inte

nsit

y (8

-31

keY

) (c

is)

79.7

± 1

.6

90.7

± 1

.9

98.3

± 1

.5

59.6

± 1

.0

66.4

± 1

.2

73.2

± 1

.1

93.1

± 1

.1

Har

dnes

s ra

tio

(9-2

0 ke

V/2

-9 k

eY)

0.12

7 ±

0.00

3 0.

126

± 0.

003

0.12

2 ±

0.00

2 0.

073

± 0.

001

0.08

4 ±

0.00

2 0.

093

± 0.

001

0.11

9 ±

0.00

2

-.)

0

0

~

~ ;0 » z 0 tT1 ..., » r

IRON K-EMISSION LINE FROM CYGNUS X-2 79

flux in the range 9-20 keY to that in 2-9 keY. In the first half of the observation interval the X-ray intensity varied by a factor of 1.5, while in the latter half the hardness ratio varied by a factor of 1.5.

We divided the observed data into seven groups. The X-ray intensity in the data groups of 1-3 varied, while the hardness ratio was constant. The hardness ratio in the data groups of 4-7 varied, while the X-ray intensity was constant.

The emission line feature around 6-7 keY appeared in the X-ray spectra of all seven data groups. These data groups were analyzed with the following methods.

We determined the continuum spectrum in the X -ray energy range 4-10 ke V by fitting the observed spectra with an exponential function, except for the energy range 6.0-7.5 keY to avoid the effect of the iron line. The reduced chi-squares of all these fittings were less than 1.2 (90% confidence level). Subtracting the obtained continuum spectrum from the observed data, we were able to derive the profile of the emission line. In Figure 1, the line profile for data group 4 is shown along with the best fitted Gaussian distribution. We again fitted each ofthe observed spectra with a Gaussian function plus the continuum spectrum whose parameters were fixed. These fitting results are summarized in Table I.

All the centre energies of the iron line obtained for data groups 1-7 are consistent with 6.7 keY to within the accuracy of determination. The maximum value of the equivalent width is ~ 40 eV. The intrinsic width ofthe iron line is narrower than 600 eV (90% upper limit).

3. Discussion

The above result indicates that the iron line from eyg X-2 has been significantly detected. The centre energy and equivalent width are consistent with those of other low-mass binary X-ray sources (Suzuki et at., 1984). The centre energy of 6.7 keY implies that the ionization state of iron is up to Fe xxv (helium-like). The width of the line profile could be broadened due to photon energy change resulting from electron scattering. The upper limit of the intrinsic linewidth indicates that the Thomson scattering depth is less than three. So the electron column density in the emission region is at most 2 x 1024 atoms cm - 2.

The mechanism of the iron line-emission is revealed by the relation between the intensity of the iron line and other parameters which are listed in Table I. In spite of the change in the iron line intensity, the continuum intensity at low energies seems to be stable, and the larger is the iron line-intensity, the smaller is the continuum intensity at high energies.

If the iron were due to thermal emission from a thin hot plasma of ~ 5 keY, the luminosity would have to be about 1036 erg s - 1 in order to explain the observed intensity of the iron line. In other words, a thin hot plasma of spherical geometry with a column density of ~ 1024 atoms cm - 2 would be unable to explain both the iron line and the high continuum luminosity in a consistent manner.

If the iron line were emitted by K-fluorescence from a hot plasma irradiated by

80 T. HIRANO ET AL.

3.0

> 2 . 5 <11

..lI:: --III 2.0 --u

» 1.5 ..... III C <11 1.0 .... C

C 0. 5 0 L-

0 . 0

-0 . 5

-1.0 4. 0 5.0 6 . 0 7.0 8 . 0 9 . 0 10 . 0

Energy (keV)

Fig. 1. The observed iron line profile.

continuum emission, elements lighter than iron are almost fully ionized in the irradiated hot plasma. Hence, the iron line produced by the fluorescence would be hardly absorbed by the hot irradiated plasma. For a hot plasma spherically surrounding a continuum emitter the fluorescence efficiency is estimated to be several tens of percent for a column density of ~ 1024 atoms cm - 2, whereas the observed fluorescence efficiency is only a few percent. This would appear to imply that the irradiated hot plasma forms a disk around the neutron star.

References

Cowley, A. P., Crampton, D., and Hutchings, J. B.: 1979, Astrophys. J. 231, 539. Giacconi, R. G., Gorenstein, P., Gursky, H. H., Usher, P., Waters, J., Sandage, A., Osmer, P., and Jugaku,

J: 1967, Astrophys. J. 18, Ll29. Hayakawa, S., Hirano, T, Kunieda, H., and Nagase, F.: 1984, Adv. Space Res. 3, 67. Hirano, T., Hayakawa, S., Kunieda, H., Makino, F., Masai, K., Nagase, F., and Yamashita, K.: 1984, Pub!.

Astron. Soc. Japan 36, 769. Pravdo, S. H.: 1983, Astrophys. J. 270,239. Suzuki, K., Matsuoka, M., Inoue, H., Mitsuda, K., Ohashi, T, Tanaka, Y., Hirano, T, and Miyamoto, S.:

1984, Pub!. Astron. Soc. Japan 36, 761.

X-RAY EMISSIONS FROM VELA X-I DURING ITS ECLIPSING

PERIOD*

N. SAT 0, S HAY A K A W A, and F. NAG A S E

Department of Physics, Nagoya University, Chikusa-ku, Nagoya, Japan


Abstract. The X-ray pulsar Vela X-I was observed with TENMA throughout the entire period of eclipse in March 1984. The energy spectra at several phase angles showed the iron emission line at about 6.4 ke V throughout the eclipse of Vela X-I and its intensity at the mid-eclipse to be about 10~o of that in the non-eclipsing phase, whereas the continuum intensity was about 1 %. The result provides means of studying the contribution of the stellar wind to the fluorescence line and the structure of the stellar atmosphere.

1. Introduction

Vela X-I (4U1900 - 40) is one of the most intensively investigated X-ray pulsars. This is considered to be a neutron star which forms a massive binary system together with an early type supergiant (BO.51b), HD 77581. The orbital period of the binary system is 8.965 days and the pulsation period of the neutron star is 282.9 s. The distance to the X-ray source is estimated to be 1.9 kpc (Sadakane et al., 1985).

This X-ray pulsar shows a complex energy-dependent pulse profile. The pulse period of Vela X-I has been monitored over ten years, and found to change on time-scales from several days to several years (Nagase et al., 1984a). The observation of Vela X-I with the TENMA satellite in 1983 enabled us to study an iron emission line at 6.4 keV (Ohashi etal., 1984).

The observation of Vela X-I was again performed during an eclipse of Vela X-I in 1984, with a set of gas scintillation proportional counters (GSPC's) on board TENMA. Data obtained by system A of the GSPC's, with a field of view of 3 0 .1 (FWHM) and an effective area of 320 cm2 , were analyzed to study the change in the energy spectrum during a time-span including the eclipse of Vela X-I.

2. Observational Results

In the X-ray light curve, sharp decreases of the X-ray intensity are seen during ingress and egress of the X-ray source. The epoch of the eclipse centre was detected at 17 : 00 UT on March 25, 1984 (JD 2445785.22 ± 0.002).



82 N. SATO ET AL.

The pulse period of283.921 ± 0.009 s was obtained from the timing analysis of pulse arrival times measured before and after the eclipse. This value is nearly the same as that measured in March 1983. The tendency of constant pulse period (Nagase eta!., 1984a, b) has continued in the last two years.

The energy spectra of Vela X-I were observed during ingress to and egress from the eclipse. The observed pulse-height spectra around egress are shown in Figure 1. Not only the spectra observed during the non-eclipsing phase but also those during eclipsing phase show iron emission lines consistently at the energy of 6.4 keY. It is clear that the relative intensity of the iron emission line to the continuum emission during eclipse is stronger than that during the non-eclipsing phase-range. The light curve of the iron emission line intensity is shown in Figure 2, together with that of the continuum intensity in the range 7-20 keY. The intensities of the iron emission line in the figure are derived from spectral fittings, in which the trial function is assumed to have the form of a power-law spectrum with low-energy absorption, a high energy cut-off and emission lines in the form of Gaussian distribution.

It is noted that the average eclipse flux in the range 7-20 keY is a few percent of the non-eclipsed flux. This is consistent with the previous result by Becker et al. (1978). We observed the light curve to be symmetric with respect to ingress and egress, with a transit time of ~ 5 hr which is contrary to the previous observation by Watson and Griffiths (1977).

10 1

> UJ 10 a ::,,:

" U UJ (f)

" (f)

I-

3 10- 1

o U

--t j 10

ENERGY (KEV)

Fig. I. The pulse-height spectra of Vela X-I during the egress from eclipse on 25 March, 1984. Each data observed at (a) <p = 0.0, (b) <p = 0.11, (c) <p = 0.13, and (d) <p = 0.17.

X-RAY EMISSIONS FROM VELA X-I 83

vela X-l 1984 . 3 . 22 - 3 . 27

&clipse

10 2 j( 1 ~I

...... ., . ..... .. .. Center

7-20 keV

... continuum I ~

10

~ " .. ~ t ~ 0

0° ~ 2 0(,8 t >. o 0 .. 1 t 00 i ++ 0

0 .... ~

~ c

" .-~ 6.4 keV

Iron-Line +t t 10- 1

82 83 84 85 86 87

Jt>-2 , 445, 700

Fig. 2. The iron line intensities (open circles) and the continuum intensities in the range 7.1-20 keY (closed circles) as a function of the observation date.

The iron line intensities just after ingress and just before egress are 0.52 ± 0.08 counts s - 1 and 0.30 ± 0.11 counts s - 1, respectively. These are about 30 and 20% of the average iron line intensity in the non-eclipsing phase. The iron line intensity at the mid-eclipse decrease to ~ 10% (0.16 ± 0.10 counts S- I) of that in the non-eclipsing phase.

3. Discussion

The present observation of Vela X-1 revealed the existence of an iron emission line with energy at ~ 6.4 keY even during the mid-eclipse of the X-ray source. The intensity of this iron line is about 10 % of the average line intensity observed during the non-eclipsing phase. This result indicates that a least 10 % of the fluorescent iron line emission is caused by an extended stellar wind. As the effective solid angle of the stellar wind irradiated by X-rays and unobscured by the optical companion during the eclipsing phase is estimated to be less than half of that during the non-eclipsing phase, the contribution of the stellar wind to the fluorescent yield is expected to be more than 20% ofthetotal iron line emission when the neutron star is out of eclipse. The iron line intensity at the edge of eclipse increases up to 20 ~ 30% of the average iron line intensity during the non-eclipse phase. This fact supports the above estimate.

To investigate orbital phase dependence of the fluorescence efficiency, we have combined the present data with the data measured in March, 1983 (Ohashi et al., 1984). The fluorescence efficiency indicates a broad peak around the orbital phase of cp = 0.4-0.5. The efficiencies around cp ~ 0.2 and cp ~ 0.8 are 20 ~ 30% less than that

84 N. SATO ET AL.

at cp ~ 0.5. This orbital phase dependense of fluorescence efficiency may be explained by some effect of the optical counterpart, if 20 ~ 30 % of the fluorescent iron line arises from the stellar atmosphere of the companion star.

A fraction of the iron line emission is suspected to be caused by a rather small region surrounding the neutron star. Quantitative analysis of the orbital phase dependence of the iron emission line will give an important clue towards understanding the distribution of matter accreting onto the neutron star, and that surrounding the binary system.

References

Becker, R H., Rothschild, R E., Boldt, E. A., Holt, S. S., Pravdo, S. H., Serlemitsos, P. J., and Swank, l.H.: 1978, Astrophys. J. 221,912.

Nagase, F., Hayakawa, S., Kunieda, H., Masai, K., Sato, N., Tawara, Y., Inoue, H., Koyama, K., Makino, F., Makishima, K., Matsuoka, M., Murakami, T., Oda, M., Ogawara, Y., Ohashi, T., Shibazaki, N., Tanaka, Y., Miyamoto, S., Tsunemi, H., Yamashita, K., and Kondo, I.: 1984a, Astrophys. J. 280, 259.

Nagase, F., Hayakawa, S., Kii, T., Sato, N., Ikegami, T., Kawai, N., Makishima, K., Murakami, T., Oda, M., Ohashi, T., Tanaka, Y., Mitani, K., and Kitamoto, S.: 1984b, Pub!. Astron. Soc. Japan 36, 667.

Ohashi, T., Inoue, H., Koyama, K., Makino, F., Matsuoka, M., Suzuki, K., Tanaka, Y., Hayakawa, S., Miyamoto, S., Tsunemi, H., and Yamashita, K.: 1984, Publ. Astron. Soc. Japan 36, 699.

Sadakane, K., Hirata, R, Jugaku, 1., Kondo, Y., Matsuoka, M., Tanaka, Y., and Hammerschlag-Hensberg, G.: 1985, Astrophys. J. 288, 245.

Watson, M. G. and Griffiths, R. E.: 1977, Monthly Notices Roy. Astron. Soc. 178,513.

ELECTRODYNAMICAL SYNCHRONIZATION OF

AM HERCULIS-TYPE STARS*

OSAMU KABURAKI

Astronomical Institute. Faculty of Science. Tohoku University. Sendai. Japan


Abstract. A new mechanism is proposed for the explanation of synchronous rotations in AM Herculis-type binaries. In contrast to the resistive mechanism ofJ oss et aT. (1979), our model predicts that an asynchronous rotation, if it is present, damps exponentially and the damping time is inversely proportional to the electrical conductivity. It is shown by using the parameters which fit for AM Herculis that a typical damping time is very short compared with the lifetime of the system.

1. Introduction

AM Herculis is a semi-detached binary system in which a highly magnetized white dwarf is accreting matter from a secondary red dwarf. Observations indicate a synchronous rotation of the white dwarf with the orbital period of 3.1 hr, within the limit of observational errors. This synchronism is remarkable and needs explanation, in view of the small moment of inertia of the white dwarf and the large specific angular momentum of the accreted matter. Joss et al. (1979) have proposed a mechanism for synchronization in which ohmic dissipation of the eddy current, induced on the secondary star by the asynchronously rotating magnetic field of white dwarf, exerts a braking torque. However, they concluded that this mechanism could bring about exact synchronism within the lifetime of the system, only when some other process had brought the rotation period to the same order of magnitude as the orbital period. We present another mechanism, which is far more effective than that of Joss et al. (1979).

The outline of our model is as follows: If the magnetized white dwarf were to rotate asynchronously with the orbital motion, it would act as a unipolar inductor and produce a strong electric field component along the magnetic field lines. Since the electric force is much stronger than the gravity, it can draw plasma from the surface layer of the white dwarf to form a magnetosphere, analogous to the case of pulsars (Goldreich and Julian, 1969). As a result, field lines become equipotentials and the electric potential difference between different latitudes on the surface of the white dwarf is projected onto the red dwarf. This potential difference distributed over the surface of the red dwarf drives a current through it. Because of the low temperature near the surface of the red dwarf, its electrical resistance forms the main load of this current circuit and determines the amount of the total current, provided that anomalous resistivity does not appear

* Paper presented at the I.A.U. Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984.


86 OSAMU KABURAKI

anywhere. The return current in the surface layer of the white dwarf exerts the braking torque through j x B force. In contrast with the case of resistive braking, the torque is proportional both to the electrical conductivity of the red dwarf and to the angular velocity of asynchronous rotation. Therefore, the rotation damps exponentially and a typical damping time is estimated to be very short.

2. Calculation of Braking Torque

We assume in an AM Her-type star that a magnetized white dwarf is rotating asynchronously (angular velocity, n) with the orbital motion (angular velocity, no). The secondary red dwarf is regarded as already in synchronous rotation, as a result of tidal force or friction. As a reference frame, a spherical polar system (r, e, cp) which is rotating with the orbital angular velocity is chosen, with the origin placed at the center of the white dwarf. The effects which arise from the fact that this is not an inertial frame are neglected as small. In this frame, the white dwarf rotates with angular velocity ro = n - no i= O. The magnetic field of the white dwarf is expressed in terms of a dipole moment which is aligned with the axis of rotation.

After a magnetosphere is formed around the white dwarf by the Goldreich-lulian (1969) mechanism, it is filled with a plasma of density n ~ nG _ J = wBl2ne, where B is the magnetic field and e is the charge of a proton. Magnetic field lines, therefore, become equipotentials, provided that there is no significant mass flow. There always exists a stationary magnetic flux tube, in each hemisphere, which connects the two stars in the system, in spite of the white dwarfs rotation. The electromotive force at the base of such a tube is Eo = - (1 Ie) wa I B s sin e, where a I is the radius of the white dwarf and B s

denotes the surface field. This causes potential differences between the magnetic field lines of different latitudes and they are projected along the field lines onto the surface of red dwarf. The whole potential difference over the red dwarf is

JOl W [( 1)1/2]Xl wa a V= Eoa l de= - aTBs 1 _ _ ~ __ 1_2

C X X2 CX I X 2

(1)

O2

(for large XI and x 2 ), where we have used the relations for a dipole field (e.g. Hill, 1979), sin Os = l/x and X = wla l , with es and w being the surface colatitude and the equatorial crossing distance, respectively. This drives a current in the red dwarf and causes a field-aligned current (the Birkeland current, see Figure 1) in the flux tube (Pedersen conductivity is small since nG _ J is very small). The electrical resistance of the red dwarf is estimated roughly as R = (2a2 0") - I by assuming a cube-like form, where a2 is the radius of red dwarf and 0" is the electrical conductivity (we regard it as isotropic because of the relatively high density there). Therefore, the total current becomes J = VIR = O"wa l a~Bslcxl x 2 . The Birkeland current closes in the surface layer of the white dwarf where the conductivity is isotropic. Denoting the depth of the current layer by h and the angle subtended at the white dwarf by the red dwarf as I1cp, we obtain the

ELECTRODYNAMICAL SYNCHRONIZATION 87

current density in the layer as j(J = l/2ha l Arp. The factor 2 is due to the presence of two tubes. The j x B force acting on this current is F <p = (l/c )j(JBs = lBs/ca l hArp. The braking torque, therefore, becomes

T~2 I J T F.a,sme(a~sined,ded~) o (J, 0

(2)

where f = (Xi 3/2 - xj3/2)lx 1 x 2. From the equation of motion for the white dwarf, - I (dw/dt) = T which is oc w (compare with the resistive mechanism in which T oc w- 1/2), we have an exponential decay of rotation, w = wo exp( - tlr), where I is

the moment of inertia and

-I T f aB;aia~ r = - = - which is oc (J

Iw 3 c2 I (3)

(compare with the resistive mechanism in which c 1 oc (J- 1/2).

As an illustration of numerical values, we use following values of parameters in the case of AM Her: no ~ 6 x 10- 4 rad sec-I, Bs ~ 3 X 108 G, I ~ 1050 g cm2 ,

a1 ~ 6 x 108 cm, a2 ~ 3 x 1010 cm, D ~ 1011 cm (separation of two stars), 8 1 ~ 107 K (surface temperature of white dwarf) and 8 2 ~ 3 X 103 K (that of red dwarf). From these values we obtain the following results: nG _ J ~ 103 cm - 3 at the base of the flux tube and hence the Hall coefficient is very much larger than unity (i.e. the Pedersen conductivity is very small) there, for the Spizter conductivity in red dwarf (J ~ 1.4 X 1013 sec (assuming that the average temperature in the resistive layer ~ 104 K), XI = (D + a2)la l ~ 2.2 x 102 , X 2 = (D - a2)la l ~ 1.2 x 102 , and f ~ 1.7 x 10 - 8. Therefore, we finally have the braking torque as To ~ 1.0 X 1044 dyne cm (assuming that w ~ no) and the damping time as r ~ 6 x 102 sec. On the other hand, the accretion torque can be estimated as Ta ~ innoD2 ~ 1034 dyne cm (for in ~ 1.7 x 1015 g sec - 1). Thus, it has been shown that the white dwarf can be brought into almost exact synchronism within a very short time. In the presence of an asynchronous rotation of the order of w ~ no, the ratio of gravitational to electric potentials for a proton is, mp W/eV ~ 10- 9 , where W ~ GMla l ~ 2.2 x 1017 ergg- 1 (for M ~ Mo) and V ~ wa'fBs/c ~ 7.2 x 1011 e.s.u.

3. Discussion

In our electro dynamical model, rotation damps exponentially and a typical damping time has been estimated as 6 x 102 sec. However, this figure should be taken as a lower limit, because of the following main reasons: (1) the resistance of red dwarf would be

88

, , , \ ,

OSAMU KABURAKI

Fig.1. A side-view of the binary system (white dwarf is enlarged). Birkeland current flows along the flux tube which connects the two stars, and closes across the field lines in the red and white dwarfs.

fairly increased if the current in it flows only in the surface layer and (2) anomalous resistivity is very likely to appear anywhere in the current circuit, probably in the flux tubes, and reduce the value of (J by many orders of magnitude.

Ifwe assume that a steady state is reached when the accretion torque is balanced by the braking torque, we have w ~ 10 - 10 Qo and in such a case the electric potential for a proton becomes smaller than the gravitational potential. However, as noted above, the resistance in the circuit seems to be rather underestimated, the actual steady state would be reached at a much larger value of w. Then, the electric potential exceeds the gravitational one, and a magnetosphere can be formed as assumed first.

Finally, the possibility of matter accretion along the flux tubes should be mentioned. Even after the formation of a magnetosphere, there can be a non-zero Ell in the flux tube which is sustained dynamically by the inertial term of infalling matter. Matter will be supplied from the secondary star since the gravitational barrier is smaller for it.

References

Goldreich, P. and Julian, W. H.: 1969, Astrophys. J. 157, 869. Hill, T. W.: 1979, J. Geophys. Res. 84,6554. Joss, P. c., Katz, J. I., and Rappaport, S. A.: 1979, Astrophys. J. 230, 176.

SPECTROSCOPIC AND PHOTOMETRIC OBSERVATIONS OF

NOV A AQUILAE 1982*

AKIRA OKAZAKI

Tsuda College, Kodaira, Tokyo, Japan

and

ATSUMA YAMASAKI

Department of Earth Science and Astronomy, University of Tokyo , Japan


Abstract. Nova Aquilae 1982 was observed spectroscopically and photometrically in January, February, and April 1982. The results of these observations, including those obtained a few days after the discovery, are presented.

Nova Aquilae 1982 was discovered by M. Honda on 27.85 January, 1982 when its visual magnitude was 6-7 (IAU eire., No. 3661). It was difficult to observe the Nova immediately after the discovery, because the Nova was so close to the Sun. In fact, no spectroscopic observations of the Nova before the middle of February have been reported, except one made by G. Sasaki (see IAU eire., No. 3661), which will be reported here.

In this note, we present some results of spectroscopic and photometric observations of Nova Aquilae 1982, including those obtained a few days after the discovery.

We obtained seven spectrograms of the Nova from January to April 1982 at the Okayama Astrophysical Observatory. The journal of our spectroscopic observations is given in Table I. We also made UBV photoelectric photometry of the Nova on three nights in January, February, and April 1982 with the 0.9 m reflectors at the Dodaira and the Okayama Observatories. Unrefrigerated photomultipliers EMI 6256A were used.

January. The spectrograms Z-1824 and Z-1827, taken by G. Sasaki at the end of January, were poorly exposed owing to the close position of the Nova to the Sun. Nevertheless, they allow us to detect broad emission lines of Hf3 and H y whose widths correspond to an expansion velocity of 1000-1500 km s - 1. These are the first spectroscopic observations of the Nova that have been reported.

Our UBV photometry of the Nova at 20h40rn (UT) on 30 January gave V = 8.20, B - V = + 0.32 and U - B = - 0.72.

February. Figure 1 represents an intensity tracing of the spectrogram CIlO-1249, which was taken fourteen days after the discovery. The Nova showed Balmer and some other



90 A. OKAZAKI AND A. YAMASAKI

TABLE I

List of our spectroscopic observations

Plate No. a Date UT Dispersion Wavelength at Hy region (A mm- l )

Z-IS24 Jan. 29 21 h 3Sm 73 U3750-4950

Z-IS27 30 21 12 73 3750-4950 CIIO-1249 Feb. 10 21 07 32 3700-4700 IS-993c Apr. 23 17 51 110 3700-5600 IS-993d 23 IS 52 110 5300-7200 IS-998 24 18 41 40 4350-5100 IS-IOOI 25 18 19 40 3800-4550

a Z: 0.9 m reflector plus Cassegrain spectrograph. CI I 0: 1.9 m reflector plus coude image-tube spectrograph. IS: 1.9 m reflector plus Cassegrain image-tube spectrograph.

Exposure time (min)

5

12 13 45 64 99

122

Remarks

Contaminated by sunlight

Underexposed

Underexposed

emission lines superposed on a rather strong continuum. The diffuse Balmer lines of HfJ and HI (half width ~ 1500 km s - I) had strong central peaks (half width ~ 200 km s - 1). It may be noted that the diffuse components were stronger in their red wing than in the blue. Narrow emission lines of HeI M026, and M471, Cn M267, Fen M416, and A4583 were identified. Diffuse emission lines of NIII-CIII VA640-4650 and He n A4686 were also present. No appreciable absorption lines of the Nova could be recognized. Interstellar absorption lines of Can Hand K were seen, where the former was blended with HB line. The equivalent width of interstellar Can K was measured to be ~ 2 A, which corresponds to a distance of ~ 6 kpc for the Nova (e.g., Allen, 1973).

UBV photometry of the Nova at 20h 4Sm (UT) on 10 February, when the spectrogram was obtained, gave V = 9.87, B - V = + 0.31 and U - B = - 0.90.

Rosino et al. (1983) obtained their first spectrogram of the Nova on 13 February, which also showed diffuse Balmer lines with central peaks. They found half-widths of ~ 650 km s - 1 and ~ 2100 km s - 1 for the peak and the diffuse components, respectively, which are larger than our values.

April. The spectrograms ofIS-993c, IS-993d, IS-998, and IS-IOOl were taken, when the Nova gradually increased its brightness to the secondary maximum (e.g., Rosino et al., 1983), about three months after the discovery. In the spectrograms, the Nova showed forbidden lines of [Nem] A3869 and A3967, [Om] A4363, M958, and A5007, and [01] },6300 and },6364, as well as Balmer lines, HeI A4921, A5875, A6678, and n065, He n }, 4686, C III }A640 and N III A4650. The strong Balmer lines and He n M686 were diffuse having central peaks, while the other lines were narrow except that [NeIll] lines were very diffuse with no appreciable peak. A part of the intensity tracing of the spectrogram IS-998 is represented in Figure 2, where HfJ and He n M686 showed the

OBSERVATIONS OF NOVA AQUILAE 1982 91

- II~ 3889

- Call K 3933 (Interstellar)

- lie 3970 + Call II 3968 (Interstellar)

- 116 4101

- Cll 4267

- lIy 4340 - C . L.

- Fell 4416

- 1101 4471

- Fell 4583

- NIII-CIIl 4640-4650

- lIelI 4686

Fig.1. An intensity tracing of the spectrogram of Nova Aquilae 1982 taken on 10 February, 1982. C.L. denotes city lights.

diffuse structure with many different velocity components in their wings. It is found that the half width of the diffuse components corresponds to a mean expansion velocity of ~ 2000 km s -1, which is in agreement with that given by Rosino et af. (1983).

Our UBV photometry at 19h 07m (UT) on 22 April gave V = 12.93, B - V = + 0.36, and U - B = - 0.46.

92 A. OKAZAKI AND A. YAMASAKI

~~~~_ - NIH ~640 ~ - CIlI 4650

- lIeII 4686

- liB 4861

- [OIIIJ 4958

- [OIIl J 5007

Fig. 2. Spectral feature around H{3 and Hen A4686 of Nova Aquilae 1982 on 24 April, 1982.

Acknowledgements

We would like to thank G. Sasaki for providing the spectrograms Z-1824 and Z-1827, and T. Abe for his assistance in the photometric observations. This work is supported in part by the Scientific Research Fund of the Ministry of Education, Science, and Culture of Japan (58340013 and 59740124).

References

Allen, C. W.: 1973, Astrophysical Quantities, 3rd ed., Athlone Press, London, p. 266. Rosina, L., Iijima, T., and Ortolani, S.: 1983, Monthly Notices Roy. Astron. Soc. 205, 1069.

MOMENT METHOD FOR THE INVERSE RADIATIVE

TRANSFER IN INHOMOGENEOUS MEDIA *

S. J. WILSON and K. K .. SEN**

Department of Mathematics, National University of Singapore, Kent Ridge, Singapore


Abstract. In the present paper, an inverse problem of radiative transfer in an inhomogeneous plane medium of scattering albedo w = Wo exp ( - ,/s) is solved by a moment method. The results are compared with those obtained by Dunn (1983) using Monte Carlo method.

1. Introduction

The direct problem of radiative transfer in inhomogeneous plane-parallel semi-infinite media has been studied extensively by Mullikin and Siewert (1980) and Garcia and Siewert (1981) for obtaining estimates for the albedo and distribution of emergent radiation. Pomraning and Larsen (1980), Larsen et af. (1980) concentrated their attention in securing elementary analytic solutions of the direct problem. Although the inverse solutions of the homogeneous media have been developed by several authors (Siewert, 1978; Dunn and Maiorino, 1980; Sanchez and McCormick, 1981) the methods for solving the inverse problem of the inhomogeneous media is in a very early stage of development. Recently Dunn (1983) had used Monte Carlo methods for obtaining a fairly accurate solution of the inverse inhomogeneous problem.

In this paper we outline a moment method for the same problem. The results obtained were compared with those of Dunn.

2. Model and Equations

We consider the half-space transfer problem in plane geometry described (cf. Larsen et al., 1980; p. 2448) by

+ 1

P olj; (x, p) + Ij;(x, p) = w(x) f Ij;(x, p') dp' , ox 2

(2.1)

-1

where Ij;(x, p) is the radiation intensity, x E [0, 00 1 is the optical depth of the medium,

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** Visiting professor.


94 S. J. WILSON AND K. K. SEN

/1 E [ - 1, 1] is the direction cosine of the propagating radiation measured with respect to the positive x-axis, and w(x) E [0, 1] is the single scattering albedo given by

w(x) = Wo e- x /s ,

where s > 0 and 0 < Wo :::; 1. The boundary conditions of the problem are

and

Following Dunn (1980) we take

!/I(O, /1) = F(Il) = 1,

(2.2)

(2.3)

(2.4)

In the inverse problem we determine the parameter Wo given s and the total albedo

3. Method of Solution

From Equation (2.1) we obtain the following moment equations:

where

and

dB -+J=w(x)J, dx

dK -+H=O, dx

+ I

J = ~ f !/I(x, /1) d/1 ; -1

+1

K = ~ f !/I(x, 11)112 d/1 . -1

Introducing the Eddington factor

I(x) = K(x)jJ(x) ,

+1

H = ~ f !/I(x, 11)11 d/1 ; -1

(2.5)

(3.1)

(3.2)

(3.3)

INVERSE RADIATIVE TRANSFER IN INHOMOGENEOUS MEDIA 95

we have from Equations (3.1) to (3.3)

d 2K = [1 -W(X)]K. dx2 f(x)

(3.4)

We solve Equation (3.4) as a two-point boundary value problem. The boundary condition as x ---+ r:f) is K = 0 (from (2.3». That at the free surface is determined from Equations (2.4) and (2.5). The incident radiation is given for all 11 E (0, 1). Hence, we

take a form for the emergent radiation ( - 1 < J1 < 0) with a free parameter a and determine this parameter from the condition (2.5). We take

s 1f;(0, 11) = -- , -1<11<0. (3.5)

s + all

The form is dictated by the general solution of Equations (2.1), (2.3) for the emergent radiation

co f lex) e-x«I/I")+(I/s))

1f;(0, 11) = Wo dx. 11

(3.6)

o

This form also takes care of the fact that 1f;(0, 11) ---+ 1 as s ---+ r:f) (cf. Garcia and Siewert, 1981). Using Equations (2.4) and (3.5) we find that

1 s (s) 1(0) = - + - In - , 22a s-a

H(O) =! + ~{1- ~ In(_s )}, 4 2a a s-a

1 s {a2 2 ( S )} K(O) = - + - - - - as + s In -- .

6 2a 3 2 s - a

From the given total albedo A, we determine the parameter a and the initial values K(O)

TABLE I

The calculated Wo

Actual s = 1 s = 100 Wo

A Calculated Wo A Calculated Wo

Dunn Case (i) Case (ii) Dunn Case (i) Case (ii)

0.70 0.1552404 0.704 0.655 0.653 0.2540444 0.704 0.603 0.632 0.90 0.2243149 0.902 0.870 0.868 0.4645445 0.901 0.896 0.859 0.99 0.2614794 0.991 0.970 0.969 0.6960621 0.993 0.994 0.972

96 S. J. WILSON AND K. K. SEN

and f(O). Equation (3.4) is then solved for a given f(x) as a two-point boundary value problem with an assigned woo Due to the presence of the exponential term in Equation (3.4), a finite difference scheme is used to solve this equation. From the computed K(x) we obtain J(x) through the Eddington factor. Using this J(x) we compute the emergent intensity 1/1(0, /1) and the total albedo A from Equations (3.6) and (2.5), respectively. The solution of the inverse problem consists in obtaining the Wo

which yields the correct A. In Table I we show the computed values of Wo for s = 1 and s = 100 for the following

two forms of the Eddington factor: Case (i)

f(x) = {{(O) , 3 '

x = 0,

x#O.

Case (ii)

f(x) = 1(0) + G -1(0)) e -six.

The results are compared with those of Dunn (1983). The moment method is simple and yields values of Wo comparable with those of Dunn. An attempt is being made to extend the scheme to solve the inverse problems in other geometries.

Acknowledgement

We are grateful to our colleague Dr R. P. Agraval for some discussions regarding the choice of the numerical method.

References

Dunn, W. L.: 1983, J. Quant. Spectr. Rad. Trans. 29, 19. Dunn, W. L. and Maiorino, 1. R: 1980, J. Quant. Spectr. Rad. Trans. 24, 203. Garcia, R D. M. and Siewert, C. E.: 1981, J. Quant. Spectr. Rad. Trans. 25,277. Larsen, E. W.: 1981, J. Math. Phys. 22, 158. Larsen, E. W., Pomraning, G. c., and Badham, V. c.: 1980, J. Math. Phys. 21,2448. Mullikin, T. W. and Siewert, C. E.: 1980, Ann. Nucl. Energy 7, 205. Pomraning, G. C. and Larsen, E. W.: 1980, J. Math. Phys. 21, 1603. Siewert, C. E.: 1978, J. Math. Phys. 19, 1587. Sanchez, R and McCormick, N. 1.: 1981, J. Math. Phys. 22,847.

PHOTOMETRIC DETERMINATION OF VARIATIONS IN THE

SURF ACE CONDITIONS FOR PULSATING ST ARS*

W. J. COUCH** and H. J. TRODAHL

Physics Department, Victoria University of Wellington, New Zealand


Abstract. Two sets of model atmosphere spectra have been used to determine variations of effective temperature, surface gravity, and radius from multicolour indices measured for pulsating stars. The two model atmosphere sets led to surface parameters that differ by considerably more than the measurement uncertainties.

We have previously reported multicolour photometry on a number of b Sct stars (Trodahl et ai., 1973; Bringans et aI., 1974; Trodahl and Sullivan, 1977; Sullivan and Trodahl, 1978) and in some cases have given variations in the temperature, gravity, and radius derived from the data. The determination of these surface parameters in this way relies on an accurate prediction of the spectral flux. The results obtained can, therefore, be expected to depend upon the model atmosphere set used, and we have explored this dependence by comparing results derived from the same set of data but using two different model atmosphere grids. We have made the comparisons using data taken on the UB V and ubvy systems as well as the VUW multicolour system.

The surface parameters are estimated by fitting the N-colour indices (cj , j = 1---+ N) to the equations

(ac.) ( ac. ) ~clt) == cit) - < Cj ) = _1 ~Te(t) + __ 1_ ~ log get) , aTe alogg

where < cj ) is the time-average colour index and Cj is the colour index predicted by a model atmosphere. Clearly a grid of atmospheres must be used in order to correctly predict the derivatives.

Once the parameters ~Te(t) and ~ log get) are known the relative departure of the radius from its average value can be determined from variations in the magnitude measured through one filter,

~mo(t) = _0 ~TeCt) + __ 0 ~ log get) - 2.13 --(aM) (aM ) ~R(t) aTe a log g < R )

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** Present address: University of Durham, South Road, Durham DHI 3LE, England.


98 w. 1. COUCH AND H. 1. TRODAHL

Again the upper case (Mo) refers to model atmosphere predictions of the magnitude through filter '0'.

The two model atmosphere grids that we have used are those reported by Carbon and Gingerich (1969) and by Kurucz et al. (1974). The predicted spectra were folded with appropriate transmission-detection functions before the required magnitude and colour index derivatives were calculated. The procedure for calculating these derivatives has been described elsewhere (Trodahl and Sullivan, 1977).

Both of these atmosphere predictions have been used to analyse the following three data sets:

(1) UBV data for 1 Mon, reported by Millis (1973). (2) ubvy data for D Sct collected at Mt. John on 2 and 3 July, 1976. (3) VUW multicolour data for 1 Mon collected at Mt. John on 15 October, 1974 and

at Wellington on 22 January, 1975. Detailed comparisons between the surface parameters obtained from the data of set 1

are shown in Figure 1. There are clear systematic differences between the parameters derived using the two model atmosphere grids. The other data sets show similar differences.

A compilation of the peak to peak variations derived from all three data sets is given in Table I. The quoted uncertainties represent the scatter in the data; systematic uncertainties appear as differences between variations based on the two modelatmospheric grids. The atmospheres of Kurucz consistently yield larger variations, particularly of effective temperature. Surprisingly it is the results based on the older and

100 t:.R/<R) t:. log 9 t:.Te (100K) I I I

I\) !.... . I\) I\) ..... f\)

D (X) .. .. ,+

U1 ... • + ... - .. ... +,

.. .. .. . .. + ... .. .. ... L

P CJ .. .. . , \D .. I\) 0 .. .. .. ~

.. .. .. ~ .. .. ... f\) .. .. . ... (1) ... ... ... (Jl

p .. ~ ... \D + .. - .. U1 .. .. ...

.. .. .. .. .. . .. .. .. .. + .. -..

Fig. I. Detailed comparison between parameters derived using the model-atmosphere grids of Carbon and Gingerich ( • ) and of Kurucz et al. ( + ). The data are the UB V results of Millis.

SURFACE CONDITIONS FOR PULSATING STARS 99

less complete models of Carbon and Gingerich that lead to the more credible results (Couch, 1976). In particular the magnitude and phase of the variations in gravity and radius that are derived using the Kurucz atmospheres are in disagreement with those expected on theoretical grounds and with radial velocity data.

We conclude that uncertainties in the spectral flux predicted by model atmospheres are likely to lead to the largest uncertainties in photometric determinations of variations of the effective temperature, gravity, and radius of a pulsating star.

TABLE I

Peak to peak variations in parameters derived using the two model atmosphere grids

Data set t'1Te (K) t'1logg t'1R/R

Carbon and Kurucz Carbon and Kurucz Carbon and Kurucz Gingerich et al. Gingerich et al. Gingerich et al.

(I Mon, UBV) 340(20) 470(20) 0.18(5) 0.21(5) 0.023(10) 0.054(10)

2 (I Mon, ubvy) 2 July, 1976 340(50) 350(50) 0.33 (10) 0.33 (10) 0.045(15) 0.07 (20) 3 July, 1976 360(40) 380(90) 0.45 (20) 0.46 (20) 0.040(10) 0.046(10)

4 (Ii Set, VUW) 15 Oct., 1974 355(15) 410(309) 0.26(6) 0.26(10) 0.022(6) 0.035(10) 22 Oct., 1974 525(75) 680(100)

References

Bringans, R. D., Sullivan, D. J., and Trodahl, H. J.: 1974, Pub!. Astron. Soc. Pacific 86, 693. Carbon, D. F. and Gingerich, 0.: 1969, in O. Gingerich (ed.), Theory and Observation of Normal Stellar

Atmospheres, MIT Press, Cambridge. Couch, W. J.: 1976, Msc. Thesis, Victoria University, Wellington. Kurucz, R. L., Peytremann, E., and Averett, E. H.: 1974, Blanketed Model Atmospheresfor Early-Type Stars,

Smithsonian Institute, Washington. Millis, R. L.: 1973, Publ. Astron Soc. Pacific 85,510. Sullivan, D. J. and Trodahl, H. J.: 1978, Monthly Notices Roy. Astron. Soc. 183, 201. Trodahl, H. J. and Sullivan, D. J.: 1977, Monthly Notices Roy. Astron. Soc. 179, 209. Trodahl, H. J., Sullivan, D. J., and Beaglehole, D.: 1973, Publ. Astron. Soc. Pacific 85, 608.

ESTIMATION OF SOME PARAMETERS OF PULSARS AND

THEIR APPLICATIONS*

WU XINJI, QIAO GUOJUN, XIA XIAOYANG, and LI FANG

Geophysics Department, Peking University, China


Abstract. The estimation of some important parameters of pulsars is discussed. The results have been compared with the RS model and applied to the estimation of radio luminosity and the beaming factor.

1. Estimation of Pobs' Pmax' and Q

According to the geometric relationship of the polar cap model (Manchester and Taylor, 1977), we can give formulae for these parameters from observational data of polarization and apparent beamwidth (IX). Firstly, we have

cos ~ = cos ~ sin e sin cp + cos e cos cp , 2 2

(1)

and

I O'l'1 I sin cp I <D = ill max = sinCe _ cp)

(2)

where 'l' is the linear polarization position angle; I, the longitude of the pulse; <D, the maximum gradient of the position angle; e, the angle between the sight line and the rotation axis; and cp, the magnetic inclination. The formula of cp by Jones (1977), is

(3)

where Tn is the time constant and < Tn) ~ 106 yr according to Jones (1977). This formula was supported by many investigators (e.g., Proszynski, 1979; Wu Xinji et ai., 1982; Narayan and Vivekanand, 1982).

From Equations (1) and (2), we find the relation between f3 and cp and obtain the maximum value f3max. The value of f3max is determined only from observational data. So the true emission cone of a pulsar can not be larger than the value f3max.



102 XINJI WU ET AL.

We define a new parameter Q (a position parameter of the sight line, Q = «() - cp) x 213- 1). Q indicates where the line-of-sight sweeps over the emission cone.

The values of f30bs and Q can be obtained from P, P, r:t., and <1>. f3max does not relate with cp, and the value of Q almost equals a constant for every value of cp.

2. Comparison with the RS Model

Ruderman and Sutherland (1975) (hereafter referred to as RS) give a hollow beam model defined by ()max and ()min. The value of f3RS is nearly equal to 2()max. Roughly, the formula for f3RS is: f3RS = 50 P - 0.69. There is a strong correlation between log f30bs

and log P (r = 0.71 for 27 pulsars), and the relationship is f30bS = 7.1 P - 0.67. This is similar to dependence for f3RS. On the average, the values of f3RS are greater than those of f30bs by about 7 times and f3RS is greater than f3max for 89% of pulsars. This result shows the angular radiation pattern might not reach em ax at all.

There is another parameter Qcr:

If Q > Qcn the integrated pulse profile belongs to a simple class (S). If Q < Qcn it belongs to a double peak class (C). The statistical results show that the pulsars of class S with Q > Qcr make up 84 % of total pulsars of class S, and pulsars of class C with Q < Qcr make up 75 % of the total pulsars of class C. The remaining pulsars have values of Q nearly equal to those of Qcr.

It is obvious that the statistical result strongly supports the hollow emission cone model by RS. The parameter Qcr is one for proper classification. Similarly, the value of Qmin is also far bigger than that of the hollow part of emission cone.

3. Modification of the Formula of Radio Luminosity

Let us adopt the formula of radio luminosity as given by Taylor and Manchester (1975):

(5)

This formula is correct, if 130 = r:t.o and cp = e. In general, however, 130 =I r:t.o and Q =I 0, as the above authors have also pointed out.

We assumed that the intensity distribution of the emission cone has the following form:

(6)

where 13 is a variable value indicating widths of a family of nested cones. For some pulsars with known cp, e, and xo, we can give the pulse's intensity distributions for various values of n. The theoretical curves for n = 2 are in agreement with the observed integrated pulse profiles of the class S. So, we choose n = 2.

PARAMETERS OF PULSARS 103

The flux density of the pulse received on Earth is

- "f0/2 [ J sin cp sin 8 2J2 P S = S400 P = 210 1 + Q I - x - dx,

(8 - cp)2 211 (7)

o

where 10 is the peak value of the pulse when the line-of-sight sweeps through the centre of the emission cone. 10 can be derived from Equation (7).

I _ 611S400 0- 1X0[1 + 2Q2 _ 3Q2(1 - Q2)-'ln(JQ-2 _ 1+ Q-')]

(8)

We can obtain an expression for the luminosity of the form

(9)

where L, is the old radio luminosity Equation (5) and

and

(11)

K, and K2 will strongly affect the value of L2. When e = cp and 130 = 1X0, we obtain L2 = L" and the new formula reverts to the old one.

There is a strong relationship between logL2 and 10gP (r = - 0.74 for 27 pulsars).

5. The Beaming Factor

Because of the geometrical effects, we can expect to observe only a small fraction f of all the active pulsars in the Galaxy. The formula off is: f = 130 sin cp (Gunn and Ostriker, 1970) and, correspondingly, that of the beaming factor is: Bbearn = f- '.

Assuming <130> = <1X0 > and cp = 90 0, we can obtain that the value of Bbearn is 5.

This value is commonly adopted. However, we know that the values of cp and Po are too small for most pulsars. We obtain that the average value of Bbearn should be 35, i.e., 7 times greater. So, the total number of the active pulsars in the Galaxy, and the corresponding birthrate of pulsars should be increased by 7 times.

References

Manchester, M. N. and Taylor, J. H.: 1977, Pulsars, pp. 217 and 224. Jones, P. B.: 1977, Monthly Notices Roy. Astron. Soc. 178, 187. Proszynski, M.: 1978, Astron. Astrophys. 79, 8.

104 XINJI WU ET AL.

Wu Xinji et al.: 1982, Chinese Astron. Astrophys. 6, 216. Narayan, R. and Vivekanand, M.: 1982, Astron. Astrophys. 113, L3. Ruderman, M. A. and Sutherland, P. G.: 1975, Astrophys. J. 196,51. Taylor, J. H. and Manchester, R. N.: 1975, Astron. J. 80, 794. Gunn, J. E. and Ostriker, J. D.: 1970, Astrophys. J. 160, 979.

PULSAR MAGNETOSPHERE WITH CONSPICUOUS

TRANS-FIELD FLOW*

SHINPEI SHIBATA

Astronomical Institute, Faculty of Science, Tohoku University, Sendai, Japan


Abstract. It is shown that (I) in the pulsar magnetosphere the violation of the ideal-MHD condition, E + v x B # 0, (i.e., conspicuous trans-field motion and non-zero field aligned electric field Ell # 0) appears owing to relativistic large inertia, and (2) an axisymmetric numerical model with tenuous plasma suggests that in the region of the trans-field flow a vacuum-like electric field and a closed current circuit develop.

1. Introduction

It is widely known that, under the ideal-MHD condition, no self-consistent model of a pulsar magnetosphere can be constructed. The reason for this, and the real global structure of the magnetosphere is not clear, however. It has been pointed out that the difficulty may be removed by introducing a circulating flow instead of a steady outflow (J ackson, 1976; Mestel et al., 1979). We intend to solve two main problems to keep the circulation model alive. The problems are (1) the reason for the transfield flow, and (2) the way that the electromagnetic field and the plasma behave in the region of the trans-field flow.

2. Appearance of the Trans-Field Flow in the Pulsar Magnetosphere

The slowdown of pulsar rotation suggests that a poloidal current circuit is produced in the magnetosphere. This corresponds to the auroral circuit I in planetary magnetospheres (Alfven, 1977). The total current I is determined by the total resistance of the circuit, so that within local theory I should always be a free parameter, and will be determined as a part of the solution when we determine an overall structure of the magnetosphere. From the ouput power of pulsars we may estimate I to be rxR'6Q6Bo/ c, where rx is a numerical factor of about unity, and Ro, 0.0' Bo and c are the stellar radius, the angular velocity of the star, the strength of the magnetic field at the poles, and the velocity of light, respectively (Sturrock, 1971).

When the Lorentz factor y of the flowing particles is sufficiently less than a critical value Ye (typically 107 ), the inertial force is relatively so small that the plasma flows nearly along the magnetic field lines and Ell ~ O. In this situation we can adopt the 'quasi-force-free approximation', in which the small inertial term is included only in the energy and angular momentum conservation laws (Mestel et al., 1979). By using a

* Paper presented at the lAO Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984.

Astrophysics and Space Science 119 (1986) \05-\07. © 1986 by D. Reidel Publishing Company

106

2.00

1050

z 1000

0.50

O. O.

S. SHIBATA

GAMMA BETA PS-I J MX

0.50

0.200E-03 O.IOOE-03 0.160E+01

1.00 1050 2000

Fig. I. The contours represent the Lorentz factor of the field-aligned flow. Trans-field flow appears beyond the dashed thick curve on which y diverges. We assume Y. = 1.6 and 0.oRo/c = 2 x 10- 4 •

guessed current density with CI. - 1 and this approximation, we find a divergence of y well within the light cylinder. An example of such a solution is shown in Figure 1. The reason of the divergence is as follows. The condition Ell ~ 0 determines the local charge density (i.e., the Goldreich-lulian density I1G-J)' In a charge separated plasma the charge density is linked to the particle density. Therefore, the condition Ell ~ 0 controls the flow velocity through the mass conservation law with suitable boundary conditions (including those for the current density). As a result, if the magnetic field parallel to the rotational axis B z' which is proportional to the compelled charge density I1G-J, decreases sufficiently along the magnetic field lines, y becomes large enough to allow trans-field flow. Though we assumed the magnetic field to be a dipole one here, if the modification due to the toroidal current is incorporated, the region of the trans-field flow will extend more.

PULSAR MAGNETOSPHERE 107

3. A Self-Consistent Behaviour of the Trans-Field Flow and the Electromagnetic Field

The next problem is what happens in the trans-field flow. A numerical model by Shibata and Kaburaki (1985) and Shibata (1985) suggests some important properties of the trans-field flow, though their parameters are not those of pulsars (i.e., relativistic) but non-relativistic ones. According to their model in the region where the plasma particles with large inertia can flow across the magnetic field lines, the current circuit is closed and the charge separation, which keeps Ell ~ 0 in the inner region, is reduced. Such a trans-field flow makes the electric field become vacuum-like. These properties are quite essential for the trans-field flow, and will also appear in the pulsar magnetosphere. The effects of the modification of the magnetic field and relativistic inertia should be incorporated in a future work.

References

Alfven, H.: 1977, Rev. Geophys. Space Phys. 15, 271. Jackson, E. A.: 1976, Astrophys. J. 206, 831. Mestel, L., Phillips, P., and Wang, Y.-M.: 1979, Monthly Notices Roy. Astron. Soc. 188,385. Shibata, S.: 1985, Astrophys. Space. Sci. 108, 337. Shibata, S. and Kaburaki, 0.: 1985, Astrophys. Space Sci. 108, 203. Sturrock, P. A.: 1971, Astrophys. J. 164,529.

ONE-ARMED OSCILLATIONS OF A NON-SELFGRA VIT ATING

POLYTROPIC DISK *

A TS UO T. OKAZAKI and SHOJI KATO

Department of Astronomy, University of Kyoto, Sakyo-ku, Kyoto, Japan


Abstract. One-armed global oscillations in a non-selfgravitating polytropic disk rotating around a star are investigated. The unperturbed disk is axisymmetric, geometrically thin, and extends infinitely in the radial direction keeping its thickness constant. Perturbations considered are in viscid and adiabatic. It is found that there are one-armed retrograde wave modes which are trapped in an inner region of the disk. The eigenfrequency 01 of the lowest order mode is given by 1011 ;:5 0K(r.) (zoIYsf, where Ys is the radius of the central star, Zo is the half-thickness of the disk, and 0K(rs ) is the Keplerian angular frequency at the surface of the star.

Possible global oscillations in nons elf-gravitating, geometrically thin disks are onearmed ones alone (Kato, 1983). A prominent characteristic of the one-armed global oscillations is the slowness oftheir rotation around the disk center; the rotation is much slower than disk-rotation. Kato (1983) showed this by considering one-dimensional (radial) oscillations of a vertically integrated disk.

In this paper we show that in the case of disks with constant thickness, the above characteristic of one-armed waves is invariable under a rigorous two-dimensional treatment of oscillations. The unperturbed steady disk adopted is an axisymmetric, geometrically thin, nearly Keplerian one with polytropic gas. The disk extends infinitely in the radial direction keeping its thickness constant. Perturbations considered are inviscid and adiabatic and vary as exp [i( wt - (jJ)], where (jJ is the azimuthal angle in the disk plane. The ratio of specific heats y in the range of ~ to ~ is considered.

The linear perturbation equation obtained is a fourth-order partial differential equation; the vertical and the radial oscillations are coupled. When the half-thickness Zo of the disk is constant, however, this partial differential equation can be easily solved by separation of variables (Okazaki and Kato, 1985).

Figure 1 shows nondimensional eigenfrequencies w* 's of some modes of oscillation, as functions of y, in the case when zo/rs = 0.01. Here w* is defined by

w [y - 1 (ZO)2J QK(rJ = w* -2- rs

(1)

and is nearly independent of zo/rs. A label attached to each curve in Figure 1 represents the mode of oscillation; E(m, n) (or Oem, n) denotes the mode whose eigenfunction is



110

.. 0 3 I ~

01 2

-1 4/3

A. T. OKAZAKI AND S. KATO

E(O,1)

E(1,1)

3/2

Y 5/3

Fig.1. Nondimensiona1 eigenfrequencies O)*'s as functions of y. A label characterizing the mode is attached to each curve. The value of zolrs is assumed to be 10 - 2.

symmetric (or anti symmetric) with respect to the equatorial plane, and has m node(s) in the radial direction and n node( s) in the vertical direction. It is notable that one-armed waves retrograde (w < 0), and I w I decreases with increase of the node number in the radial direction.

Other mode characteristics for our present disk models are briefly summarized as follows. (Detailed results are given in Okazaki and Kato, 1985.) There is no oscillation mode which has no mode in the vertical direction, i.e., the lowest modes are the (0, 1) modes. The (0, 1) modes extend in the radial direction until r ~ (2-3)rs • Their wave amplitudes, which are taken to vanish at the disk surface (the boundary condition), increase with r, arrive at peaks at radii slightly inside their inner Lindblad resonances, and then evanesce outwards.

References

Kato, S.: 1983, Publ. Astron. Soc. Japan 35, 249. Okazaki, A. T. and Kato, S.: 1985, Publ. Astron. Soc. Japan 37, 683.

CO OBSERVATIONS, GEOMETRY, AND GALACTIC

STRUCTURE*

B.1. ROBINSON and R. N. MANCHESTER

Division of Radiophysics. CSIRO. Sydney. Australia

and

W. H. McCUTCHEON

University of British Columbia. Vancouver. Canada

(Received 2 July. 1985)

Abstract. 2.6 mm carbon monoxide and 21 cm hydrogen line observations of the Galaxy define six directions where gas is seen tangentially along a spiral feature and four directions where extended structures cross the R = Ro circle. These directions provide a geometrical framework for any spiral structure pattern. Also simple equations are derived to define the normalized radius Rj Ro of gas with a particular radial velocity in terms of the observed tangential velocity of gas with the same Rj Ro = sin ITo without specific knowledge of Ol(R), Olo or Ro.

Star formation is initiated in giant molecular clouds, which are readily detected by the 2.6 mm emission of the CO molecule. To trace star formation in the Galaxy, a well-sampled survey along the galactic plane from I = 294 a to 13 a was carried out with the 4 m telescope at Epping (Robinson et al., 1983). This survey has recently been extended from 1= 279 0 to 300 0 at b::::; - 0~75 (Robinson et al., 1984a). The observations have been complemented by a series of cuts in latitude (± lOin b) at 3 0 intervals in 1 from 279 0 to 357 0 (Manchester et al., 1983; Robinson et aI., 1984a). The southern CO data have been compared (Robinson et al., 1983, 1984b) with northern surveys of the galactic plane carried out at Columbia University (12 0 .::;; ,.::;; 60 0 ; Cohen et al., 1980) and the University of Massachusetts (358 0

'::;; I.::;; 86 0 ).

Along the terminal-velocity locus in the longitude-velocity plane there are major concentrations of CO emission which can be interpreted as directions where gas is seen tangentially along a spiral feature. These directions are I = 283 0 , 310 0 , 328 0 , 335 0 , 32 0 ,

and 54 0 (plus the well-defined 3 kpc expanding arm seen tangentially at 1 = 342 0 ). On the southern side of the Galaxy there are clear holes in the CO emission between the longitudes of the tangential points. H II regions are also clumped in these tangential directions.

When 2.6 mm CO and 21 cm H -line data are combined (Robinson et al., 1983, 1984a) a number of extended structures are seen which change the sign of their radial velocity at particular longitudes, indicating a crossing of the R = Ro circle (Ro being the distance



112 B. J. ROBINSON ET AL.

of the solar system from the galactic centre). These directions are near I = 282 ° , 327 ° , 11°, and 50°.

The six tangential directions (T) and four crossings (C) of R = Ro are schown in Figure 1. These directions provide a geometrical framework for any spiral structure pattern.

Much work on galactic structure over the last thirty years has been based on modelling of the galactic differential rotation to determine kinematic distances. With reference to Figure 2, V"' the radial velocity with respect to the Sun of gas in circular orbit at g, is given by van de Hulst et al. (1954):

Vg = Ro {w(R) - wo} sin I. (1)

Determination of R from Vg apparently requires a knowledge of w(R), wo, and Ro. This can be shown not to be so. Consider gas near the tangential point T at the same radius R; its radial velocity is (K wee et al., 1954)

(2)

where IT is the longitude of the tangent at radius R and is given by sin IT = RjRo. We can use this relationship and Equation (2) to eliminate Row(R) and Rowo from Equation (1). The simple result is

(RO)' sin I Vg = Vrnax - x sm 1= Vrnax x -.--. R smlT

(3)

This result applies for RjRo < 1 and for circular orbits.

Fig. I. Plan view of the galactic plane showing tangential points (T) and crossings of the R/Ro = I circle (C) derived from CO and H I observations. These points define a geometrical framework for spiral structure. Also sketched on the figure are spiral arms with pitch angle 12 0 ± 10 derived from the

observations. The dots in the vicinity of the solar system show the location of OB associations.

CO OBSERVATIONS, GEOMETRY, AND GALACTIC STRUCTURE 113

Fig. 2. Geometry of circular orbits in the galactic plane relating (by Equation (3» the radial velocity relative to the Sun of gas at g with the maximum radial velocity at the same radius R from the centre

(point T).

If the galactic rotation is flat beyond R = Ro with velocity Vo (e.g., Blitz et al., 1980), Equation (1) simplifies to

(4)

Equations (3) and (4) define the normalized radius RjRo of gas with observed velocity Vg in terms of the observed V max (for R < Ro) or Vo (for R > R o), without specific knowledge of w(R), wo, or Ro. The loci of constant Rj Ro can be plotted simply on the longitude-radial velocity plane (see Figure 2 in Robinson et al., 1983; or Robinson et al., 1984b).

The simple relations given by Equations (3) and (4) have been used in Figure 1 to outline a spiral pattern from CO and H I data. The pitch angle of the arms is 12 a ± 10. The pattern satisfies the constraints imposed by the CO latitude survey (Manchester et al., 1983), and by H I and 6 cm formaldehyde absorption measurements on H II

regions of known recombination line velocity. The pattern is similar to that derived from the velocities of H II regions by Georgelin and Georgelin (1976) and Downes et al. (1980).

References

Blitz, L., Fich, M., and Stark, A. A.: 1980, in B. H. Andrews (ed.), Interstellar Molecules, D. Reidel Pub!. Co., Dordrecht, Holland, p. 213.

Cohen, R. S., Cong, H., Dame, T. M., and Thaddeus, P.: 1980, Astrophys. J. 239, L53.

114 B. J. ROBINSON ET AL.

Downes, D., Wilson, T. L., Bieging, J., and Wink, J.: 1980, Astron. Astrophys. Suppl. Ser. 40, 379. Georgelin, Y. M. and Georgelin, Y. P.: 1976, Astron. Astrophys. 58, 189. Kwee, K. K., Muller, C A., and Westerhout, G.: 1954, Bull. Astron. Inst. Neth. 12, 211. Manchester, R. N., Whiteoak, J. B., Robinson, B. J., Otrupcek, R. E., and Rennie, C J.: 1983, in W. B. Burton

and F. P. Israel (eds.), Surveys of the Southern Galaxy, D. Reidel Pub!. Co., Dordrecht, Holland, p. 137. Robinson, B. J., McCutcheon, W. H., Manchester, R. N., and Whiteoak, J. B.: 1983, in W. B. Burton and

F. P. Israel (eds.), Surveys of the Southern Galaxy, D. Reidel Pub!. Co., Dordrecht, Holland, p. I. Robinson, B. J., Manchester, R. N., and McCutcheon, W. H.: 1984a, Poster version of present paper, IAU

Regional Meeting, Kyoto, October 1984. Robinson, B. J., Manchester, R. N., Whiteoak, J. B., Sanders, D. B., Scoville, N. Z., Clemens, D. P.,

McCutcheon, W. H., and Solomon, P. M.: 1984b, Astrophys. J. 283, L31. van de Hulst, H. C, Muller, C A., and Oort, J. H.: 1954, Bull. Astron. Inst. Neth. 12, 117.

HYDRODYNAMICAL MODELS OF THE ORION-KL NEBULA*

TORU OKUDA

Institute of Earth Science. Hakodate College. Hokkaido University of Education. Hachiman-cho. Hakodate. Japan

and

SATORU IKEUCHI**

Department of Physics. Hokkaido University. Sapporo. Japan


Abstract. The interaction between an isotropic protostellar wind and an ambient molecular cloud is investigated by two-dimensional hydrodynamic computations. The wind-cloud interaction model is promising for explanation of the observed properties of the Orion-KL Nebula.

1. Introduction

The recent radio and infrared observations of molecular clouds have revealed the existence of relatively large velocity fields, which are anisotropic in nature, in regions of active star formation within dense molecular clouds. A number of sources (AFGL490, AFGL961, H-H7-11, L 1551, NGC2071, CepA, and Orion nebula) have been shown to exhibit such characteristic phenomena (Bally and Lada, 1983). The Orion-KL Nebula is the best observed and studied molecular cloud among these sources. CO observations by Erickson et al. (1982) showed that this source has an extraordinarily high velocity with a bipolar nature.

Several shock wave models for such objects have been developed up to now. In these models it is assumed that a young star or protostar is ejecting material as a stellar wind which drives shock waves into the surrounding molecular cloud. The initially isotropic wind flow may be channelled into two antiparallel jet-like streams as a result of the interaction with the surrounding anisotropic molecular cloud. The shock wave models also try to explain the optical phenomena in Herbig-Haro (H-H) objects, and the infrared H2 emission in the vicinity of bipolar sources. However, as regards the Orion-KL Nebula, there remains so far an open problem on the formation of the H2 ennSSlon.

In this paper we investigate the global effects of the isotropic stellar wind on the surrounding molecular cloud, focussing on the bipolar flow and the H2 emission region of the Orion-KL Nebula. The analyses are made by two-dimensional hydrodynamical computations, including the recent results on H2 dissociation and radiative cooling by

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto. Japan, between 30 September-6 October, 1984. ** Present address: Tokyo Astronomical Observatory, University of Tokyo, Tokyo, Japan.

AstrophysiCS and Space Science 119 (1986) 115-121. © 1986 by D. Reidel Publishing Company

116 THE ORION-KL NEBULA

Lepp and Shull (1983). The effects of magnetic fields are not taken into account, although these may play an important role in 'smearing' the shock waves.

2. Method

2.1. MODELING OF THE ORION-KL NEBULA

We suppose an isotropic stellar wind from a central source within the Orion - KL region. The central source may be the infrared source IRc2. The stellar wind is assumed to blow out steadily from a boundary of radius r * . We consider an anisotropic density distribution for the surrounding molecular cloud, which is likely to be disk-shaped (Plambeck et al., 1982; Hasegawa et al., 1984).

In connection with the theoretical study of star formation, Hayashi et al. (1982) showed a certain class of equilibrium solutions for rotating axisymmetric isothermal clouds, which was also obtained independently by Toomre (1982). We use the cloud configurations of Hayashi et al. (1982), which is given, in spherical polar coordinates (r, 8, cp), by

po(r, 8) = 4pw (~y (sin 8)2(Y- 1)/[(1 + cos 8)Y + (1- cos 8)Y]Z, (1)

where the parameter y represents the flatness of equi-density contours, and re means the scale length of the cloud.

We adopt this expression together with a modified condition as

{ po(r, 8) at

Po =

Pw at

po(r, tJ) ~ Pco' (2)

po(r, 8) < Pro .

Defining the cloud mass Me to be the total mass in the region where po(r, 8) > Pw' we have

(3)

The disk diameter and the cloud mass around Orion-KL were estimated to be ~ 0.2 pc and 300 Mo by Hasegawa et al. (1984), respectively. We take the mass Me defined by Equation (3) to be 200 Mo. This gives the cloud size re ~ 0.18 pc, which corresponds to the diameter found by Hasagawa et al. (1984). The model parameters adopted here are listed in Table 1.

The initial conditions used at t = 0 correspond to static cloud conditions of pressure balance, the density Po, and the ambient temperature To = 20 K at r> r * with the boundary conditions of the wind velocity v*, the wind density p* = M/(4nr~v*), and the wind temperature T * = 50 K at r = r * . The initial density contours of the cloud are shown in Figure 1.

Case

A B

J "N

T. OKUDA AND S. IKEUCHI 117

TABLE I

Model parameters of stellar wind and molecular cloud

M v* Me noo y (Mo yr- 1) (km s - 1) (Mo) (cm - 3)

4.3 X 10- 3 100 200 2 X 105 3 3.0 X 10- 3 70 200 2 X 105 3

0.50 0.25 0.0 30.0

direction 7

0.0 10.0 20.0 30.0 r/r.

Fig. 1. Initial density contours ofthe cloud with 7 = 3. The plane with e = 90° means the equator of the cloud. Hatched part shows the region of constant density with Po = Poo •

2.2. NUMERICAL METHOD

We use the same spherical polar coordinates (r, e, cp) as before. The numerical scheme for the flow equations is based on the Lax-Wendrofftwo-step method (Okuda, 1983). We consider only H2 molecules as the dominant coolant, based on the recent detailed analyses of the dissociation and radiative cooling by H2 molecules over a wide range of densities and temperatures developed by Lepp and Shull (1983).

3. Numerical Results

For cases A and B, the mass loss rate of the wind from inner boundary r = r * (0.003 pc) increases linearly with increasing time untill it attains given mass loss rates in times of 370 and 260 yr, respectively. After that an isotropic stellar wind blows steadily into the static cloud. Since the resultant flow features for case B are qualitatively similar to


case A, except that the shocked temperatures in case B are rather lower than those in case A, we discuss here the results of case A.

The overall flow due to the stellar wind can be divided into four regions: (a) the supersonic un shocked stellar wind, (b) the shocked stellar wind, (c) the shocked ambient medium, and (d) the preshock ambient medium. The shocked gases (b) and (c)

0.5 0.25 30.0

10.0

10.0

log CS1/.f.o }

20.0

r / rlt

Case A

t : 1410yrs

~ -I

100 kms

30.0 4QO

Fig.2(a). Flow vectors and density contours of the wind flow and the cloud at t = 1410 yr for case A.

togT(K}

20.0

0.0 10.0

Case A

t: 1410 yrs

20.0 r /r.

40.0

Fig.2(b). Temperature contours of the shocked region at t = 1410 yr for case A. Hatched part denotes the region of the observed H2 emission peak I when the distance of the Orion-KL Nebula is taken to be 480 pc,

if the bipolar source is viewed nearly edge-on.


are divided by a contact discontinuity. In our calculation, the separations of the regions (a) and (b), and regions (c) and (d) are characterized as a rather high temperature jump behind the inward and outward facing shock fronts. However, the contact discontinuity between the regions (b) and (c) cannot be recognized clearly, because the medium is here smoothed by an artificially introduced diffusion term.

" ----/ /---""'-."::.=----.. T. .... -..... 2.0 -- -~ e. ...... \ I I 1--- \ , I I 1

~ I , I 1

l-I I I I

~ I I I I 01 I Te ~ 0 I I 01

I 0 1.0

1.0 '--_'__-'----"'=-t~'___'__-'-_L..-L---''--.L___'__'_~___' 0.0 0.0 10.0 20.0 30.0

Fig. 3(a). Temperature and density distribution in equatorial and polar directions at t = 1410 yr for case A, Subscripts e and p express the values in the equatorial and polar directions, respectively.

E oX

>

80

40

Ae -, .... " \ -- \

1 ~,_ I lip - , - ", .......... 1_- _,"" I

,;;--14'E

u lUI

~ ~

< -16

o ~0.-0~~~~~-'--~~~~~~-L~---'--~~-18 IQ.O 20.0 30.0

Fig.3(b). Radial velocity v and H2 emission rate A in the equatorial and polar directions at t = 1410 yr for case A.


The flow induced by the isotropic wind becomes apparently anisotropic at an early phase. The shape of the cloud is distorted only in the vicinity of the central region and particularly in the polar direction. However, the flow is nearly radial everywhere. This is because the shocked temperatures are rather low due to the considerable cooling by H2 molecules and the resultant pressure gradient force does not much affect the transverse momentum equation.

As a measure of the anisotropy of the flow, we compare the major (Rrnax) and minor (Rmin) flow radii which correspond to the polar and equatorial directions. Then we define a collimation factor asJc = Rrnax/Rmin, which is ~2.5 and 1.5 for t = 900 and 1410 yr, respectively. For the Orion-KL, the collimation factor/c is estimated to be ~ 1 from the map of the CO emission by Bally and Lada (1983). However, the H2 emission lobes (Beckwith et at., 1978), which extend far more distantly into the CO emission region, seem to exhibit a higher degree of anisotropy of the flow.

The numerical results for t = 1410 yr (Figures 2(a) and (b» would correspond to the present Orion-KL Nebula if the bipolar flow is viewed nearly edge-on. The shocked region is as high as 800 K ::s T::S 1400 K and elongates to the polar direction. Details of the shocked regions in the equatorial and polar directions are shown in Figures 3(a) and (b).

We expect a strong shock, that is, an abrupt deceleration of the flow in the vicinity of the inward shock, whereas the radial velocities vp and Ve are only gradually decelerated, as seen in Figure 3(b). This may be partly attributed to the effect of the artificial diffusion. Accordingly, the thermalization of wind energy near the inward shock may have been underestimated. However, the outward shock structure is thought to be well calculated, since we did not use any artificial diffusion there.

The temperature T - 1200-1500 K behind the outward and inward facing shocks are too low, compared with the postshock temperature Ts - 3.6 x 104(vs/30 km s - If K expected from the shock velocity Vs - 30-40 km s - 1. This is caused by considerable energy loss due to H2 molecules behind the shock front and by the coarse mesh size t'1r used here. Ifwe consider the dynamical time-scale td - t'1r/vs and cooling time-scale tc - ~ kT/(A/n) in the shocked region, we have td ~ tc for T:;::' 104 K and td :;::, tc for T - 500 K. This means that our time-dependent solution of the flow cannot resolve a sharp discontinuity with high postshock temperature Ts but show correctly the large scale features of the shocked region with T - 103 K.

4. Summary

(1) The shocked region due to the isotropic wind elongates to the polar direction of the cloud and develops up to the distance of the H2 emission peak 1 from IRc2 in a time-scale '" 1400 yr, if the bipolar source is viewed nearly edge-on. The characteristic features of the observed bipolar flow and H2 emission region seem to be well reproduced in the present model. The collimation factor of the bipolar flow becomes ~ 1.5, which is comparable to the observed value. The excitation temperatures of the H2 molecules in the Orion-KL region have been observationally estimated to be ~ 1000-3000 K.


Although the shocked temperatures obtained here are somewhat low compared with the excitation temperatures, the shocked region would correspond to the observed H2 emission region.

(2) The anisotropic flow produces high and low velocity outflows in the polar and equatorial directions of the cloud, respectively. However, a low velocity outflow with a typical expansion velocity ~ 18 km s - 1 within ~ 0.02 pc from IRc2 (Genzel et aI., 1981) is not well reproduced in the present model.

(3) From the numerical results, we interpret the peak emission and high velocity components of H2 line profiles are attributed to the shocked ambient gas (outer part of the shocked region), and the shocked wind gas (inner part of the shocked region), respectively. On the other hand, though we speculate that CO emission with broad velocity width in Orion - KL will be formed in the cold unshocked wind region, the extent of the unshocked region obtained here is insufficient to explain the observation of extended CO emission. In this respect, we will need a better set of model parameters of the stellar wind and the cloud.

References

Bally, J. and Lada, C. J.: 1983, Astrophys. J. 265, 824. Beckwith, S., Persson, S. E., Neugebauer, G., and Becklin, E. E.: 1978, Astrophys. J. 223,464. Erickson, N. R., Goldsmith, P. F., Snell, R. L., Berson, R. L., Huguenin, G. R., Ulich, B. L., and Lada, C. 1.:

1982, Astrophys. J. 261, Ll03. Genzel, R., Reid, M. J., Moran, J. M., and Downes, D.: 1981, Astrophys. J. 244, 884. Hasegawa, T., Kaifu, N., Inatani, J., Morimoto, M., Chikada, Y., Hirabayashi, H., Iwashita, H., Morita,

K., Tojo, A., and Akabane, K.: 1984, Astrophys. J. 283, 117. Hayashi, C., Narita, S., and Miyama, S. M.: 1982, Prog. Theor. Phys. 68, 1949. Lepp, S. and Shull, J. M.: 1983, Astrophys. J. 270, 578. Okuda, T.: 1983, Publ. Astron. Soc. Japan 35, 235. Plambeck, R. L., Wright, M. C. H., Welch, W. J., Bieging, J. H., Baud, B., Ho, P. T. P., and Vogel, S. N.:

1982, Astrophys. J. 259,617. Toomre, A.: 1982, Astrophys. J. 259, 535.

RADIO RECOMBINATION LINES OF HYDROGEN ATOMS

ASSOCIATED WITH STIMULATED EMISSIONS IN IONIZED

REGIONS*

MASAO SHINOHARA

College of Humanities and Sciences, Nihon University, Tokyo, Japan


In normal H II regions, the recombination lines of hydrogen atoms are produced mainly by spontaneous emission. However stimulated emission influences the radio recombination lines, because slight population inversion of atoms can make the self-absorption coefficients negative. Recombination lines can be produced by stimulated emission when an ionized region with negative self-absorption is in front of a strong continuum source. Shaver (1978) has shown that the observable extragalactic radio recombination lines can be produced mainly by this process.

Wadiak et al. (1983) have discussed the radio recombination lines produced by stimulation from radio quasars. They have presented calculations for ionized regions at electron temperatures ranging from 5 x 103 K to 2 X 104 K. However, the possibility that ionized regions surrounding strong continuum sources like quasars have electron temperatures higher than usual H II regions should be considered, because the exciting mechanism for these regions has not yet been established. In ionized regions at such high electron temperatures self-absorption and stimulated emission processes are not the same as in regions at lower electron temperatures.

In this paper, the maximum intensity ratio of stimulated radio recombination lines to the continuum in ionized regions at electron temperatures ranging from 104 K to 8 X 104 K are shown.

The equivalent width of a radio recombination line produced by stimulation is (Wadiak et al., 1983)

(1)

Assuming that the line widths are formed only by thermal Doppler broadening, the expected intensity ratios of line to continuum are given by

(2)

Doppler broadening and radiative damping widen the lines and reduce the ratios of



124 M. SHINOHARA

line to continuum. The ratios are also diminished by the level population being almost in LTE, which occurs at higher electron densities than 104 cm - 3, or when there is a saturating ratiation field regulating transitions among the high levels of atoms. The R factor is the maximum value of the ratio of line to continuum. Figure 1 shows the obtained R factors.

1

R

10- 1

10- 4

10-6

50 100 200

Fig. I. The ratio R of line to continuum. The electron density, the emission measure, and the velocity of internal motion are assumed to be 104 cm - 3, 108 cm - 6 pc, and 500 km(s - 1, respectively. The solid lines

signify emission lines, and the broken lines absorption lines.

Putting the filling factor at 10 - 3, the largest effective emission measure of the ionized regions is found to be 108 cm - 6 pc. With an emission measure at 108 cm - 6 pc, the velocity of internal motion at 500 km s - I, and the intensity of continuum radiation at 1 mJy, the maximum line intensities at 104 K are 20 mJy for H-100a and 44 mJY for H-240a, both in emission, while those at 4 x 104 K are 2.4 mJy for H-100a and 2.2 mJy for H-240a, are in absorption.

These values show the radio recombination lines produced by stimulation that is . barely observable if the continuum intensity is sufficiently large. However, the ratio may be smaller than the maximum value because of saturating radiation and high electron

RADIO RECOMBINATION LINES OF HYDROGEN ATOMS 125

densities. Churchwell and Shaver (1979) have reported a search for extragalactic radio recombination lines, including those from quasars, using the 305 m Arecibo telescope. They have detected no lines. The upper limit ofline strengths given by them are around 3 mJ y, and those of the ratios of line to continuum are on the order of 10 - 3.

References

Churchwell, E. and Shaver, P. A.: 1979, Astron Astrophys. 77,31. Osterbrock, D. E.: 1978, Phys. Scripta 17, 137. Shaver, P. A.: 1978, Astron Astrophys. 68,97. Shinohara, M.: 1984, Ann. Tokyo Astron. Obs. 2nd Series 19,4. Wadiak, EJ., Sarazin, C.L., and Brown, R. L.: 1983, Astrophys. J. Suppl. 53,351.

THE SCUTUM RING OF HII REGIONS*

TOSHIHIRO HANDA

Department of Astronomy. University of Tokyo. Tokyo. Japan

and

YOSHIAKI SOFUE

Nobeyama Radio Observatory (NRO**). Tokyo Astronomical Observatory. University of Tokyo. Nobeyama. Minamimaki. Nagano. Japan


Abstract. A ring of compact radio continuum sources was found at' = 24% b = O~O, which we call the Scutum ring. Radio continuum, H I line, and CO line observations are suggested that it is a star-forming region triggered by an expanding diffuse H II region.

1. Introduction

A ring of compact radio continuum sources centered at I = 24 ~ 6, b = ° ~ 0, about 30 I in diameter was found in the Nobeyama Radio Observatory (NRO) 10 GHz survey of the galactic plane region (Sofue et ai., 1984). A comparison with the observations at other frequencies indicates these compact sources (a few arc min in size) have flat spectra, indicating a thermal gas origin. Hereafter we call this ring as the Scutum ring.

2. The Distributions of Ionized Gas

The observation was carried out at 10, 5, and 2.7 GHz. The observation at 10 GHz was a part of the galactic plane survey, which has carried out at NRO with the 45 m telescope. The observations at 5 and 2.7 GHz were carried out with the 100 m telescope at the Max-Planck-Institut fUr Radioastronomie. Other details about the radio continuum observations were written by Handa et al. (1985). Figure 1 shows the radio continuum surface brightness distribution of the Scutum ring at 10 GHz.

The features are enveloped by a diffuse radio emission. The spectral-index distribution of this envelope derived from the 10, 5, and 2.7 GHz maps is about - 0.1, which suggests its thermal origin. The physical quantities of the diffuse component are shown in Table 1.

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** NRO, a branch of the Tokyo Astronomical Observatory, University of Tokyo, is a cosmic radio observing facility open for outside users.


128

+ 0 ~ 5

b 0: 0

- 0 ~ 5

25 ?0

T. HANDA AND Y. SOFUE

24 ~ 5

I 24 ?O

Fig. 1. The distribution of surface brightness of the Scutum ring. The unit of the numbers on the contours is 1.43 x 10- 21 W m- 2 Hz- 1 ster- 1.

TABLE I

Derived quantities for the extended component of the Scutum ring

Frequency (GHz) Total flux density (Jy) Spectral index for total flux density Brightness temperature at the center (K) Emission measure at the center (pc cm - 2) Electron ensity (cm - 3 )

Outer radius of the shell (pc) Inner radius of the shell (pc) Hn mass (Mo) Excitation parameter (pc cm - 2) Rate of Ly photons (photons s - 1 )

10.05 64 ± 8

0.0 ± 0.4 0.14 ± 0.01 6.4 x 103

8.0 71 22

2.9 x 105

198 4.3 x 1050

4.75 63 ± 12

0.65 ± 0.06 6.2 X 103

7.9

2.9 X 105

195 4.1 X 1050

A distance of9.1 kpc was assumed. We used an optically thin plasma model with a uniform temperature of 5000 K and uniform density.

The H 110a recombination line survey with the Bonn discrete 100 m telescope (Downes et aI., 1980) indicates that most of the sources are compact Hn regions, and are located at a 'tangential point' 9.1 kpc distance from the Sun. The velocity dispersion of the compact H II regions in the association is 7.3 km s - 1, which results in 106 M 0

for the virial mass of the Scutum ring.

THE SCUTUM RING OF Hn REGIONS 129

3. The Distribution of H I Gas and CO Clouds Around the Scutum Ring

An H I gas arc associated with the Scutum ring was found by the Maryland-Greenbank H I line survey (Westerhout and Wendlandt, 1982). Figure 2 shows the H I line brightness temperature distribution of the Scutum ring at 107.5 ± 1.0 km s - 1.

+ 0 ~ 5

b o ~ o

- 170 '--______ -'--______ --'

25 °1) 24 ~ O

Fig. 2. The distribution of H I line brightness temperature made from the Maryland-Greenbank survey. The velocity range is 107.5 ± 1.0 km s - 1 (V LSR)' The unit of the numbers on the contours is

2.0 K km S-I.

Some CO clouds associated with the ring were found in the Columbia CO line survey (Dame, 1984). In addition, and arc of CO emission associated with the Scutum ring was found by an observation with the Nagoya 4 m telescope (Handa et aI., 1985). The shapes of these arcs suggest that there is a shocked region around the Scutum ring.

130 T. HANDA AND Y. SOFUE

4. Conclusions

We conclude that the Scutum ring is a star-forming region triggered by an expanding diffuse H II region, which has been suggested as a model for sequential star-formation (Elmegreen and Lada, 1977). The Scutum ring may be in a later phase of a Rosette nebula-type structure.

References

Dame, T. M.: 1984, NASA Technical Paper, No. 2288. Downes, D., Wilson, T. L., Bieging, J., Wink, J.: 1980, Astron. Astrophys. Suppl. 40, 379. Elmegreen, B. G. and Lada, C. J.: 1977, Astrophys. J. 214,725. Handa, T., Sofue, Y., Reich, W., Furst, E., Suwa, I., and Fukui, Y.: 1985, Publ. Astron. Soc. Japan

(submitted ). Sofue, Y., Hirabayashi, H., Akabane, K., Inoue, M., Handa, T., and Nakai. N.: 1984. Pub!. ASll'On. Soc. Japan

36, 287. Westerhout, G. and Wendlandt, H.-U.: 1982, ASlron. ASlrophys. Suppl. 49, 143.

SURF ACE PHOTOMETRY OF SIMPLE H II REGIONS*

S. YOSHIDA, M. NAKANO, T. KOGURE, T. SASAKI, S. D. WIRAMIHARDJA**

Department of Astronomy. University of Kyoto, Japan

S. MIZUNO

Kanazawa Institute of Technology. Kanazawa. Japen

and

K. SAKKA

Kyoto School of Computer Science. Kyoto. Japan


Abstract. We have carried out surface photometry of six simple H II regions which are characterized by the existence of an exciting star earlier than BO, and a nearly round shape. On the basis of on calibrated image data and adopting a spherical model, we derive the distributions of gas and dust densities in the H II regions.

1. Introduction

H II regions are among the young objects in the Galaxy. Their internal structure may give some information bearing on the dynamics of gas before and after the formation of their exciting stars.

To investigate such internal structure, we have selected H II regions from the Sharpless Catalogue (Sharpless, 1959) with the following two criteria: (1) the nebula is excited by a star of spectral type 09.5-BO.5, (2) the apparent shape is nearly round. About ten H II regions were selected by these criteria, and we call them 'simple H II regions'. We have carried out photographic surface photometry of six of them (S237, S254, S255, S257, S259, S297). The photographic plates were taken in two wavelength bands, one has a passband of 225 A centered on HCl (E-band), and the other is the standard V-band.

From these calibrated maps of the surface brightness, we have derived internal distributions of the ionized gas and dust particles. Since the brightness in the V-band is almost entirely attributable to the continuum light of the central star scattered by dust grains in H II regions, we can derive the distributions of dust grains by solving the appropriate integral equations iteratively. Then we can correct for the internal extinction, and derive the density distributions of ionized gas from the HCl brightness maps.

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** On leave from the Bosscha Observatory, Institute of Technology Bandung, Indonesia.


132 S. YOSHIDA ET AL.

2. Observations and Image Processing

The photographic observations have been made with the 105/150/330 cm Schmidt telescope at the Kiso Observatory. The plate-filter combinations are 103aE + RG645 for the E-band, and HaD + GG495 for the V-band.

The calibration of these plates was made with the image processing system developed by Mizuno (1982).

3. Model Calculations

We have calculated the internal ionized gas and dust density distributions from surface photometric data under the following assumptions : (1) spherical symmetry; (2) isothermal structure with Te = 8000 K, and small optical thickness for the Hex-line; (3) dust grains which are composed of graphite core-ice mantle (core radius 400 A and

en I X X

:::E u

(f) z w 0

U1 cc L)

100 . 0~~~~~~~~~~~~~~~~

80 . 0

60 . 0

40 . 0

20 . 0 5254 --- -- -- --3 . 0

r D c:

-- ---4 . 0 5."

Fig. I(a). The distributions of ionized gas of S254 and S297 are plotted as a function of distance from the center.

10 . 0 I I I I

(1")

I 8 . 0 x X

:::E U 6 . 0

U1 z 4 . 0 lJ...J 0

I- 2 . 0 U1 :=l 0

Fig. l(b). Same as Figure I(a), but for the distributions of dust grains.

SURFACE PHOTOMETRY OF SIMPLE Hn REGIONS 133

mantle radius 1750 A); (4) uniform foreground extinction. We have treated only the single scattering case.

On the basis of these assumptions, we have formulated the relation between the internal density distribution and the observed radial distribution of surface brightness as integral equations. These equations have been solved by an iteration method. A part of the results is shown in Figure 1.

From these results, we can notice the presence of dust depletion zones at the centres in all of the observed simple H II regions. The gas-to-dust mass ratios are two orders of magnitude higher than the usual value of 100 except for the case of S292, for which the effect of the dust lane crossing its surface is severe. IR observations of some compact HII regions (e.g., Aitken etal., 1977) suggest high gas-to-dust mass ratios in these objects as well.

Furthermore, the larger the radius of the central dust depletion zone is, the flatter the gradients of the radial distribution of ionized gas density become. Welter (1980) made numerical calculations of the evolutions of spherical H II regions under the condition of enhanced central density. His results show that the gas distributions become flatter as the nebulae become older. If these results are applicable to our results, then it may be that the central dust depletion zones in the H II regions get larger with their evolution. The mechanisms of this growth of central dust depletion zones in the course of nebular evolution should be a subject of future works.

Acknowledgements

The authors wish to express their hearty thanks to the staff members of the Kiso Observatory for giving us the opportunity to carry out the discussed observations. The data processing has been carried out with the aid of the IBM 3031, PANAFACOM U-400, and SMP 80/50 computers at the Kanazawa Institute of Technology, and the F ACOM M382 at the Data Processing Center of the Kyoto University, and the VAX-l 1/750 at the Kwasan Observatory.

References

Aitken, D. K., Griffiths, J., and Jones, B.: 1977,Monthly Notices Roy. Astron. Soc. 179, 179. Mizuno, S.: 1982,Astrophys. Space Sci. 87, 12l. Sharpless, S.: I 959,Astrophys. f. Suppl. 4,257. Welter, G. L.: 1980, Astrophys. f. 240,514.

INFRARED POLARIMETRY OF THE STARS IN THE INNER

GALAXY*

Y. KOBAYASHI, 1. JUGAKU

Tokyo Astronomical Observatory, Japan

H.OKUDA

Institute for Space and Astronautical Science, Japan

and

S. SATO,mdT.NAGATA

Kyoto University, Japan


Near-infrared photometric and polarimetric observations were made for stars embedded in the galactic plane. The sources were picked up from two selected regions in the galactic plane (l = 20 0 and 30 0 ). In total, 59 sources were observed, 35 of which were observed with polarimetry in the K-band (2.2 )..lm) and 44 were observed with photometry by the near-infrared broad band system. The observations were made by using the 2.2 m telescope of the University of Hawaii on Mauna Kea. The polarizations have been determined from observations made by a polarimeter with a rotating half-wave retarder. The instrumental polarization is always less than 0.05 %, much smaller than the detected polarizations.

The observed results are presented for galactic longitudes of 0 0 , 20 0 , and 30 0 • The results for longitude 0° are reproduced from Kobayashi et al. (1983), but we exclude two intrinsically peculiar stars, GCS-3 and 4. The degrees and position angles of polarization are shown in Figure 1 (a -c). The polarization vectors are distributed nearly parallel to the galactic plane, although a higher dispersion in the distribution of position angle of the polarization vectors is seen in the direction of 1 = 30 0 •

The polarizations are well correlated with the H-K index; the degree of polarization increases with H-K (Figure 2(a-c». The coefficient of proportionality is dependent on the longitude; the largest is in the direction to the galactic center and it decreases with the longitude.

Position angles of the polarization are confined in a relatively small range nearly parallel to the direction of the plane. However, there is some systematic variation with H-K in the direction of 1= 0 0 , and a large dispersion is seen in the direction 1= 30 0 •

In this region, the polarization directions are concentrated in two groups around position angles 30 0 and - 20 0 direction are displayed in Figure 2( c) as filled circles.

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, between 30 September-6 October, 1984.


136 Y. KOBAYASHI ET AL.

-28 30',--,-,,---,--,---,--,--,--~

L= 0 40

CSI 50 lf1 en

o

10

20

30 1 7H44 M

1%

I

L=20 25

26 CSI lf1 27 en

28 U LJ 29 Q

30

31

32 18H20M155

42 40 R. R. (1950)

Fig.la.

8 0 52 44 R.R. (1950)

Fig. lb.

Fig. l(a-c). The observed stars are plotted with circles for the position, and bars for the amplitude and direction of the polarization. For longitude 30 0 , the filled circles show that they belong to the - 20 0

direction.

STARS IN THE INNER GALAXY 137

1=30 36

37 1%

~ IS)

lJl 38 m

38 ~ u ISl 0 w 40 q

0 ¢ 4 1

0

42

43 18H43M48S 40 32 24 16

R.R. (1950)

Fig. Ie.

They have a comparatively small polarization efficiency, suggesting that they are in a region of different magnetic field direction and correspond to a superposition of additional polarization vectors. However, supposing that the magnetic field is aligned along the spiral structure, we are looking tangentially to a dense region, such as the 5 kpc

8 I 1= 0

/ 7

t t~j 6 /

5 P(%)

4 r ~ 3 r / -

2 I- ~+ t -/

I- +# -

0 -;

0 2 3 4

H-K

Fig.2a.

138

B

?

S

p(%)5

4

3

2

o o

B

?

6

p(%)5

4

3

2

o o

Y. KOBAYASHI ET AL.

1=20

1=30

+

2 H-K

Fig. 2b.

2

H-K

Fig.2c.

3

~

3 4

Fig.2(a-b). The observed polarization amplitude vs [H-K]. Dotted lines show the ratio of Pk (%) to E(H-K) derived from the observations at longitude 0°. The calculated polarization amplitude against [H-K] are also displayed. Solid bars on the calculated curve indicate the distances from the Earth in steps

of 5 kpc.

STARS IN THE INNER GALAXY 139

ring, in the longitude 30°. So the projected difference in the polarization directions may be much larger than that of the magnetic fields.

The fact that the observed polarizations are fairly regular and nearly parallel to the galactic plane favours the view that they are of interstellar origin, although somewhat contaminated by some intrinsic polarization of the source.

A model calculation has been made to fit the observations. The assumptions adopted in the calculations are as follows:

(1) The magnetic field is concentric around the galactic center. (2) The polarizing efficiency depends on the function of P K sin ejA K' where e is the

angle between the magnetic line of force and the line-of-sight. (3) The interstellar extinction is estimated from the gas distribution inferred from CO

and H I observations (Tipei et al., 1983; Bohlin et al., 1978). The results are shown in Figures 2(a) and 2(b). The overall behaviour is well fitted. Although the observations are rather limited and the data analysis is simple, the

following conclusions could be made: (1) The observed polarization amplitudes correlate with the amount of extinction,

and the polarization direction shows systematic structures. Therefore, the observed polarization is preferentially of interstellar origin.

(2) The observations reach to the inner region of the Galaxy. The longitude dependency of the polarization efficiency shows that the magnetic field configuration is similar to that in the solar vicinity, i.e., it is running circularly in the galactic plane.

(3) Infrared polarization measurements are useful to probe the global structure of the magnetic field in the inner galaxy.

References

Bohlin, B. c., Savage, B. D., and Drake, J. F.: 1978, Astrophys. J. 224. 132. Kobayashi, Y., Okuda, H., Sato, S., Jugaku, J., and Dyck, H. M.: 1983, Pub/. Astron. Soc. Japan 35, 101. Tipei, Li, Riley, R. A., and Wolfendale, A. W.: 1983, Monthly Notices Roy. Astron. Soc. 203, 87.

EFFECT OF MAGNETIC FIELD ON A SHOCK-INDUCED THERMAL

INSTABILITY*

SEUNG SOO HONG

Dept. of Astronomy. Seoul National University. Korea and Space Astronomy Laboratory. University of Florida. U.S.A.

and

BON CHUL KOO

National Astronomical Observatory. and Dept. of Astronomy. Seoul National University. Korea


Abstract. The effect of a magnetic field on a thermal instability has been studied in a radiatively cooling region behind an interstellar shock of moderate propagation velocity ( ~ 10 km s - 1). It is shown that the presence of a magnetic field of a few microgauss is very effective in preventing the thermal instability from building-up density concentrations. In the absence of the magnetic field, the shock-induced thermal instability will amplify a pre-shock density inhomogeneity by more than an order of magnitude. However, in the field's presence, the amplified density contrast is shown to be only a factor 2. Implications for the 'trace of a sweeping broom' in the Pleiades nebula are discussed.

We extend the hydrodynamic formulation by McCray et al. (1975) to the hydromagnetic case in order to examine how effectively a thermal instability can amplify pre-shock density inhomogeneities, in the presence of a magnetic field. Noting the presence of multi-layered features, such as the 'trace of a sweeping broom' in the Pleiades nebula, we apply our hydromagnetic formulation to a shock of 10 km s - 1 propagating through an H I cloud whose initial density is 10 cm - 3.

The structure of a one-dimensional, steady state shock has been computed, following the scheme ofField et al. (1968). For the cooling rate per unit volume A (erg cm - 3 S - 1), we considered only the fine structure transitions of C + , 0, Si + , and Fe + (Aannestad, 1973), so that the cooling rate can be written as A = n 2C(T), where n denotes the hydrogen number density and the cooling function C(T) describes the temperature dependence of the cooling rate.

Our calculations show that: (1) A moderate magnetic field ( ~ 3 x 10 - 6 G) could curtail drastically the develop

ment of thermal instability. It is found that under the pre-shock conditions of density fluctuations of wavelength 0.1 pc and the fractional density contrast of 20 %, the linear scale of inhomogeneity decreases to 0.03 pc, after the passage of the shock which enhances the density contrast by a factor of 2.

(2) In the long wavelength limit, the instability occurs when S = (d log C(T)/d log T), the logarithmic slope of the cooling function, becomes 0.60, 0.49, and 0.44, with



142 SEUNG SOO HONG AND BON CHUL KOO

increasing magnetic field 1, 2, and 3 x 10 - 6 G, respectively. These criteria are found to be weaker than those for an initially homogeneous and static medium in thermal equilibrium, suggesting that a system which is cooling in an unperturbed state is more unstable than one in thermal equilibrium. This is in agreement with Field's (1965) result.

A typical width of filaments in the Pleiades reflection nebula is about 0.005 pc (Allen, 1973; Amy, 1977). Federman (1982), and others, reported some evidence indicating that they may be associated with a moderately strong shock of ~ 10 km s - 1. In order to produce such filamentary structures from a thermal instability, in the presence of a magnetic field, the scale of the density fluctuation is required to be about 0.03 pc. For such a short scale fluctuation, the resulting density contrast is expected to be less than a factor of 2. Therefore, we may conclude that if an interstellar shock propagates perpendicularly to the direction of the magnetic field, it is not likely to form the 'trace of a sweeping broom', as seen in the Pleiades, from such a thermal instability. However, if the shock propagates parallel to the magnetic field, the thermal instability could produce such multi-layered structures. Unfortunately, we are not in a position to fully assess these results, since we do not have sufficient information on reflection nebulae which have filamentary structures.

As pointed out earlier, our study has been based on an assumption that the cooling rate is proportional to the square of the density. Obviously, molecular hydrogen could change the density-dependence of the cooling rate A. Careful studies of the interstellar cooling rate, including the contribution by dust, would undoubtedly improve our understanding of the observed filamentary structures in the interstellar medium.

Acknowledgements

This work was partially supported by the Ministry of Education through the Research Institute for Basic Sciences, Seoul National University.

References

Aannestad, P. A.: 1973, Astrophys. J. Suppl. 25,223. Allen, C. W.: 1973, Astrophysical Quantities, 3rd ed., Athlone Press, London. Arny, T.: 1977, Astrophys. J. 217, 83. Federman, S. R: 1982, Astrophys. J. 253,601. Field, G. B.: 1965, Astrophys. J. 142,531. Field, G. B., Rather, J. D. G., Aannestad, P. A., and Orszag, S. A.: 1968, Astrophys. J. 151, 953. McCray, R, Stein, R F., and Kafatos, M.: 1975, Astrophys. J. 196, 565.

ON THE RADIAL DISTRIBUTIONS OF MOLECULAR CLOUDS

IN GALAXIES*

MASATAKA FUKUNAGA

Astronomical Institute, Tohoku University, Sendai, Japan


Abstract. The dynamics of the interstellar gas (the IS gas) driven by the viscous torque of a system of giant molecular clouds (the Me gas) is considered with the infinitesimally thin disk layer approximation. The flow explains the radial distributions of molecules observed in galaxies.

We consider the fluid dynamics of interstellar (I S) gas which is dominated by the viscous molecular cloud (Me) gas. The model for the IS gas is the same as that in previous papers (Fukunaga, 1983, 1984a; hereafter referred to as Papers I and II, respectively) except that the gas layer is taken to be thin in this paper. The basic model is as follows: (i) The layer of IS gas is infinitesimally thin. (ii) Since H2 is very abundant compared with other constituents of IS gas (mainly HI) within the optical disks of galaxies, its dynamics will be dominated by the MC gas. (iii) The viscous torque ofMC gas acts not only on the MC gas itself; but also on the H I through a possible mass transfer effect. (iv) Redistribution of IS gas does not change the gravitational field. (v) The surface density of H I is constant where MC gas is present.

The velocity dispersion of random motion ofMC gas is estimated by the assumption that viscous heating and cooling due to inelastic direct collisions balance, so that the MC gas is in a steady state, with a finite velocity dispersion (Fukunaga, 1984b). The velocity dispersion of MC gas is, then, a function of the galactic rotation, the mass-tosize ratio of the clouds, and the surface density. We use the kinematic data of Liszt and Burton (1983) for the molecular ring of our Galaxy to obtain numerical values of these parameters.

The kinematic viscosity coefficient v is given by

(J2 fifo v = - ----=--

2fo 1 + (flfo)2

where (Jis the r.m.s. velocity dispersion of random motion ofMC gas, fo is a frequency, of the order of the epicyclic frequency, and f is the sum of the inverse of the relaxation time for gravitational encounters and the frequency of direct collisions in the infinitesimally thin MC gas.

Figures 1 and 2 show evolution patterns for the surface density of M C gas in galaxies with typical rotation curves. These figures show that the Me gas forms ring-like peaks



144 M.FUKUNAGA

10.0 20.0

R CKPCl (a)

300.0 r-~----~----~r-----~-------,

0.0 ~0~.0n-----~----~1~0~.~0------------~20' .0

R (KPCl (b)

Fig. I. The radial flow of viscous MC gas in a galaxy with a double peaked rotating curve. The time variation of the surface density of MC gas is plotted in units of the column density of hydrogen nuclei NH (panel a), in the case where the rotation curve is similar to that of our Galaxy (panel b). The time interval

between each curve is 3 X 109 yr. The initial surface density is constant in radius r < 9 kpc.

at the transition region of rotation, where the galactic rotation changes from the inner rigid one to the outer differential one (see also Papers I and II). Outward from the peaks an exponential decline appears for a long distance, as is shown by the semi-log plots in Figure 2 (see also Paper II).

This characteristic behaviour of viscous MC gas explains the radial distributions of molecules in galaxies, if the H2 molecule is predominantly included in giant molecular clouds. The density distribution ofMC gas in the galaxy with a double peaked rotation curve shown in Figure 1 coincides with the distribution of molecules in our Galaxy, both qualitatively and quantatively (Burton and Gordon, 1978; Sanders et al., 1984). The

MOLECULAR CLOUDS IN GALAXIES 145

,.. (\j ~ • L

<.J "-(\j W v

1. 1'1

~

e.l~e~.e~~--~--~~~1~e~.~e~--~U-~----J2e.e

R CKPC)

(a)

3ee.e r-------~------~--------r_------,

e . e~e~.e~------------~1~e~.~e------------~2·e.e

R (KPC) (b)

Fig. 2. The radial flow of viscous MC gas in a galaxy with a flat rotation curve. The time variation of the surface density of MC gas is plotted with a semi-log scale (panel a), in the case where the rotation curve is flat with a small rigidly rotating central part (panel b). The time interval is the same as in Figure I. The

initial surface density is constant in radius for r < 7 kpc.

exponential distribution in Figure 2 reproduces well the distribution of molecules observed in M51, MI01, etc. (Scoville and Young, 1983; Solomon etai., 1983).

References

Burton, W. D. and Gordon, M. A.: 1978, Astron. Astrophys. 63, 7. Fukunaga, M.: 1983, Publ. Astron. Soc. Japan 35, 173. Fukunaga, M.: 1984a, Publ. Astron. Soc. Japan 36, 417. Fukunaga, M.: 1984b, Publ. Astron. Soc. Japan 36, 433.

146 M.FUKUNAGA

Liszt, H. S. and Burton, W. B.: 1983, in W. L. H. Shutter (ed.), 'Kinematics, Dynamics, and Structure of the Milky Way', Astrophysics and Space Science Library, Vol. 100, p. 135.

Sanders, D. B., Solomon, P. M., and Scoville, N. Z.: 1984, Astrophys. J. 276, 182. Scoville, N. and Yoyung, J. S.: 1983, Astrophys. J. 265, 148. Solomon, P. M., Barrett, J., Sanders, D. B., and de Zafra, R.: 1983, Astrophys. J. 266, Ll03.

GRAIN FORMATION EXPERIMENTS BY A PLASMA JET

APPARATUS*

T. TANABE, F. KAMIJO, and T. ONAKA

Department of Astronomy. Faculty of Science. University of Tokyo. Bunkyo-ku. Tokyo. Japan

A. SAKATA

Laboratory of Applied Science, University of Electro-Communications, Chofu, Tokyo, Japan

and

S. WADA

Laboratory of Chemistry, University of Electro-Communications, Chofu, Tokyo, Japan


There have been many absorption/emission band features discovered in the spectra of certain astronomical objects, which are considered to originate from dust grains in space. However, chemical components and/or chemical structures of the dust grains are not well known, and these pose some very significant problems in present-day astrophysics. Several condensation calculations have been performed, based on the assumption of thermodynamical equilibrium, but the grains expected from such calculations do not represent the characteristic features observed in the spectra of interstellar or circumstellar dust. In order to identify these band features within our present knowledge, it is quite necessary to perform experimental investigations. Some condensation experiments have been carried out, and had some success already.

However, these experiments have two serious drawbacks. First, they usually employed the so-called gas-evaporation method, which cannot generate atomized gases because of its low evaporation power. Such experiments probably simulate the condensation processes from molecular gases. Therefore, these may not be appropriate for the investigation of condensation in space. The atomization of the starting gases must be realized. Second, the experiments performed so far are distinctly separated into two groups; one is condensation of carbon systems, and the other of silicon-oxygen systems. However, in order to investigate condensation processes in space, it is important to study it with a mixture of all components.

We carried out grian formation experiments by a newly-developed plasma jet apparatus. Figure 1 shows the schematic diagram of the apparatus. The torch is operated with argon as the working gas, with a flow rate of about 3 I min - 1. Reactant gas is mixed with the argon on the way to the torch, the flow rate being about 0.01 g min - 1. The torch head provides an arc jet of argon plasma and its temperature



148

VACUUM CHAM BER 200 torr Ar

SUBSTRATES

T. TANABE ET AL.

QUARTZ TUBE

WORKING GAS SUPPLY SYSTEM

REACTANT GAS SUPPLY SYSTEM

THERMOCOUPLES

Fig. I. Schematic diagram of the plasma jet apparatus.

reaches 1 x 104 K. This high energy enables us to realize the atomization of starting gases, and we use mixtures of H, C, 0, and Si atoms, which are considered to be of high importance in grain forming regions. The plasma jet is injected into a reactor vacuum chamber filled with 200 Torr Ar gas, where it becomes rapidly quenched, and forms solid particles.

The duration of one experiment was typically half an hour. The synthesized particles were deposited on the inner surface of a collection quartz tube, and on the substrate placed at the end of the tube. An optical fiber lead the emission of the plasma to a UV-visual monochromater, which showed no molecular lines and was considered to indicate that the atomization was realized, as desired. Assuming a Boltzmann distribution between level populations in the plasma flame, we estimated the temperature near the nozzle by means of the relative intensities of Ar I lines. The temperatures obtained in this way were almost the same for all experiments done so far, being about 8000 K. Electron microscopy analyses showed the synthesized grains to have rather irregular shapes, with diameters smaller than 100 nm. Electron diffraction patterns indicated that the grains were amorphous.

The absorption spectra of the synthesized grains, from various reactant gases, showed nearly the same character in the UV -visual regions, but in the infrared region there appeared a variety offeatures in each condensate. The grains synthesized from methane as reactant gas had only the broad 3.4 )lm absorption band. Only silicon grains were condensed from silane as reactant gas. From initial gases containing H, C, 0, and Si atoms, we obtained grains which showed broad absorption bands at 2.9,3.4,9.5, 11.5, and 21 )lm. We tentatively assign the 2.9 )lm feature to O-H bonds, the 3.4 )lm one to

GRAIN FORMATION EXPERIMENTS 149

C-H bonds, and the 11.5)lm one to Si-C bonds. The 9.5 and 21 )lm features are probably due to Si-O bonds. From these preliminary results, it can be concluded that grains synthesized by quenching from gases consisting ofH, C, 0, and Si atoms contain both Si-O and Si-C bonds, irrespective of the relative abundances, when the ratio of oxygen to carbon atoms is less than or equal to unity. These results are rather distinct from those of condensation calculations, which indicate that the chemical components of condensates depend strongly on the C/O abundance ratio.

HYDROST ATIC MODELS OF BOK GLOBULES*

TATSUHlKO HASEGAWA

Astronomical Institute. Tohoku University. Sendai. Japan


Abstract. Hydrostatic models of small, isolated dark clouds are presented. A dynamical, thermal, and chemical equilibrium is considered in these models.

We have constructed spherical, hydrostatic models of isolated, low-mass Bok globules assuming that the globules are supported by thermal and turbulent pressures. In these models, the density, gas temperature, and molecular abundances are determined by solving simultaneously the equations of dynamical, thermal, and chemical equilibrium.

MODEL 4

20

'l 25 0>(:

/f/s 15

/;-20 01

}-I

L U

01

0 15 y::

10 I-

Z 0 10

T 5

5

0 0 00 0010 0020 0.30 0.40

R(PC)

Fig. I. Gas temperature T (K) and hydrogen nucleon number density nH (cm- 3 ) in model 4.


Astrophysics and Space Science 119 (1986) 151-154. © 1.986 by D. Reidel Publishing Company

152 T. HASEGAWA

Ay{mcgl

9.2 7:6 5.9 4.4 3.1 2.0 1.2 0.6

100 Model 4 80 Me

40

~ Tg

~ 20

",. 10

'" 'w § ·25

.i <:

~

-"-·26

0.4

r (pC)

Fig. 2. Heating rates (dashed curves) and cooling rates (solid curves) in model 4. 'dpe' means photoelectric heating from dust, and 'd' means dust cooling. 'CR' means cosmic-ray heating. Other notations will be

self-explanatory. Gas temperature Tg (K) and dust temperature Td (K) are also shown.

We present four calculated model clouds and compare the column densities of many molecular species in these models with those observed in the globules B335, Ll34, and L183. The parameter values assumed, and the representative physical quantities

TABLE I

Assumed parameters and representative physical quantities

Model No. 2 3 4

Parameters

Mass (M0) 20 80 20 80 Internal turbulent velocity (km s - 1 ) 0044 0.74 0.74 1.23 External pressure Pjk (K cm - 3) 3.3 X 104 3.3 X 104 2.3 X 105 5.5 X 105

Physical quantites

Radius (pc) 0041 0.78 0.25 0.39 n(H2) at center (cm - 3) 3.5 X 103 2.0 X 103 9.7 X 103 9.5 X 103

Tga, at center (K) 9.0 704 6.6 5.3 Total visual extinction A, (mag.) 5.1 5.8 11.5 18.2

HYDROSTATIC MODELS OF BOK GLOBULES 153

TABLE II

Comparison of our models with the globule B335

Modell Model 3 B335

Mass (Mo) 20 20 22 Radius (pc) 0.41 0.25 ~0.2

Visual extinction (mag.) 5.09 11.48 >7.4 Column densities

log (N(cm- 2 » HI 20.25 20.10 CO 17.62 18.09 17.95 l3CO 16.0 CS 12.57 12.93 13.6, 12.6 OH 13.92 14.37 14.38

NH3 8.\0 12.33 14.81, 14.6 H2 CO 11.51 12.96 13.77 HCO+ 11.63 12.90 detected CH 14.69 14.63 < 15.3 HCN 14.24 14.75 SO 12.42 15.47 ~14

CN 15.05 15.52 13.08 OCS 9.56 12.58 <12.6 CI 16.54 16.69

Comparison of our models with the globules Ll34 and Ll83

Model 2 Model 4 Ll34 Ll83

Mass (Mo) 80 80 ;::50,65 70, 100 Radius (pc) 0.78 0.39 ~0.5 (Av 1 mag.) 0.7 Visual extinction (mag.) 5.84 18.28 >8 > 12 Column densities

log(N(cm-2» HI 20.45 20.26 ~ 19 > 18.8 CO 17.66 18.31 18.1 l3CO 16.0 > 16 CS 12.78 13.08 12.9 OH 14.07 14.78 14.7 NH3 8.47 13.45 undetected 15.5 H 2 CO 11.58 13.81 13.6 13.3 ~ 14.3 HCO+ 11.80 13.54 13.3 CH 14.74 14.65 14.0 <13.7 HCN 14.30 14.79 SO 12.77 16.39 ~14 ~ 14.3 CN 15.11 15.57 <13.3 <13.6 OCS 9.83 13.57 <13.3 CI 16.63 16.72 > 16.5

154

x

Cl 0 ---.J

o

-5

- 10

-15

-20 o.

8

H2O

H2S

NH.

6

T. HASEGAWA

MODEL 4(8) Av( MAG)

4 2

co

0.10 0.20

R(PC) 0.30

o

coz.HtGS

0.40

Fig. 3. Relative abundance of molecular species to hydrogen nucleon in model 4. Only 20 species of the 100 are shown. Near the cloud boundary, curves are neglected for those species with very low abundance.

obtained are given in Table I. Comparisons are made in Table II. In Figure 1, the gas temperature distribution and the density distribution in model 4 are shown. Figure 2 represents the cooling and the heating rates of all the processes considered in our model 4. Figure 3 represents the molecular abundance variation.

Fairly good agreement in the physical and chemical quantities can be seen in Table II, but the better agreement of models 2 and 4 needs very high external pressure (Table I). Thus, from our four models so far, invalidity of the hydrostatic assumption is suggested.

CEP A: A POSSIBLE PROTO-CLUSTER *

SAEKO S. HAYASHI

Department of Astronomy, University of Tokyo, Yayoi, Bunkyo, Tokyo, Japan

and

NORIO KAIFU and TETSUO HASEGAWA

Nobeyama Radio Observatory (NRO*), Tokyo Astronomical Observatory, University of Tokyo, Nobeyama, Minamimaki, Nagano, Japan


Abstract. We present high resolution CS and CO maps of Cep A region made with the 45 m telescope at Nobeyama. The CS map shows that a dense cloud surrounding the proto-star cluster extends in the North-South direction and is probably rotating. The bipolar molecular flow apparent in the CO maps is well-collimated along East-West direction within 0.2 pc from the proto-stars. The dense cloud is gravitationally unstable and appears to be in a contracting phase to form a cluster of massive stars.

1. Observations

Cep A is an active star forming region characterized by high velocity molecular flow, and embedded in the Cep OB3 association-molecular cloud complex (Sargent, 1977; Rodriguez et al., 1980). In the center of Cep A, there are several infrared sources and at least three ultra compact H II regions (hereafter referred to as IRS/UCHII). Two groups of strong H 20 masers are associated with the ultra compact H II regions.

We have made high resolution observations of Cep A by the CS (J = 1-0), C34S (J = 1-0), CS (J = 2-1), CO (J = 1-0), and 13CO (J = 1-0) lines, using the 45 m telescope at the Nobeyama Radio Observatory in 1983 and 1984. The half power beam width (HPBW) were 33" for CS (J = 1-0) lines, 17" for CS (J = 2-1) lines and 14" for CO lines. Eight sets of acousto-optical radio spectrometers (AOS) were used in parallel. At the distance of730 pc, the mapping area corresponds to about 0.7 x 0.6 pc for the CS (1-0) and 0.4 x 0.4 pc for the CO observations, respectively. About ten sets of spectral data of 13CO and CS (2-1) were taken, in order to estimate the physical properties of the molecular cloud.

2. Results and Discussion

Figure 1 represents the distributions of the integrated intensities of the CS (J = 1-0) emission (Figure l(a» and blue-shifted and red-shifted high velocity CO emission (Figure l(b)). The CS emission indicates a massive molecular cloud surrounding the

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** NRO, a branch of the Tokyo Astronomical Observatory, University of Tokyo, is a cosmic radio observing facility open for outside users.


156

u w o <J

S. S. HAYASHI ET AL.

Cep A CS 1-0

50" 0" -50 " t::,. R. A.

CO 1-0 red blue

50" 0" -50" t::,. R. A.

Fig. I(a). The distribution of CS (J = 1-0) intensity integrated over V(lsr) = - 18 km s - 1 and - 4 km s - 1. The average velocity in this region is - II km s - 1. The contour units are K* km s - 1.

Fig. I (b). The composite map of high velocity CO emission toward the center of Cep A. The thick contours are blue-shifted emission integrated over V(lsr) = - 31 km s - 1 and - 21 km s - 1. The dashed contours are red-shifted emission integrated over V(lsr) = - 1 km s - 1 and + 9 km s - 1. The emission from the reference

position is about 2.7 K* km s - 1 for this range.

central region. The cloud extends along the North-South direction and the emission is rather weak towards the IRS/UCHII. The CS emission, as a whole, suggests a systematic velocity gradient, which can be interpreted as a combination of rotation and contraction. Comparing the CS and C34S data with the local thermal equilibrium assumption, the optical depth and the excitation temperature of CS work out at about 8 and 10 K, respectively. The column density of CS around the IRS/UCHII is 3 x 1014 cm - 2, and the mass of the dense cloud is estimated to be 500-3000 Mo.

From the 50% contours of T1 (CS), the size of the dense molecular cloud core around the proto stars is 0.5 pc, and the average density is larger than 4 x 104 cm - 3.

Myers and Benson (1983) discussed the equilibrium and stability of a pressure-bounded isothermal sphere. If we adopt the values given above to compare with the results of Myers and Benson, we find the cloud to be gravitationally unstable, whether it is supported by thermal or turbulent pressure. The radial motion then has to be due to contraction.

The CO emission suggests that the high velocity flow in the vicinity of the protostars is nearly in the East-West direction. The blue-shifted emission is detected only toward the east, while the red-shifted emission is confined to the west. The optical depth of 13CO is 1 to 2.4. The kinetic temperature for the average velocity V(lsr) = - 11 km s - 1 in the central region is 50-60 K.

CEP A: A POSSIBLE PROTO-CLUSTER 157

The CS (1-0) and the CO emission show complementary distributions. The CS emission, which can be seen from Figure l(a), extends in the North-South direction. The CO intensity, integrated over V(lsr) = - 18 and - 2 km s - 1, is concentrated toward the proto stars and elongates along the East-West direction. The high velocity components of CO emission are also aligned to this direction. Another red-shifted CO component is confined to the North-Western part. The CS emission represents the denser part of the molecular cloud. The density of the hydrogen molecule turns out to be larger than 104 cm - 3. The CO emission characterizes a region of about 103 cm - 3.

Therefore, all this suggests that the denser part of the molecular cloud confines the diffuse molecular flow, which itself aligns perpendicularly to this denser part.

3. Summary

High resolution observations of molecular line emission around the proto stars in Cep A are presented. A dense cloud surrounding the proto stars extends along the North-South direction and is probably rotating. The molecular flow is in an East-West direction in the vicinity of the protostars. The properties and the kinematical structure of the dense molecular cloud suggest that Cep A is in a contracting phase and will generate massive stars. Later, these stars will form a new subgroup of the Cep OB3 association.

References

Myers, P. C. and Benson, P. J.: 1983, Astrophys. J. 266, 309. Rodriguez, L. F., Ho, P. T. P., and Moran, J. M.: 1980, Astrophys. J. 240, L149. Sargent, A. I.: 1977, Astrophys. J. 218,736.

FORMATION OF THE SOLAR SYSTEM*

J.J.RAWAL

Nehru Planetarium. Nehru Centre. Bombay. India


Abstract. Prentice (1978a, b), in his modern Laplacian theory of the origin of the solar system, has established a scenario in which he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant", 1.69. In an attempt to understand this law in an alternative way, Rawal (1984a) assumes that during the collapse of the solar nebula the halts at various radii are brought about by the supersonic turbulent convection and arrives at the relation of the formRp = Roa P , where Ro is the radius of the present Sun and a = 1.422, is referred to, here, as the 'Roche' constant. Kepler's third law assumes the form: Tp = To(a 3/ 2 )p, To being the rotational period of the Sun at the time it attained its present radius. Rp satisfy Laplace's resonance relation without any exception. The present paper investigates inter· relations among the concepts of supersonic turbulent convection, rotational instability, and Roche limit.

1. Introduction

Since the time Copernicus discovered that the planets revolve around the Sun, astronomers have been trying to understand the origin of the solar system. Numerous theories for the origin of the solar system have so far been advanced (ter Haar and Cameron, 1963; ter Haar, 1967; Williams and Cremine, 1968; Woolfson, 1969; Alfven and Arrhenius, 1970a, b; Nieto, 1972; Reeves, 1978; and Prentice, 1978a, b). Among all these theories of the formation of the solar system, Laplace's nebular hypothesis is favoured (see Reeves, 1978). However, it faces a few problems (for full details, see above mentioned references). The difficulties faced by Laplacian hypothesis are considered by Prentice (1978a, b). He presents an outline of the Laplacian theory, which he calls 'modern Laplacian theory' for the origin of the solar system. In this he considers Larson's concept of central core formation, and the influence of a supersonic turbulent stress on the cloud, showing how this stress leads to the formation and detachment of a discrete system of gaseous rings. The ratio of the orbital radii Rp of successively disposed gaseous rings is a constant and forms a geometric progression similar to the Titius-Bode law of planetary distances (ter Haar, 1950; Dermott, 1968; Nieto, 1972; and Rawal, 1978). To be more precise, Prentice, in his modern Laplacian theory, gets ratio of the orbital radii Rp of successively disposed gaseous rings to be a constant given by

R:: 1 = [ 1 + ;j J = const. = 1.69, (Ll)

* Paper presented at the IAU Third Asian·Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984.


160 J. J. RAWAL

where m is the mass of a disposed gaseous ring, M the remaining mass of the proto solar nebula and f the moment-of-inertia coefficient.

In an attempt to understand the Titius-Bode law in an alternative way, Rawal (1984a) starts with the concept of the Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by supersonic turbulent convection, as developed by Prentice, and arrives at the relation

(1.2)

where Rp are the radii of the solar nebula at various halts during the collapse, Ro the radius of the present Sun, and a = 1.442 is referred here as the Roche constant. Rawal (1984a) tabulates values of Rp. This suggests that a ring-structure feature may be a common and natural feature of heavenly bodies, and, in particular, of the major members of the solar system (also see Rawal, 1981, 1982). In reconciling this work with that of Prentice, he finds that

R [ m J2 Rp

: 1 = 1 + Mf = 1.442 = a . (1.3)

Thus, the modern Laplacian theory of Prentice is supported. It turns out that the rotational instability at the equator of the proto solar nebula arises at various stages of its contraction precisely by the step of the Roche constant, which is the same as Bode's constant in the modern Laplacian theory, and leads to the formation and detachment of a discrete system of gaseous rings, the whole process being controlled by the phenomenon of supersonic turbulent convection. The usefulness of the work is that once the radius of the primary is known, the appropriate relation can be set up very simply and uniquely. The discussion could be considered as an alternative way of deriving the Titius-Bode law.

Rawal (1985) has further shown that Kepler's third law assumes the form Tp = ToCa 3!2)P, To being the rotational period of the Sun at the time when it attained the present radius. Further, he finds that the Rp satisfy Laplace's resonance relation without any exception.

The question now arises: What interrelations, precisely, exist among supersonic turbulent convection, rotational instability and the Roche limit? The present paper investigates this question.

2. The Role of Rotation and Supersonic Turbulent Convection and Their Relations with Roche Limit

The free collapse of the infalling proto solar cloud is halted as soon as sufficient energy is supplied to dissociate and ionize the hydrogen and helium gas to the levels required for both thermodynamic and hydrostatic equilibrium.

FORMATION OF THE SOLAR SYSTEM 161

The total energy E(Re) of a uniformly rotating turbulent cloud of equatorial radius Re existing in hydrostatic equilibrium is given by

(2.1)

where

_ f pGM(r) d _ Cn (f3, 8) GM2

Qgrav - V - , r Re

(2.2)

v

is the self-gravitational potential energy of the cloud, Cn (f3, 8) may be called a concentration coefficient, since it depends on how centrally condensed the proto solar cloud is. It depends upon the turbulence parameter [3, the rotation parameter 8 = w;R~/GM as well as on the polytropic index n. For a strongly centrally condensed structure which is uniformly rotating, we have

(2.3)

This relation tells us that rotation enhances the store of potential energy. We may note that in a centrally condensed cloud only the outer layers are significantly disturbed by rotation, while the central regions barely notice the centrifugal force. Rotation, therefore, has a stabilizing influence.

As [3 increases so does Cn ([3, 0) (Prentice, 1978a, b), which means the store of the gravitational energy of the cloud is increased by the turbulence. This behaviour is due to the fact that the turbulence is greatest in the outer less dense layers of the cloud and causes them to be pushed outwards proportionately much more than the inner dense layers where the turbulence is small (see Prentice, 1978a, b). Thus, the turbulence causes the star to become more centrally condensed.

Turbulence, therefore, enhances Cn ([3, 8), while for a fully rotating star, rotation adds a further factor of ~. The thermal kinetic energy Uth , the turbulent kinetic energy Uturb

and the rotational energy Urot of the gas-cloud are given as

1 f vp~T 1 Uth = - -- dV = - (1 - 3[3) Qgrav , 2 p 2

(2.4)

v

where v is the mean number of degrees of freedom per atom; p, the density; ~ the gas constant; T, the temperature; and p, the mean molecular weight;

(2.5)

and

(2.6)

162 J. J. RAWAL

where f is the moment-of-inertia coefficient. In deriving Equations (2.4) and (2.5), we made use of the equation of hydrostatic support

dPtotal pGM(r) (2.7)

where

pf!llT ppGM(r) Ptotal = -- + '--'--- (2.8)

/1 r

IS the total radial stress at radius r. The final term in Equation (2.1) is the total dissociation and ionization energy in CGS units.

The free collapse from interstellar density can be halted as soon as E(Re) < O. A strict inequality applies here, since some energy is radiated away from the surface during the collapse. Using Equation (2.1), we see that for stabilization, we require that

(2.9)

Unfortunately, the above condition is nowhere met during the collapse from 104 to 102 Ro, except for the most extreme cases where 13;:::: 0.2. For such large values of 13, the physical characteristics of the cloud become absurdly extreme. More to the point, it is found (Prentice, 1978a, b) that the values of 13, which are required to account for the physical properties of the planetary system such as the Titius-Bode law and the distribution of planetary masses, are typically of order of only 0.1. We are, therefore, led to conclude that supersonic turbulent convection is unable completely to stabilize the cloud during the collapse from a radius of ~ 104 R 0' though, the modification of the mixing-length theory of convection developed by Prentice (1978a, b) certainly greatly helps towards the achievement of this goal.

A plot (Prentice, 1978b) of the additional amount of energy which is required to achieve hydrostatic equilibrium throughout the fully rotating turbulent protosolar cloud for various values of 13, as a function of the equatorial radius R e , shows that, in the absence of any additional source of energy, no complete thermodynamic equilibrium can be attained until the diameter of the proto solar cloud has typically shrunk to the value ~ 300 R o' corresponding to the present orbit of Venus, 13 being equal to 0.1. The cloud is, therefore, dynamically unstable in the interval 104 to 300 Ro and collapses freely in that interval (also see Schatzman, 1967, 1971; Hayashi, 1961, 1966; Cameron, 1962). Nevertheless, since the free-fall time r.u- at any point in the cloud varies as 1/jP(r), where per) is the mean mass density interior to the radius r, it follows that the central regions of the cloud will reach the centre sooner than the outer ones, since per) is a centrally-peaked function whether one considers a cloud in free fall (Larson, 1969) or a cloud existing in supersonic convective equilibrium (Prentice, 1973).

It has therefore been proposed (Larson, 1969) that a small fraction of mass (say, mJ of the central region of the cloud collapses dynamically all the way through to stellar


size; to a radius, say rc , where the hydrostatic temperature exceeds both the dissociation and ionization temperatures, and where the energy released is sufficient to stabilize the rest of the infalling cloud.

It is seen that for all values of f3 typically in the range 0-0.15, we initially require a central core-mass fraction 2-4 % M 0 to accumulate at the centre to stabilize the infalling cloud when it first becomes sufficiently opaque to absorb the emitted radiation near a radius of '" 104 Ro. Thus, the inner few percent of the cloud mass never achieve any equilibrium until they reach normal stellar size, and so remain detached from the rest of the protosolar cloud during the proto star's pre-Main-Sequence contraction. Any metal-rich central inhomogeneity which was formed at the end ofthe grain-breaking era as described by Reddish and Wicramasinghe (1969) and Prentice and ter Haar(1971), may, therefore, survive the turbulent era of planetary formation, when the rest ofthe low density (10- 13 g cm - 3) cloud is uniformly mixed up by supersonic convection. Therefore, when the proto solar cloud finally moves onto the Zero-Age Main Sequence, it consists of a small metal-rich central core, of mass as much as 0.04 M 0' surrounded by a homogeneous envelope of normal composition.

As soon as the cloud has become stabilized at a radius near '" 104 R o, it proceeds inwards over a Kelvin-Helmholtz time-scale. However, as the cloud contracts, it immediately becomes destabilized again, as further energy is required to complete the dissociation and ionization processes to the levels required for complete equilibrium. The central regions of the cloud proceed to collapse inwards again, releasing more energy as they fall onto the central embryonic core and, thereby, stabilizing the cloud. This quasi-static state persists until the maximum of the additional amount of energy has been passed near a radius 1000 Ro. The cloud, therefore, exists in a state of quasi-static equilibrium during the interval 104 -103 Ro with the rate of collapse at the surface being governed by the rate of accumulation of material at the centre. Once the maximum point of the additional amount of energy has been passed the collapse proceeds at the normal Kelvin-Helmholtz rate.

According to the calculations (Prentice, 1978b) during the period of quasi-static equilibrium, the rate of collapse at the surface of the cloud lies somewhere between 160 th and toth of the free-fall rate and once the cloud has become fully stabilized near a radius of '" 1000 R o, the collapse proceeds much more slowly.

Though magnetic forces do playa vital role during the very early stages of the Sun's formation in the regime of interstellar densities, they have very little influence on the structure and dynamical evolution of the proto solar nebula during the contraction phase from radius 104 to 2 Ro. It is possible that they play an important role during the long slow final phase of the Sun's pre-Main-Sequence contraction from radius 2 Ro down to Ro, when the interaction of the solar wind with a strong primordial magnetic field is required to rid the proto sun of the last vestige of its rapid rotation (Prentice and ter Haar, 1971; Weber and Davis, 1967). During the brief period of planetary formation which takes some 3 x 105 yr to complete, the magnetic forces can safely be ignored.

A second influence of turbulent stress on the structure of the cloud is the formation of a very steep density inversion at the photosphere. If the turbulent convection dies

164 J. J. RAWAL

down above the photosphere over an overshoot height which is at most a few pressurescale-heights,

Hph = f?ltTphR;h/p,GM = f3Rph/(P,)ph ~ 10- 3 Rph '

where

(P,)ph = f3p,GM/f?ltTR ph

is the ratio of turbulent stress to gas pressure at the photo surface, then overall pressure equilibrium demands that the density Pe at the base of the non-turbulent atmosphere just above the photosphere, exceeds the density Pph just beneath by the factor Pe/PPh = 1 + (P,)ph ~ 100. Moreover, the rising and falling supersonic convective motions create, at each point in the cloud, a turbulent viscosity which eliminates differential motions and the rotations in the cloud over a time-scale of the same order as the local free-fall time. Thus the supersonic turbulent stress maintains uniform rotation and an equilibrium density profile throughout the convective structure.

Jeans (1928) has shown that as the rotation parameter increases from 0 to 1, the various equipotential surfaces in the cloud become distorted from sphericity and bulge outwards at the equator. If, however, the cloud is strongly centrally condensed, then only the outermost layers are significantly disturbed by the rotation and the so-called atmospheric approximation is applicable to compute the equilibrium structure of the outer layers. According to this approximation, the mass M(r) interior to any radius r in the outer layers satisfies the equation M(r) = M = const., and the equation of hydrostatic support is written as

1 - GM [R; , s 'J - "p(s, z) = -- - r - 8 - s , P R; r2 Re (2.10)

where sand z are cylindrical polar coordinates referred to the axis of rotation; and p = pes, z), the total pressure; while r = (S2 + Z2)1/2. If the equipotential surfaces of the various physical quantities p, s, T/M everywhere coincide, then the solution of the Equation (2.10) may be formally written as

p = p(\f') , P = p(\f') , T/ p, = F(\f') , (2.11)

where the equipotential function \f' == \f' (s, z) is given by

\f'(s, z) = (_3 ) [Re _ 1 + 8 (~ -l)J. 2 + 8 r 2 R; (2.12)

The photosphere being defined by the equation \f'(s, z) = O. The above equation allows us to compute the equipotential surfaces of the rotating

cloud in terms of those of the spherical non-rotating cloud (8 = 0). Since, the polar radius Rp of a very centrally-condensed cloud is hardly affected by rotation (Monaghan and Roxburgh, 1965), it follows from Equation (2.12) that as 8 is increased, the


equatorial radius Re(8) increases according to

(2.13)

while the moment-of-inertia coefficient f(8) declines according to the law

f(8) = f(0)[R e(0)]2 = f(O)/[l + 8]2 Re(8) 2

(2.14)

Thus, as 8 is increased from 0 to 1, the equatorial radius increases by about 50%, while f is reduced by a factor of 0.44. Precisely at this time a steep density inversion takes place at the equator of the solar nebula leading to the formation and detachment of the gaseous ring of non-turbulent material at the equator. Considering the rotational evolution of the proto sun towards the point of rotational instability in detail, one arrives at the relation

R [ m]2 --p- = 1 + - = const. ~ 1.44 , Rp _ 1 Mf

(2.15)

where m is the mass of a disposed gaseous ring and M the remaining mass of the protosolar nebula. Thus, Bode's constant turns out to be the same as the Roche constant, discussed by Rawal (1984). Thus, we incline to conclude that during the time the rotation parameter 8 increases from 0 and attains the value 1 corresponding to instability limit, the protosolar nebula decreases its radius from Rp to Rp_ I' where Rp is the Roche limit of the nebula now having radius Rp _ I' At this time supersonic turbulent convection dies down resulting in the steep density inversion at the equator and shedding out a ring of matter of width (Rp - Rp _ I)'

Acknowledgements

The author gratefully acknowledges the substantial financial support from Maharashtra's Chief Minister's Fund and Jhaverbhai Patel Research Centre's Trust, Bombay without which it would not have been possible for him to attend the Third Asian-Pacific Regional Meeting of the International Astronomical Union and interact with other researchers of the region. The author also thanks the Local Organising Committee of the Meeting for its substantial financial support.

References

Alfven, H. and Arrhenius, G.: 1970a, Astrophys. Space Sci. 8, 338. Alfven, H. and Arrhenius, G.: 1970b, Astrophys. Space Sci. 9, 3. Cameron, A. G. W.: 1962, Icarus 1, 13. Dermott, S. F.: 1968, Monthly Notices Roy. Astron. Soc. 141,363. Hayashi, c.: 1961, Publ. Astron. Soc. Japan 13,450. Hayashi. c.: 1966. Ann. Rev. Astron. Astrophys. 4, 171.

166 J. J. RAWAL

Jeans, J. H.: 1928, Astronomy and Cosmogony, Cambridge Univ. Press, London. Larson, R. B.: 1969, Monthly Notices Roy. Astron. Soc. 145,271. Monaghan, J. J. and Roxburgh, I. W.: 1965, Monthly Notices Roy. Astron. Soc. 131, 13. Nieto, M. M.: 1972, The Titius-Bode Law of Planetary Distances, Its History and Theory, Pergamon, Oxford. Prentice, A. J. R.: 1973, Astron. Astrophys. 27, 234. Prentice, A. J. R.: 1978a, in S. F. Dermott (ed.), The Origin of the Solar System, Wiley, London, p. Ill. Prentice, A. J. R.: 1978b, The Moon and the Planets 19, 341. Prentice, A. J. R. and ter Haar,.: 1971, Monthly Notices Roy. Astron. Soc. 151, 177. Rawal, J. J.: 1978, Bull. Astron. Soc. India 6, 72. Rawal, J. J.: 1981, The Moon and the Planets 24, 407. Rawal, J. J.: 1982, Indian J. Radio Space Phys. 11, 100. Rawal, J. J.: 1984, Earth, Moon, Planets 31,175. Rawal, J. J.: 1985, Earth, Moon, Planets, in press. Reddish, V. C. and Wickramasinghe, N. c.: 1969, Monthly Notices Roy. Astron. Soc. 143, 189. Reeves, H.: 1978, in S. F. Dermott (ed.), The Origin of the Solar System, Wiley, London. ter Haar, D.: 1950, Astrophys. J. 111, 179. ter Haar, D.: 1967, Ann. Rev. Astron. Astrophys. 5, 267. ter Haar, D. and Cameron, A. G. W.: 1963, in R. Jastrow and A. G. W. Cameron (eds.), The Origin of the

Solar System, Academic Press, New York, p. I. Schatzman, E.: 1967, Ann. Astrophys. 30,963. Schatzman, E.: 1971, in C. deJager (ed.), Highlights of Astronomy, D. Reidel Pub!. Co., Dordrecht, Holland,

Vo!' 2, p. 197. Weber, E. J. and Davis, L., Jr.: 1967, Astrophys. J. 148,217. Williams, I. P. and Cremin, A. W.: 1968, Quart. J. Roy. Astron. Soc. 9,40. Woolfson, M. M.: 1969, Rep. Progr. Phys. 32, 135.

THERMAL-CHEMICAL INSTABILITY IN A PRE-GALACTIC GAS

CLOUD*

YUTAKA SABANO and MAKOTO TOSA

Astronomical Institute, Faculty of Science, Tohoku University, Sendai, Japan


Abstract. The growth of thermal-chemical instability in a pre-galactic medium is followed by numerical simulation of gas dynamics. Results show that a primordial gas cloud breaks into self-gravitating subcondensations with the mass of normal stars.

The hydrogen molecule would work as an efficient coolant in a pre-galactic medium which is free from heavy elements. It can be shown, by linear perturbation analysis, that molecular reactions lead to a thermal instability with condensation, which is caused by strong temperature-dependence of the collisional dissociation process (Sabano and Yoshii, 1977; Yoshii and Sabano, 1979; Silk, 1983). In the present paper we study the nonlinear growth of perturbations by a one-dimensional simulation of gas dynamics, which includes molecular reactions as well as an energy equation. We numerically follow the time-evolution of a spherically-symmetric perturbation, which is superposed on initially uniform medium under free-fall contraction, by a Lagrangian, hydrodynamical programme with an artificial viscosity (Richtmyer and Morton, 1967).

Figure I shows time-evolutions of perturbations with masses of m = 0.1 M 0

and 1.0 Mo, for initial state of no = 7.2 x 109 cm - 3, To = 2.2 X 103 K, and fo = 4.5 x 10 - 4, where linear theory gives a positive growth rate for the instability (Silk, 1983). Results for the fluctuation with the small mass of m = 0.1 Mo show a rapid growth of density contrast driven by chemical reactions, which is a characteristic of thermal instability of the isobaric condensation mode in the limit of short wavelength of perturbation (Sabano and Yoshii, 1977). On the other hand, results for the larger mass of m = 1.0 Mo distinctly show the effect of self-gravitation. After the initial growth of the thermal mode, the central density continues to grow, following gravitational contraction.

We note that the Jeans mass in the initial state, M J = 120 Mo, is much reduced after a phase-change caused by the thermal-chemical instability, and even a low-mass fluctuation with m = 1.0 M 0 eventually turns to be bound by self-gravitation. It is thus concluded that a primordial gas cloud, driven by such a thermal-chemical instability, would break into fragments, with mass in the range of normal stars, suggesting that Population II objects can be formed as normal stars (see also a review by Sabano and Yoshii, 1984).


Astrophysics and Space Science 119 (\ 986) 167-168. © 1986 by D. Reidel Publishing Company

168

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Y. SABANO AND M. TOSA

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0

b

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e

d_

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~

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Fig.!. Time-evolutions of perturbations with masses ofm = 0.1 Mo and ofm = 1.0 Mo. The distributions of number density n, temperature T, molecular fraction f, and pressure P are plotted against Lagrangian mesh points at stages (a) t = 0, (b) 1.32 x 109 s, (c) 2.9 X 109 s, (d) 4.7 x 109 s, and (e) 6.4 x 109 s for m = 0.1 M o , and at stages (a) t = 0, (b) 4.5 x 109 s, (e) 5.8 x 109 s, (d) 6.0 x 109 s, (e) 6.2 x 109 s, and

(f) 6.5 x 109 s, for m = 1.0 M o , respectively.

References

Richtmyer, R. D. and Morton, K. W.: 1967, Difference Methods for Initial-Value Problems, 2nd ed., Interscience Pub!., New York, Ch. 12.

Sabano, Y. and Yoshii, Y.: 1977, Publ. Astron. Soc. Japan 29,207. Sabano, Y. and Yoshii, Y.: 1984, Sci. Rep. Tohoku Univ., Ser. VIII 5, 51. Silk, J.: 1983, Monthly Notices Roy. Astron. Soc. 205, 705. Yoshii, Y. and Sabano, Y.: 1979, Pub!. Astron. Soc. Japan 31, 505.

DYNAMICS OF THE MAGELLANIC SYSTEM AND THE

GALAXY - PRESENT STATUS OF THEORETICAL

UNDERST ANDING*

TAD A YUKI MURAl and MITSUAKI FUJIMOTO

Department of Physics and Astrophysics, Nagoya University, Chikusa-ku, Nagoya, Japan


In an attempt to interpret the Magellanic Stream (Mathewson et aI., 1974), a new tidal simulation for the triple system, the Galaxy, the Large Magellanic Cloud (LMC), and the Small Magellanic Cloud (SMC), has been performed to represent the past 1010 yr, on relaxing a simplifying assumption of the bound state of the SMC with respect to the LMC for the whole 1010 yr. The parameters for the SMC orbit at the present epoch are varied around those of the best fit orbit of a previous simulation (Murai and Fujimoto, 1980). All the other parameters are the same as those of the previous simulation, including the parameters for the LMC orbit, as well as the flat rotation velocity of 250 km s - 1 assumed to extend without limit for the Galaxy.

An orbit of the SMC, of which tangential-velocity components at the present epoch differ by some 10 km s - 1 from those of the best fit orbit of the previous simulation, results in a satisfactory reproduction of the Magellanic Stream. The radial-velocity distribution of this simulation along the Magellanic Stream resembles the observed one much better than that of the previous model (Figure 1).

The SMC, which had been independently orbiting around the Galaxy, was captures by the LMC at a close encounter with it about 1.7 x 109 yr ago (Figure 2). Since then the SMC has been bound to the LMC, forming a binary system with the LMC. The SMC orbit around the LMC, however, is irregular in shape and the SMC made a second close encounter some 200 million years ago. As a result, the SMC was severely disturbed, resulting in the formation of the Magellanic Stream. The outer part of the SMC is now being disrupted.

The history of the Magellanic Clouds System envisaged here may be relevant to numerous characteristics of the clouds, such as the recurrent burst of star formation and the new result of the splitting of the SMC proposed by Mathewson and Ford (1984).



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MAGELLANIC SYSTEM AND THE GALAXY

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200

150

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SMC (thin line). The SMC was captured by the LMC about 1.7 x ]09 yr ago.

References

Mathewson, D. S. and Ford, V. L.: 1984, in S. van den Bergh and K. S. de Boer (eds.), 'Structure and Evolution of the Magellanic Clouds', fA U Symp. 108, 125.

Mathewson, D. S., Clearly, M. N., and Murray, J. D.: 1974, Astrophys. J. 190, 291. Murai, T. and Fujimoto, M.: 1980, Publ. Astron. Soc. Japan 32, 581.

EMISSION LINE VELOCITY SURVEY OF SPIRAL GALAXIES

WITH BRIGHT NUCLEI*

A. J. TURTLE

University of Sydney, N.S. w., Australia

and

W. D. PENCE**

Anglo-Australian Observatory, Epping, NSW, Australia


Abstract. High resolution spectrographic observations of 220 nearby galaxies with bright nuclei have been made mainly at H/1 and [0 III 1 ,l,5007 to search for signs of nuclear activity. In many cases evidence for weak activity has been found.

Over recent years many examples of activity in the nuclei of spiral galaxies have been reported. At the most extreme QSOs probably fall into this category, followed on a lesser scale by the Seyfert galaxies. Phillips et al. (1983) have investigated several nearby spirals with nuclear properties similar to the classical Seyferts but generally weaker in activity. Possibly the nuclei of all spiral galaxies at some stage undergo one or more bursts of activity; if so, there may be a wide variation in the degree of activity. While nearby galaxies with nuclei that are currently very active have probably all been recognized, other close nuclei (velocity < ~ 5000 km s - 1) may have weaker activity which is hitherto undetected. For instance, unexpected phenomena were revealed by high resolution studies of NGC 1365 (Phillips et al., 1983) and NGC 6221 (Pence and Blackman, 1984).

We report here on a comprehensive optical survey designed to obtain statistics on the degree of activity in bright spiral galaxies. Other workers (e.g., Heckman et al., 1980; Keel, 1983) have also made spectroscopic surveys of nuclei, mainly to study relative line strengths. The work described here includes more galaxies and is more concerned with velocity information derived from long-slit spectra taken in the region of Hf3 and [0 III] ),5007 with high spatial and spectral resolution.

Satisfactory observations were obtained for 220 galaxies south of D = + 30 0 and with velocity generally less than 5000 km s - 1 selected from the Second Reference Catalogue of Bright Galaxies (de Vaucouleurs et al., 1976). The principal selection criterion was the nuclear brightness classification. All 47 classified as 'extremely bright' were observed along with 62 % of the 'very bright' and 29 % of the 'bright'. Preference was given to

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** Now at Space Telescope Science Institute, Baltimore, U.S.A.


174 A. J. TURTLE AND W. D. PENCE

barred spirals. About 20 of the sample were already known to exhibit marked nuclear activity but they were still included to preserve uniformity. 33 objects were also observed in HIX and [Nu].

The observations were spread over several occasions, from September 1982 to July 1983, at the 3.9 m Anglo-Australian Telescope using the RGO spectrograph and the IPCS detector to give a FWHM of ~ 1 A. Each galaxy was observed for 500-1000 s. The 3 arc min slit was set on the nucleus and usually oriented along the minor axis if this was known. As much of the observing was done in bright moonlight, the long slit enabled night sky contributions to be estimated and removed. In addition, a spectrum of one or two random H II regions within the galaxy was often obtained. These spectra were useful for statistical comparisons with nuclear spectra.

The data were divided by a flat field and reduced to a uniform wavelength scale. Further reduction was performed semi-automatically with interactive assistance using the graphics display of the Anglo-Australian Observatory. Spatial profiles along the slit were extracted for any H{3 or A5007 emission, along with profiles of the adjacent continuum. Spectra from the nuclear region were summed over a few seconds of arc to give a single spectrum and any separate H II regions were treated similarly. In the initial analysis a simple gaussian function was fitted to each spatial profile and to each emission line.

Emission in at least one line was detected in over 60% of the sample. Two sub-samples have a detection rate of over 70% - the 'extremely bright' nuclei and, irrespective of nuclear brightness class, the intermediate (X) bar structure group. In about 16 % of all galaxies only H{3 was detected and only A5007 (usually very weak) in about 7 %. There are several indicators of energetic activity in at least 30 % of the nuclei surveyed. These results can be summarised as follows. Many more nuclei have a ratio ofline intensities /(5007)j/(H) > 1 than do the H II regions away from the nucleus. The spectral widths (FWHM) of any narrow nuclear emission lines, as given by the fitted gaussian functions, are also often much greater than those for the H u regions. If widths larger than 200 km s - 1 are taken as suggesting 'activity', then the number of nuclei in this category is about 30 for H{3, and over 60 for A5007. When the emission lines from a nucleus had adequate signal-to-noise, the profiles were inspected for asymmetry. Over 50% (or about 60 by number) of these nuclei had a blue wing in either H{3 or A5007, or both, and another 10% had a red wing.

A detailed interpretation of these results will be presented elsewhere. However, it is already apparent that well over a quarter of the sample surveyed: namely, catalogued bright spiral galaxies with particularly bright nuclei, show clear signs of present activity within their nucleus. A significant proportion of the remainder probably exhibit activity at a weaker level. It may be that intermittent strong activity or continuous mild activity is very frequent, at least amongst the class of nucleus contained in this investigation.

Acknowledgement

A.J.T. thanks the Anglo-Australian Observatory for the use of its computing facilities.

SPIRAL GALAXIES WITH BRIGHT NUCLEI 175

References

De Vaucouleurs, G., de Vaucouleurs, A., and Corwin, H. G.: 1976, Second Reference Catalogue of Bright Galaxies, University of Texas Press, Austin.

Heckman, T. M., Balick, B., and Crane, P. c.: 1980, Astron. Astrophys. Suppl. Ser. 40, 295. Keel, W.: 1983, Astrophys. J. Suppl. 52, 229. Pence, W. D. and Blackman, C. P.: 1984, Monthly Notices Roy. Astron. Soc. 207,9. Phillips, M. M., Charles, P. A., and Baldwin, J. A.: \983, Astrophys. J. 266, 485. Phillips, M. M., Turtle, A. J., Edmunds, M. G., and Pagel, B. E. J.: 1983, Monthly Notices Roy. Astron. Soc.

203,759.

OPTICAL LIGHT VARIATION OF THE SEYFERT GALAXY

NGC 4151 *

HIROSHIOHTANI**

Department of Astronomy. University of Kyoto. Japan

JOHN MEABURN

Department of Astronomy. University of Manchester. England

CHRISTOS GOUDIS

Department of Astronomy. University of Patras. Greece

AHMAD EL·BASSUNY and MOHAMMED SOLIMAN

Helwan Observatory. Cairo. Egypt


Abstract. The optical light variation of the nucleus of the galaxy NGC 4151 was monitored mainly using the 74 inch telescope of the Helwan Observatory, Egypt.

In 1983 (Meaburn et aI., 1984, 1985), the object was highly variable. In February, a distinct depression by 0.2 mag. in the continuum of the visual region was detected over

FEB 5 15 25

N I I I I I

-0 z: cr: -1,2 =\-, ~ Vl

~ -1,0 - ...

LU - ... ~ > U i= -0,8 -« -J "-LU e:. LU Cl +0'6 ~~" ::;) l-

e- "11--Z l!)

I- Cont. 1-.5672--« +0·8 L

Fig. 1. Parts of the light curves in 1983 in U and a continuum region around A5672 measured with a 13" diaphragm (Meaburn et al., 1984, 1985). The magnitude is relative to star No.2 of Penston et al. (1971).

* Paper presented at the IAU Third Asian·Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** Visiting astronomer of the University of Manchester in 1982 and 1983.


178

w > le( ...J W a:

H. OHTANI ET AL.

.96$

Mar Apr

NGC4151

I ~m = 0 · 2mag

u

1\ ,~ )-- ---- f' H.. ~ ____ -------~!-, ?- --- 03

~.

~ ""-f( ~" ig~~o _----;-~~ . ..,-

1. 1

1983

Fig. 2. The light curve observed in 1984. The diaphragm size and the reference star are the same as in Figure 1. The ranges of variations observed in 1983 are indicated, for comparison, at the left edge.

two nights (Figure 1). If this phenomenon is interpreted as an occultation of the nucleus by one of the opaque clouds which compose the broad line region, an upper limit of the nuclear size can be estimated to be as small as a few AU, with a typical cloud velocity of 5000 km s - 1.

During about ten days in early April of 1984 (Figure 2), the nucleus was so quiet that little variation was detected, as it also was in the period monitored by Lawrence et al. (1981). In addition, the object was as faint as had ever been observed by the various authors. Such a very inactive appearance in the optical region during this time seems to relate closely to the faintness at X-ray frequencies in the preceeding three months (Matsuoka and Ikegami, 1984).

References

Lawrence, A., Giles, A. B., McHardy, I. M., and Cooke, B. A.: 1981, Monthly Notices Roy. Astron. Soc. 195, 149.

SEYFERT GALAXY NGC 4151 179

Matsuoka, M. and Ikegami, K.: 1984, in Proceeding of the Conference on UV and X-ray Emissionfrom Active Galactic Nuclei, Garching, 1984.

Meaburn, J., Ohtani, H., and Goudis, c.: 1985, Astron. Astrophys. (in press). Meaburn, J., Ohtani, H., and Goudis, c.: 1986, Astron. Astrophys. (in press), and in 1985, J. E. Dyson (ed.),

Active Galactic Nuclei, Manchester Univ. Press, p. 184. Penston, M. J., Penston, M. V., and Sandage, A.: 1971, Publ. Astron. Soc. Pacific 83, 783.

EMISSION LINE VELOCITY FIELD IN THE CENTRAL REGION

OF M82*

MINORU SASAKI and MAMORU SAITO

Department of Astronomy, Faculty of Science, University of Kyoto, Kyoto, Japan


Abstract. Velocity field in the central region ofM82 has drawn in detail mainly from Hoc. This velocity field is consistent with that ofNe II 12.8 J.lm except for the region near a huge dust lane, and it cannot be explained by pure rotation around the galactic center. Origin of peculiarities of the velocity field is briefly discussed.

1. Introduction

For the origin of galactic activities, the galaxy-galaxy interaction has been supposed to be a significant cause. For example, many host galaxies of quasars have distorted shapes, probably due to tidal interaction (Gehren et al., 1984), and infrared galaxies also have peculiar shapes (Aaronson and Olszewski, 1984).

The irregular galaxy M82 is interacting with M81, and the central region is a strong source of optical emission lines, infrared emission, non-thermal radio continuum, and molecular emission lines. These various activities are considered as results of star formation activity in this region during some 107 yr or more. To study the origin of this activity, detailed dynamical information would be needed.

The velocity field of the Ho: emitting gas in the central region of M82 has been given by Burbidge et al. (1964) and Heckathorn (1972). We have also observed this region at the wavelength region of Ho: and D lines with the 188 cm telescope of the Okayama Astrophysical Observatory. The dispersion of spectrograms is 63 A mm - 1 at Ho:, and the plate scale is 30" mm - 1. The accuracies of positions are less than 2" in the inner region, and 4" over the outer region; and those of velocities are less than 10 km s - 1

for stronger lines, and 20 km s - 1 for weaker lines. The results on the rotation curves of the sodium D absorption lines and the Ho: emission lines along the major axis have been published (Saito et aI., 1984, hereafter referred to as Paper I). The methods of observation and reduction have been described in Paper I. This paper presents the velocity field of the Ho: emitting gas in the central region of 35" x 1'.

2. Results

Figure 1 shows the velocity field obtained from 11 spectrograms whose data are listed in Table I. Three of them are shown in Figure 2. The velocity field is similar to Heckathorn's (1972) one, even with the finer spatial resolution of our observation. OUf



182 M. SASAKI AND M. SAITO

N

o 180

-"""'" .( E~

260

140

10"

Fig. 1. Velocity field of emission lines mainly from Hac Solid lines are isovelocity contours of ours, dashed lines are outer contours of radio continuum (Kronberg et al., 1981), circles are near infrared point sources (Bettoni and Galletta, 1982), and plus is peak position of 2.2 ~m infrared radiation (Rieke et al., 1980).

TABLE I

Observations of M82

Plate No. Date Position Exposure Position in the galaxy angle (min)

IS 856(1) 7 Apr., 1981 62° 90 Nucleus SW end of slit IS 856(2) 7 Apr., 1981 62° 20 Nucleus SW end of slit IS 857 (2) 7 Apr., 1981 62° 60 3" south from nucleus IS 973 (1) 15 Apr., 1982 62° 15 3" north from nucleus IS 981 18 Apr., 1982 62° 120 3" north from nucleus IS 982 18 Apr., 1982 62° 90 Nucleus centered IS 984 19 Apr., 1982 110° 90 3" north from nucleus IS 1101(1) 5 Apr., 1983 110° 30 Nucleus centered IS 1101(2) 5 Apr., 1983 110° 90 14" north from nucleus IS 1103(2) 6 Apr., 1983 110° 35 3" north from nucleus IS 1238 3 Apr., 1984 62° 35 13" north from nucleus

results are also consistent with velocities of Nell 12.8 j.lm (Beck et al., 1978), except for the northeast side near the huge dust lane, where the Nell velocities are about 20 km s - I

larger than HQ(. The difference between the optical and infrared line velocities seems to be due to large opacity of the dust lane for the optical lines.

The velocity field is not consistent with a pure rotation around the galactic center. First, the galactic center obtained from a peak position of the 2.2 j.lm radiation does not

(a)

1101 (I)

(b)

IS 1103(2)

(c)

IS 984

:::~ ;~ J He] ),5876

NalD

EMISSION LINE VELOCITY FIELD IN M82

[OJ] )'6300J I (01) ).6364=-.J ~L[ II) ).6584

L Ha )'6563

[N II) .1.6548

Fig. 2. Spectrograms in the central region of M82.

183

NW

SE

agree with the place where the velocity gradient is steepest. Second, a low-velocity region extends along the minor axis at the western side. The same tendency in the velocity field appears in the millimeter lines of CO J = 1-0 (Rickard et a/., 1977) and J = 2-1 (Sutton et ai., 1983), although the CO velocities are about 80 km s - I larger than ours. Third, at the southeast side, the velocities are less than the systemic velocity of 195 km s - 1

(Paper I). Linewidths of the emission lines increase suddenly at the southeast side. This feature

is clearly seen in Figure 2(b). This region seems to adjoin the outer region found by Axon and Taylor (1978), where the emission lines have two velocity components. We note some more broad profiles of the emission lines ofHC( and [N II] appearing in Figure 2(c). The profiles show triangular forms and extend to the red side. They indicate large internal motions of gas in the H II region A.

3. Discussion of the Infall Motion

In the central region of M82, absorption lines of OH at A = 18 cm (Nguyen-Q-Rieu et ai., 1976) and H I aU = 21 cm (Crutcher et ai., 1978) are strongest at velocities higher than the systemic velocity, while the emission lines such as HC( and CO A = 2.6 mm (Sutton et ai., 1983) are strongest at lower velocities. This fact means that a higher velocity component exists mainly in front of the radio continuum source. The radio recombination lines of Hn C( (Bell et a/., 1984) also produce the same result, because the ratio of stimulated to spontaneous emission lines is larger at higher velocity. Since the radio lines mainly originate within the extended radio continuum source of M82, these results show the existence of infalling motion or inhomogeneous distribution of rotating gas around the center, but definitely cannot be explained by an expanding motion.

184 M. SASAKI AND M. SAITO

The observed velocities ofHa filaments (Heckathorn, 1972) and the H I halo (Cottrell, 1977) are red shifted on the NW side and blue shifted on the SE side. This velocity field is not produced by expanding motion of gas outside the disk, because Ha filaments are due to scattered light from a central source. This velocity field is a rotation around the optical major axis. The Ha velocity field of Figure 1, however, shows that velocities of the inner filaments are rather blueshifted on both sides, so contracting motion seems to become dominant at the regions just outside the active central region.

Acknowledgements

We wish to thank the staff of Okayama Astrophysical Observatory, Dr N. Kaneko, and Mr S. Nakatani for their help with the observations. We also would like to thank Dr Y. Nakai and Dr K. Iwasaki for their help with the measurements. The measurements were performed with Perkin-Elmer Micro-l0 Microdensitometer Systems of Tokyo Astronomical Observatory and Kwasan Observatory.

References

Aaronson, M. and Olszewski, E. W.: 1984, Nature 309, 414. Axon, D. 1. and Taylor, K: 1978, Nature 274, 37. Beck, S. c., Lacy, 1. H., Baas, F., and Townes, C. H.: 1978, Astrophys. J. 226,545. Bell, M. B., Seaquist, E. R, Mebold, u., Reif, K., and Shaver, P.: 1984, Astron. Astrophys. 130, I. Bettoni, D. and Galletta, G.: 1982, Astron. Astrophys. 113, 344. Burbidge, E. M., Burbidge, G. R, and Rubin, V. c.: 1964, Astrophys. J. 140, 942. Cottrell, G. A.: 1977, Monthly Notices Roy. Astron. Soc. 178, 577. Crutcher, R M., Rogstad, D. H., and Chu, K: 1978, Astrophys. J. 225, 784. Gehren, T., Fried, 1., Wehinger, P. A., and Wyckoff, S.: 1984, Astrophys. J. 278, 11. Heckathorn, H. M.: 1972, Astrophys. J. 173, 501. Kronberg, P. P., Biermann, P., and Schwab, F. R: 1981, Astrophys. J. 246,751. Nguyen-Q-Rieu, Mebold, U., Winnberg, A., Guibert, 1., and Booth, R: 1976, Astron. Astrophys. 52,467. Rickard, L. 1., Palmer, P., Morris, M., Turner, B. E., and Zuckerman, B.: 1977, Astrophys. J. 213, 673. Rieke, G. H., Lebofsky, M. 1., Thompson, R I., Low, F. J., and Tokunaga, A. T.: 1980, Astrophys. J. 238,

24. Saito, M., Sasaki, M., Kaneko, N., Nishimura, M., and Toyama, K: 1984, Pub!. Astron. Soc. Japan 36, 305. Sutton, E. c., Masson, C. R, and Phillips, T. G.: 1983, Astrophys. J. 275, L49.

X-RA Y OBSERVATION OF AGN'S FROM TENMA *

S. MIYOSHI

Department of Physics, Kyoto Sangyo University, Kamigamo, Kita-ku, Kyoto, Japan

S. HAYAKAWA, H. KUNIEDA, F. NAGASE, and Y. TAWARA

Department of Astrophysics, Nagoya University, Chikusa-ku, Nagoya, Japan


Abstract. In order to investigate the structure and mechanism of active galactic nuclei through X-ray observation, detailed energy spectra are examined with the gas scintillation proportional counters on board TENMA. For three selected objects, PKS 2155 - 304, Centaurus A and IC 4329 A, the observational results in the intensity variation, the spectral shapes and the iron line features are presented.

1. Introduction

The Japanese X-ray astronomy satellite TENMA observed X-ray emission from several active galactic nuclei (AGN's) with two sets of gas scintillation proportional counters (GSPC's). These detectors are characterized by a good energy resolution of 10% at 6 keY. They consist of two systems each with effective area of 320 cm2 . One system -A - is of 3 ~ 1 (FWHM) hexagonal field of view, and the other system - B - is of 2 ~ 6. Here we present the observational results of three AGN's, PKS 2155 - 304 (BL Lac object), Centaurus A (NGC 5128; radio-galaxy), and IC 4329 A (type 1 Seyfert galaxy), observed with the system A GSPC's from October 1983 to June 1984.

2. Observational Results and Discussion

2.1. PKS 2155 - 304

On 1 and 3 October, 1983, TENMA observed the BL Lac object PKS 2155 - 304. Each observation consisted of 4 and 5 satellite orbits, with exposure times of 3752 s and 2752 s, respectively. Subtracting the off-source background we obtained the net X-ray intensity from 2 to 6 keY in each satellite orbit. The light curve is shown in Figure l(a). The average intensity from 2 to 10 keY in each day is 8.6 and 8.8 x 10 - 11 erg s - 1 cm - 2,

which are comparable to the intensity found in 1978 by HEAO-1, but three times larger than that in 1979 by HEAO-2. An intensity variation by a factor of two on a time-scale of five hours is clearly seen on 1 October. This time-scale of intensity change is shorter than a change by a factor of two in a day observed in 1978 by HEAO-1 (Snyder et aI.,



186 S. MIYOSHI ET AL.

PKS 2155-304 TENMA 1983

8 t 2 -6 keY

NE t t t f f j '-!

f

u Q)

t Vl

"- 4 Vl

C ::J 0

"'u '0

0 ' (

'2 18 24 ' I

12 18 24 hours

Oct. 1 Oct. 3 (a)

101 PKS 2155 -304 I I I

'I=ij'; + ~

'v) 102 -N r- -+ IE

-I-u -+-

(f) + Z + 0

103 ++ I- -0 -

::r: +t-t+ a...

>< ttt :::J 10 4 .....I - -

IJ...

Z 0 I-0

16 5 ::r: r- -a...

106 I L

1 2 5 10 20 50

ENERGY (keV) (b)

Fig. I. X-ray (2-6 keY) light curve (a) and the deconvolved X-ray spectrum (b) of PKS 2155 - 304.

1980; Urry and Mushotzky, 1982) and 40% (1.2-3.5 keY), and 100% (3.5-10.2 keY) changes in eight hours in 1979 by HEAO-2 (Agrawal et ai., 1983).

The energy spectra obtained with the GSPC's were first summed up for each day. Each spectrum can be simulated by a power law. The photon indices c>:, and the

X-RAY OBSERVATIONS OF AGN'S FROM TENMA 187

intensities on 1 and 3 October are not appreciably different from one another. The deconvolved spectrum of the whole data is shown in Figure l(b). The intensity of (8.7 ± 0.4) x 10- 11 ergs- I cm- 2 , and the photon index ex of 2.11 ± 0.19, averaged over the two days are consistent with those of the HEAO-l observation, but differ appreciably from those of the HEAO-2 observation in the lowest activity. We were unable to obtain a significant absorption measure less than the upper limit (20-confidence) of 2 x 1020 H-atoms cm - 2.

2.2. CENTAURUS A

Centaurus A (Cen A) was observed from 30 March to 4 April, 1984. The total exposure time was 55700 s. The mode of observation enabled us to obtain the energy spectra both on and off source, the latter being employed as the background spectrum. During the observation time the intensity of Cen A was rather stable. No rapid change in the X-ray intensity during the observation interval was conspicuous. However, the X-ray intensity gradually increased by 30% over a period of six days. The average flux was (1.34 ± 0.15) x 10 - 10 erg s - 1 cm - 2 in the 2-6 keY band, corresponding to an X-ray luminosity Lx - 2.6 X 1042 erg s - 1 (2-20 keY), assuming a distance of 5 Mpc. The long-term behaviour of the X-ray flux has been summarized by Feige1son et al. (1981). Two enhancements have been observed during 1972-1976, and in 1978-1979. The

, I

10 0 \ > w \ ~

'-u + w (f)

'- + ~ r.n f-

+++ Z ~ 0 U

10-1

{l 10

E ERGY ( K EV )

Fig. 2. The observed pulse height spectrum of Cen A. The solid lines represent the best-fit convolved spectrum and the emission line feature.


present result indicates that Cen A was in a low state during the observation interval in 1984.

The observed pulse height spectrum is shown in Figure 2, in which one sees the feature of the emission line and absorption edge of iron around 6-7 keY. The solid line indicates the best-fit convolved spectrum by a power-law spectrum with a soft X-ray absorption. The iron absorption edge and emission line are indicated using a Gaussian distribution, in the fitting. (Data in the energy range above 3 ke V was used in the fitting.)

The observed spectrum above 3 ke V is well fitted by the above spectrum with the reduced chi-square value of 0.84. The fitting gives the photon index of lI. = 1.69 ± 0.06 and the absorption measure of NH = (1.2 ± 0.1) x 1023 H-atoms cm - 2. This value of lI. is consistent with the previous observations by OSO-8 in 1975-1976 (Mushotzky et al., 1978) and by HEAO-l in 1978 (Baity et al., 1981). It is noted that the data below 3 keY deviate from the fitted spectrum as seen in Figure 2, indicating an excess of soft X-ray emission. The fitting also indicates evidence of the iron line at 6.45 ± 0.23 keY, although the emissions are marginal, with an equivalent width of 84 ± 64 eV. The

fluorescence efficiency, i.e., the ratio of the iron line to the continuum intensity from 7.5 to 30 keY is 1.05 ± 0.80%. The presence of the iron line, though marginal, is not inconsistent with the result obtaiI'.ed by OSO-8 (Mushotzky et al., 1978). An absorption edgeisfoundat7.3 ± 0.2 keV, leading to an iron abundance of Fe/H = (4 ± 2) x 10- 5 .

This value is consistent with the cosmic abundance.

> w ~

'u w (f)

'(f)

Z 18 t-18 :r: a..

10 0

10-1

10

ENERGY (KEV J

Fig. 3. The deconvolved X-ray spectrum of Ie 4329 A observed by TENMA GSPC's. The solid line represents the best-fit spectrum.

X-RAY OBSERVATIONS OF AGN'S FROM TENMA 189

From the EINSTEIN observations (Feigel son et al., 1981) the X-ray flux of Cen A is considered to be emitted mostly from the active nucleus. The photon index observed by TENMA during the low intensity state of Cen A is consistent with those obtained by OSO-8 during the high intensity state, and no evidence for spectral change was obtained during the TENMA observations in spite of the change in total flux by a factor of 0.3. This fact seems consistent with the synchrotron self-Compton model (Jones

et al., 1974; Mushotzky et al., 1978). The 6.4 keY center energy of the iron fluorescence

line implies that the ionization state of iron is lower than FeXIX and, therefore, that the temperature of the reprocessing matter is less than 1 x 107 K.

The observed pulse height spectrum below", 3 keY is difficult to fit consistently with that in the higher energy range. This feature of soft X-ray excess is similar to that observed for NGC 4151 by Holt et al. (1980). As the galactic absorption in the line-of-sight toward Cen A is '" 1 X 1021 H -atoms cm - 2, the absorption measure of 1.2 x 1023 H -atoms cm - 2 can be mostly attributed to Cen A itself. Hence, an inhomogeneity in the density and/or in the abundance of the absorbing matter may cause the observed excess of soft X-ray emission.

2.3. IC 4329 A

IC 4329 A is an extreme type 1 Seyfert galaxy (Disney, 1973). The observation of this source byTENMA was performed on 31 May-5 June, 1984. After careful checking, the on- and off-source data for 16800 s and 9500 s, respectively, were available for the present analysis. Since the time variation was insignificant during this observation, we combined all useful data to derive the energy spectrum. The observed spectrum is shown in Figure 3 and fitted to a power law variation with photon spectral index IX and absorption measure NH • We thus obtained IX = 1.60 ± 0.07 and NH = (9.2:': ~:D x 1021 H-atoms cm - 2 with a reduced chi-square value of 1.0. The energy flux in the range 2-10 keY is obtained as /(2-10 keY) = (12.1 ± 1.6) x x 10 - 11 erg s - 1 cm - 2. This is appreciably higher, and the value of IX is somewhat smaller, than that obtained from the HEAO-l A-2 observations (Piccinotti et al., 1982; Tennant and Mushotzky, 1983; Mushotzky, 1984).

A closer inspection of the observed spectrum indicates the emission and absorption features associated with iron. However, no single peak at 6.4 or 6.7 keY is significant. An upper limit of the equivalent width of either emission line is obtained as 200 keY (30-), in which the red shift of z = 0.0157 (Wilson and Penston, 1979) and the Doppler broadening with 5000 km s - 1 are taken into account.

The present observation of IC 4329 A shows no appreciable flux variation over six days, whereas the flux is higher than that observed by Ariel V (Elvis et ai., 1978) and HEAO-1, but lower than that by HEAO-2 (Petre et ai., 1984). This is a characteristic of Seyfert AGN's, whose X-ray emission does not appreciably change within days but changes on a time-scale of year. Despite the flux variation, the spectral slope seems to be kept nearly constant.


References

Agrawal, P. C, Singh, K. P., and Riegler, G. R.: 1983, Proc. of 18th r.CR.C Bangalore, India, XGl-3. Baity, W. A., Rothschild, R. E., Lingenfelter, R. E., Stein, W. A., Nolan, P. L., Gruber, D. E., Knight, F. K.,

Matteson, J. L., Peterson, L. E., Primini, F. A., Levine, A. M., Lewin, W. H. G., Mushotzky, R. F., and Tennant, A. F.: 1981, Astrophys. J. 244,429.

Disney, M. J.: 1973, Astrophys. J. 181, L55. Elvis, M., Maccacaro, T., Wilson, A. S., Ward, M. J., Penston, M. V., Fosbury, R. A. E., and Perala, G. C:

1978, Monthly Notices Roy. Astron. Soc. 183, 129. Feigelson, E. D., Schreier, E. J., Delvaille, J. P., Giacconi, R., Grindlay, J. E., and Lightman, A. P.: 1981,

Astrophys. J. 251,31. Holt, S. S., Mushotzky, R. F., Becker, R. H., Boldt, E. A., Serlemitsos, P. J., Szymkowiak, A. E., and White,

N. E.: 1980, Astrophys. J. 241, L13. Jones, T. W., O'Dell, S. L., and Stein, W. A.: 1974, Astrophys. J. 188, 353. Mushotzky, R. F.: 1984, Adv. Space Res. 3, Nos. 10-12, 157. Mushotzky, R. F., Serlemitsos, P. J., Becker, R. H., Boldt, E. A., and Holt, S. S.: 1978, Astrophys. J. 220,

790. Petre, R., Mushotzky, R. F., Krolik, J. H., Holt, S. S.: 1984, Astrophys. J. 280, 499. Piccinotti, G., Mushotzky, R. F., Boldt, E. A., Holt, S. S., Marshall, F. E., Serlemitsos, P. J., and Shafer,

R. A.: 1982, Astrophys. J. 253,485. Snyder, W. A., Davidsen, A. F., Wood, K., Kinzer, R., Smathers, H., Shulman, S., Meekins, J. F., Yentis,

D. J., Evans, W. D., Byram, E. T., Chubb, T. A., Friedman, H., and Margon, B.: 1980, Astrophys. J. 237, Ll1.

Tennant, A. F. and Mushotzky, R. F.: 1983, Astrophys. J. 264, n. Urry, C M. and Mushotzky, R. F.: 1982, Astrophys. J. 253, 38. Wilson, A. S. and Penston, M. V.: 1979, Astrophys. J. 232, 389.

LARGE-SCALE CONFIGURATION OF THE MAGNETIC FIELD

IN SPIRAL GALAXIES*

Y SOFUE

Nobeyama Radio Observatory, Minamisaku, Nagano, Japan

U, KLEIN, R. BECK, and R. WIELEBINSKI

Max-Planck-Institut for Radioastronomie, Bonn, F.R. G.


Abstract. Global configuration of magnetic field in several spiral galaxies were determined by analysing characteristic variation of Faraday rotation within the galaxy disks. The majority has an open spiral, bisymmetric field configuration, while some (10-20%) have a ring field.

We propose a simple method to discriminate one of the two major proposed configurations of magnetic field in spiral galaxies, from a characteristic variation of rotation measure and position angle of linear polarization along the major and minor axes. If the variation is anti symmetric with respect to the galaxy center, the field is in a ring-like configuration; while, if it is symmetric, the field is in a bisymmetric, open spiral configuration (Figure 1).

Galaxy

Milky Way' M31 a

M33 a

M51" M81 a

NGC253 NGC2903 NGC6946' IC342

TABLE I

Field configurations in spiral galaxies

Field configuration

BSS (= bisymmetric, open spiral) Ring BSS BSS BSS BSS? BSS BSS? Ring

a See the literature cited in Sofue et af. (1985).



192 Y. SOFUE ET AL.

Min.oxis Min. axis

~+-______ r-____ g_a~la~,y ~;O~

I

Field line

RM ( P. A.l

(0) Ring Field (b) BSS Field

Fig. 1. Two major configurations of magnetic field distribution in spiral galaxies. If the field configuration is ring-like (left), the variation of rotation measure and position angle of linear polarization along the major axis of the galaxy is antisymmetric with respect to the galaxy center. On the other hand, if the field lines run in an open spiral, bisymmetric configuration, the variation is symmetric with respect to the center

(right).

In order to apply the method for the determination of field configurations, we performed intensive measurements of linear polarization at 5 GHz along major and minor axes for ten spiral galaxies using the 100 m telescope in Bonn. Distributions of the polarization intensity and polarization angle along the axes were obtained for the three galaxies, NGC 253, NGC 2903, and IC 342 (Figure 2).

By applying the method proposed in Figure 1, we have derived the field configuration in NGC 2903 to be that of a bisymmetric open spiral, while IC 342 has a more ring-like field configuration. Adding this to the literature data, we conclude that spiral galaxies seem to have either a ring or a bisymmetric spiral magnetic field configuration. Table I shows the field configurations for several nearby spiral galaxies obtained so far.

180

o

90

4

Sp 2

mJy) o

(2a)

MAGNETIC FIELD IN SPIRAL GALAXIES

IC 342

T r • 1

T t ' - '"

0 r 0

0 0

I -15' -10' - 5' o

X

0

I

0

i • + J ~ , , ~ ,

0

0

0 0

I 0

0 0

5' 10' 15 -10' -5'

180' ~~--~--~----,---r---~---'-,

90'

e 0

90'

4

Sp 2 (mJyl

o

(2b)

NGC 2903

o

00

-1 5' -10 ' -5'

o Q 00000000

o X

IS' -10' -5'

o y

o

J t • .

0

o o

o 0

5'

o 00

193

•

0

10'

Fig.2a-b. Variations of the position angle of linear polarization at 5 GHz for spiral galaxies IC 342, NGC 2903, and NGC 253 (filled circles), and the distributions of polarization intensity along the major (X)

and minor (Y) axes.

194 Y. SOFUE ET AL.

Reference

Sofue, Y., Klein, U., Beck, R., and Wielebinski, R.: 1985, Astron. Astrophys. (in press).

CORRELATION BETWEEN THE PHYSICAL PARAMETERS

AND MORPHOLOGICAL TYPE OF SPIRAL GALAXIES*

SUG-WHAN KIM** and MUN-SUK CHUN

Department of Astronomy and Meteorology, Yonsei University, Seoul, Korea


Abstract. From PDS scans of the late-type spiral galaxies NGC 1313, 1365,6946, and 7793, we determine the surface brightness distributions. These distributions enable us to calculate physical parameters such as R:, )i.e' (x-I, )i.o, DIE, C21 , and MIL. The values of some of these parameters were also compiled from other studies, and all were compared with morphological type T. One of the meaningful results shows that there is a certain correlation between DIB and T, which is constant until T:::; I or 2, and then increases sharply for T;:>: 1 or 2. This may support the validity of the intrinsic formation theory.

Some correlations between physical parameters and morphological type T of spiral galaxies have been studied by Freeman (1970), and Yoshizawa and Wakamatsu (1975). However, correlations such as those involving disk to bulge ratio DIB and bulge parameters were found to be poor. These did not help us to understand the structure of disk galaxies. However, we now consider these poor correlations to be due to contaminations coming from the collection of sample galaxies studied by several authors, and some bias in values of the central surface brightness flo.

We have calculated the physical parameters of the four late-type spiral galaxies NGC 1313, 1365,6946, 7793 from their surface brightness distributions (Chun, 1982; Kim and ehun, 1983). The data of the earlier-type galaxies were obtained by Burstein (1979) and Boroson (1981). All the galaxies from T = - 4 to T = 8 which we have sampled in this paper were scanned by a PDS system, and we assume these data to be homogeneous.

The following results are relevant here, from this study. (1) As for the bulge parameters, even if there are large scatters for the earlier-type

galaxies, the nuclear effective radius R; decreases linearly with increasing T. Moreover, the nuclear effective surface brightness fle' plotted against R;, shows that a smaller nuclear bulge tends to have a brighter fle' This lead us to suggest that the later galaxies' types are, the brighter fle they have. This result is different from the view of Yoshizawa and Wakamatsu (1975) on the properties of nuclear bulges. Judging from this, R; is a concentration parameter in a R 1(4 law, and a possible indicator of quantitative classification, while fle' as a function of R;, shows evidence of a mass segregation effect.

(2) As for the disk parameters, flo tends to be brighter for a larger scale length :J( - 1.

However, because of the large scatter, this result is not conclusive. It is also found that

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** Now at the Korean National Astronomical Observatory.


196

co a 0

~ a: W

9 ::::> co

~ ~ en (5

SUG-WHAN KIM AND MUN-SUK CHUN

25r-----~------~----.n_~

20

15

10

5

o Burstein

• Boroson

6£6

7793 .. ,

+ t f • O~--~~------~~------~ 4 0 5 W

MORPHOLOGICAL TYPE T

Fig. I. The disk to bulge ratio DIB plotted against the morphological type T with the results of Burstein (1979) and Boroson (1981).

Freeman's type-I galaxies are distributed at nearly constant J.lo, while type-II galaxies are located at nearly constant r:I. - 1. That the type-II galaxies are brighter than the type-I galaxies is the same result as was found by Freeman (1970). Freeman (1970) insisted on theuniversalityofJ.lo = 21.65 ± 0.30(0) mag. s -2for 28 galaxies from SO to 1m. But different J.lo values; which are 21.28 ± 0.71(0-) for Yoshizawa and Wakamatsu's (1975) 24 galaxies, 21.83 ± 0.68(0) for Kormendy's (1977) 8 galaxies, 20.88 ± 0.50(0-) for Burstein's (1979) 12 galaxies, and 21.79 ± 0.78(0-) for Boroson's (1981) 15 galaxies; have been obtained subsequently. Our four late-type galaxies give J.lo = 20.32 ± 0.58(0), which is brighter than any other J.lo values. This may suggest that there is no universal value of J.lo in late-type galaxies.

(3) The disk to bulge ratio DIB has a strong correlation with T, which is constant for T s:; 1 or 2, but increases sharply after that (Figure 1). This result is consistent with Yoshizawa and Wakamatsu's (1975), but not Freeman's (1970). The different tendency between SO and spiral galaxies implies (i) T = 1 or 2 is a possible division between two sets of disk galaxies; (ii) using DIB it is difficult to divide the SO galaxies into subgroups,

PARAMETERS AND THE TYPE OF SPIRAL GALAXIES 197

while the spiral galaxy group can be sub-classified through DIB; and (iii) the validity of the intrinsic formation theory, which was once suggested on the thesis of a limited number of samples by Burstein (1979) and Boroson (1981), is also supported by the results on our four late-type spiral galaxies.

References

Boroson, T.: Astrophys. J. Suppl. 46, 177. Burstein, D.: 1979, Astyophys. J. 234,435. Chun, M. S.: 1982, J. KoY. Astron. Soc. 15,41. Freeman, K. c.: 1970, Astrophys. J. 160,811. Kim, S. W. and Chun, M. S.: 1984, J. KoY. Astron. Soc. 17,23. Kormendy, J.: 1977, Astrophys. J. 217,406. Yoshizawa, M. and Wakamatsu, K.: 1975, Astron. Astrophys. 44,363.

GLOBAL INSTABILITY OF THIN STELLAR nISCS*

TAKAO FUJIWARA** and SHUNSUKE HOZUMI

Department of Astronomy, University of Kyoto, Kyoto, Japan


Abstract. We have determined the dominant global modes of stellar discs by integrating the linearized collisionless Boltzmann equation. The models examined are the Kuzmin discs with two types of the distribution function. It is found that the growth rate correlates well with the central value of Q.

We use a new method to find the dominant unstable modes of stellar discs. The method consists in integrating the linearized collisionless Boltzmann equation numerically. The dominant mode can be determined by solving the equation as an initial value problem until the perturbation has come to show an exponential growth. We checked the accuracy of the method by comparing our results for the isochrone disc with those of Kalnajs's modal analysis (reported in Zang and Hohl, 1978), relative errors in the growth rate and pattern speed being less than 1 %. (The details of the method will be published in a separate paper.)

We here examine two-armed modes of the models which have the surface density distribution of the Kuzmin (1956) disc (or Toomre's (1963) model 1), written as Jl(r) = (2n) - 1 (1 + r2) - 3/2 in suitable units. Two types of distribution function are examined. Miyamoto (1971) has given a family of distribution functions for this disc which has Q's rising with radius. Kalnajs (1976) has also given equilibrium disc models having nearly constant Q's. In both cases, the distribution function is specified by a model parameter (see Figure 1(a)). The retrograde component of the distribution function is introduced in such a manner,described in Nishida et al. (1984), that needs no additional parameter.

The growth rates and pattern speeds of the dominant modes are plotted in Figure 1(b). It can be seen that the growth rate correlates surprisingly well with the central value of Q. This is consistent with the N-body analysis of the Kuzmin disc with softened gravity by Athanassoula and Sellwood (1983), though they found the tightest correlation with the fraction of mass on 'nearly circular' orbits. The correlation between the pattern speed and the central value of Q is not good: the modes of Miyamoto's models have lower pattern speeds and, therefore, larger co-rotation radii, for the same value of Q at the centre. The appearance of every dominant two-armed mode was that of a trailing spiral.

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. ** Present address: Kyoto City University of Arts, Kyoto, Japan.


200

Q

T. FUJIWARA AND S. HOZUMI

5 (0)

4 Miyamoto 2

~/ / /

/ / / / /

/ / / / / /

/ //// / / /

/ //~ / //

3

/;/~/ Miyamoto 4 // /

/~/// 2

",,// ,/ ., ., '" ~

~

o o 2

[ Kalnajs6

\' Kalnajsl0

3 4 5 6

0.5

(b)

x

0.4 x Pattern

0 x speed

x

0.3 0 x x

" 0.2 x

Growth ~

rate x

0.1

0.0 1.0 1.2 1.4

Q(r=O) 1.6

Fig. I. (a) The runs of Q for Miyamoto's functions with parameters 2-4 (dashed lines) and for Kalnajs's functions with parameters 6- I 0 (solid lines). (b) Growth rates and pattern speeds of the dominant two-armed modes for Miyamoto's functions (circles) and for Kalnajs's functions (crosses), plotted against

the central value of Q.

It can be concluded from our results that the growth rate of instabilities is sensitive to the central part of the disc, and that a tight correlation exists between the growth rate and the central value of Q as far as the present models are concerned. It remains unclear whether these conclusions can be generalized to discs with different mass distributions, and with different forms of the retrograde part of the distribution function.

Acknowledgements

The authors wish to thank Professor S. Kato for continuous encouragement. They are grateful to Drs S. Inagaki and M. T. Nishida for fruitful discussions. Numerical computations were carried out on a F ACOM VP 100 at the Data Processing Center of the Kyoto University.

References

Athanassoula, E. and Sellwood, J. A.: 1983, in E. Athanassoula (ed.), 'Internal Kinematics of Galaxies', f A U Symp. 100, 203.

Kalnajs, A. 1.: 1976, Astrophys. J. 205, 751. Kuzmin, G. G.: 1956, Astron. Zh . 33, 27. Miyamoto, M.: 1971, Publ. Astron. Soc. Japan 23, 21. Nishida, M. T. , Watanabe, Y., Fujiwara, T., and Kato, S.: 1984, Publ. Astron. Soc. Japan 36, 27. Toomre, A.: 1963, Astrophys. J. 138, 385. Zang, T. A. and Hohl, F.: 1978, Astrophys. J. 226,521.

A MATHEMATICAL MODEL OF THE INITIAL STAGE IN THE

FORMATION OF A DISK GALAXY*

B.BASU

Department of Applied Mathematics. University of Calcutta. India

(Received 14 August, 1985)

Abstract. The collapse of a homogeneous, initially spheroidal halo under self gravitation, has been considered. It is found that a weak magnetic field (as is plausible to belong to such a cloud) has little influence on the collapse, except probably sufficiently close to the centre where the gas density, and consequently the magnetic field, becomes rather high. The equatorial collapse is centrifugally balanced at a certain stage, while collapse in the perpendicular direction continues. A thick stellar disk is formed within a time-scale < 3 x 109 yr. Brisk star formation takes place while the collapse of the gaseous disk is still in progress. This gives rise to the halo stars with low metal content and high Z -motion. A bulge is formed at the centre simultaneously. This is the first phase offormation of a disk galaxy. The thin disk is formed at a later stage as the remaining primordial gas and the gas released by the evolution of stars in the thick disk gradually settles on to it.

The presented model is rather a crude one. Many aspects have not been considered, and many details have not been worked out. It is hoped that a more detailed and comprehensive model will be arrived at in the future.

1. Introduction

The problem of how galaxies are formed out of the primordial cosmic gas in general, and how they are formed as different Hubble classes in particular, has recently evoked great theoretical interest among astronomers. During the last decade a large number of models for galaxy formation have been proposed, each with differing viewpoints depending on the observational phenomena sought to be explained, and the physical situations under which the collapse of the protogalaxy has to proceed. The epoch of star formation, and the specific angular momentum of the gas at that epoch seem to be very important in deciding which Hubble class the galaxy will belong to. The disk galaxies, in particular, by virtue of their many interesting observable characteristics, and the marks of a spread of age stamped on their different components, have attracted the keen attention of authors of theoretical investigations (e.g., Brosche, 1970; Sandage et ai., 1970; Larson, 1976; Gott and Thuan, 1976; Tinsely and Larson, 1978; Ostriker and Thuan, 1975; Fall and Efstathiou, 1980; Silk and Norman, 1981; Kashlinsky, 1982; Jones and Wyse, 1983; Wang and Scheuerle, 1984).

Various collapse models have been considered so far. In most cases, a spherical collapse of the halo with some power law distribution of the form r- n (including n = 0) for its density has been chosen. The collapse of a non-spherical massive halo has



202 B. BASU

recently been considered by Jones and Wyse (1983). As the collapse continues, the kinetic energy of the gas motion is thermalized. But Rees and Ostriker (1977) have shown that clouds of galactic masses (10 1°_1012 M 0) cool so efficiently that the collapse can proceed strictly at the free fall rate. It is believed that the star formation follows in quick succession.

That the contraction from a spherical or spheroidal configuration of a protogalaxy to a thick disk, populated by the halo stars, and then to a thin disk, containing gas and later generation stars, proceed rather quickly was proposed long ago by Sandage (1963). For the observational support of this viewpoint, he found the age difference between the oldest halo clusters and the oldest cluster in the thin disk (e.g., M67; NGC 188) to be practically nil. In particular, the formation of the thick disk by free fall or nearly free fall collapse, and the occurrence of star formation in quick succession appears to be certain from the observed fact that the metallicity gradient among these stars is practically non-recognizable (Jones and Wyse, 1983).

In the present work we have considered the collapse of a spheroidal gas cloud of uniform density. The cloud is idealized to possess a magnetic field parallel to the minor-axis. Its initial slightly spheroidal shape is due to the small rotation acquired by gravitational interactions with other fellow clouds in its course through space. As the collapse proceeds, the radial collapse is halted at some stage, centrifugally; but the collapse parallel to the minor-axis continues. A disk of thickness equal to a few percent of the original scale is formed within a time-scale < 3 x 109 yr, but before the disk attains such a configuration brisk star formation takes place in it. This is the thick disk containing the 'halo stars', all formed within a time-scale which is shorter than the time-scale of evolution of these stars. Such a picture explains the homogeneity of age among these stars. The remaining virgin gas forms the thin disk subsequently. This thin disk is enriched gradually by the metal rich gas left in course of evolution of the stars in the thick disk.

The central part of the spheroid will condense more rapidly and independently of the outer parts of the disk, attaining a centrifugally balanced structure with a mass of the order of 10% or so of that of the cloud. This component gradually develops as the bulge of a disk galaxy through star formation.

2. Collapse of a Massive Rotating Gaseous Cloud

We consider the collapse mechanism of a spheroidal gas cloud which is rotating about the minor-axis. A magnetic field, unless sufficiently high initially, does not significantly influence the gravitational collapse of a rotating body until its density increases to a large value. We assume first, therefore, that the influence of the magnetic field can be neglected. The relevant set of equations for our problem are the equation of momentum conservation, the equation of mass conservation, and the equation of state. We assume cylindrical symmetry and neglect the gas pressure gradient in comparison with the gravitational and centrifugal forces. The equatorial collapse is halted when the radial

FORMATION OF A DISK GALAXY 203

attraction is balanced by the centrifugal force. For an oblate spheroid, this is given by

~ 3GMr c [na - lJ, 2a4 4c

(1)

where a and C are the semi-axes of the spheroid; M r , its mass up to a radial distance r measured in the z = 0 plane; G, the constant of gravitation; and w(r) is the angular velocity at r; Fr being the radial force, since

cot -I because c < a .

When the body contracts, angular velocity w increases due to conservation of angular momentum. So a stage will come when w will exceed the limit given by (1) and the collapse in the equatorial plane will be halted. Subsequently, the collapse will proceed along the axis of rotation and the body will continue to flatten. As the body flattens, the mass conservation will yield

2 2 P /32 ~ pa C = poaoco or - = -, (2) Po c

where 1//3 = a/ao is the radial shrinkage factor, when the equatorial collapse has ceased (here the subscript zero stands for the initial values).

At any time when the value of Zo at any point has reduced to Z, we have

~ = ~ = /32 Po Zo Co P

(3)

by (2), and the time, taken when the initial gas spheroid flattens to about 10% of its initial thickness is given by

,= dZ (4)

[ p {Zo (1 _ g 10g(/32Zo/Z )) _ ~}JI/2 Z P Zo/Z Zo

Z ~ ZollO

where P = l2GPoZ~K and Q = 2RT, R being the universal gas constant and T the temperature, assumed here to remain constant. K is a positive fraction given by

0.25 < K = (1 -~ cot- I ~) < 1 ;

204 B. BASU

K thus gives a measure of the flattening. The relation (4) is obtained by some algebraic simplification of the integral of the equation of Z-motion which is

P - 2RT log- , Po

and using (3). If we assume that Po ~ 10 - 27 g em - 3 and Zo ~ 1023 em, T ~ 103 K (Hoyle, 1953),

then (4) yields

1.26 x 109 yr < r<2.6 x 109yr. (5)

Thus, a massive rotating cosmic gas cloud collapses to a thick disk like that of a disk galaxy in a time-scale of the order of 109 yr.

We can now investigate whether the star formation process continues simultaneously with the process of formation of the thick disk. The relevant equation for examining this, is

(6)

which is obtained from the equation of Z-motion using relations (1) and (3). Solution of this equation yields that the gas density P greatly exceeds the initial density Po within the same time-scale as given by (5). This implies that star formation almost certainly takes place during the time of formation of the thick disk. But, because of the presence of the rotational velocity, the process of star formation is rather less efficient than in elliptical galaxies, so that much of the virgin gas still remains to form the thin disk of the galaxy soon after (Wang and Scheuerle, 1984).

3. Condensation of the Bulge

We assert that during the process of the formation of the thick disk, the central bulge is formed independently, and more quickly, by virtue of the rather higher density of gas actually prevailing in the central region. The central condensation does not follow the same geometry as the outer disk of the galaxy.

Considering the virial equilibrium of a gaseous body, we have the relation

(7)

where Tm = !/w2 = K.E. of the rotating mass; Tk = ~(MRT/I1) = K.E. of molecular motion; JIt = MH2j8np = magnetic energy; and n is the potential energy. / is the moment of inertia of the body and other symbols have their usual meanings.

FORMATION OF A DISK GALAXY 205

In the spheroidal system

where

is the eccentricity of the spheroid. Writing M = ~npa2c, we find that

where

¢ = cot - 1 C _ ~ (a2 _ C2)1/2 . (a 2 _ C2)1/2 a2

For a sufficiently flat system e ;;:; 0.8 and ~ ---> ~n, and we have I = tMa2 •

Substituting these values in (7) we obtain the critical mass Me for gravitational stability as

(8)

where we have assumed T ~ 1000 K, ao = Co = 3 X 1022 cm (initial size of the central condensation), and a = 2c = 2 kpc (final size of the bulge).

We have also taken w ~ 8 x 10 - 16 S - 1 (Spitzer, 1968), as the value for our Galaxy. Considering conservation of the spheroidal mass, which yields p ex r- 2 Z - 1, and

conservation of the magnetic flux, given by Hex r- 2, we obtain Hex pZ = const. = Ho. Ho has been calculated to be about 5 x 10 - 8 G, assuming isotropic collapse in the

initial stage of the extended gas cloud (where we take Hex p2/3) and using the relation given by H ~ 6.25 X 10- 5 G when p = 30 hydrogen atoms (Spitzer, 1978).

The substitution of these values in (8) yields

Me ~ 2.0 X 109 Mo.

Thus, a rather large stable mass may condense independently at the centre, in the initial stage. This mass may be still higher if the magnetic field be higher than was assumed here. With the addition of more mass to it as the outer body continues to collapse, the inner body will ultimately give way to fragmentation leading to the formation of stars in the bulge. With a sufficiently high magnetic field close to the centre, even the formation of a massive non-stellar condensation is likely and it may persist.

206 B. BASU

This corresponds to the concept of a superdense non-stellar core as is believed to exist at the centres of disk galaxies. These bodies are believed to be the seats of the high energy activities observed in such galaxies.

Acknowledgement

The author wishes to express his thankfulness to Dr Tara Bhattacharyya for her assistance in the preparation of this work.

References

Brosche, P.: 1970, Astron. Astrophys. 6, 240. Fall, S. M. and Efstathiou, G.: 1980, Monthly Notices Roy. Astron. Soc. 193, 189. Gatt, J. R. and Thuan, T. x.: 1976, Astrophys. J. 204,649. Hoyle, F.: 1953, Astrophys. J. 118,513. Jones, B. J. T. and Wyse, R. F. G.: 1983, Astron. Astrophys. 120, 165. Kashlinsky, A.: 1982, Monthly Notices Roy. Astron. Soc. 200, 585. Larson, R. B.: 1976, Monthly Notices Roy. Astron. Soc. 176,31. Ostriker, J. P. and Thuan, T. x.: 1975, Astrophys. J. 202, 353. Rees, M. J. and Ostriker, J. P.: 1977, Monthly Notices Roy. Astron. Soc. 179, 541. Sandage, A.: 1963, Ann. Rept. Dir. Mt. Wilson and Palomar Observatories, p. 16. Sandage, A., Freeman, K. C, and Stokes, N.: 1970, Astrophys. J. 160,831. Silk, J. and Norman, CA.: 1981, Astrophys. J. 247, 59. Spitzer, L., Jr.: 1968, Diffuse Matter in Space, Interscience Pub!., New York; p. 220. Spitzer, L., Jr.: 1978, Physical Processes in the Interstellar Medium, Wiley Interscience Pub!., New York, p. 243. Tinsely, B. M. and Larson, R. B.: 1978, Astrophys. J. 221, 554. Wang, Y. M. and Scheuerle, H.: 1984, Astron. Astrophys. 130, 397.

EVOLUTION OF DISK GALAXIES REGULATED BY SUPERNOVA

REMNANTS*

YUTAKA D. TANAKA

Department of Astronomy, Kyoto University, Kyoto, Japan

SATORU IKEueRI

Tokyo Astronomical Observatory, Tokyo University, Tokyo, Mitaka, Japan

and

ASAO RABE

Department of Physics, Hokkaido University, Sapporo, Japan


Abstract. Assuming that a disk galaxy is composed of an ambient pervasive gas, small clouds, molecular clouds and stars, its evolution is studied through examining the interchange processes among them. Main results obtained are: (\) The star formation rate is directed by the formation process of molecular clouds. (2) Depending upon the parameters there may be three or four types of evolution of disk galaxies: the no star formation case, the active in the past and inactive at present star formation case, the burst-like star formation case and the very active in star formation case.

In order to make clear the evolution of galaxies, we must know the physical processes in the interstellar medium (ISM), especially, the star formation process. For this purpose, we propose the interchange model in the ISM, which is supposed to be composed of hot gas, warm gas, small clouds and (giant) molecular clouds (Rabe et al., 1981; Ikeuchi et al., 1984). The interchange processes among them include: gas sweeping by supernova remnants, ionization and evaporation of clouds, growth and formation of molecular clouds through cloud-cloud collisions and star formation from molecular clouds. Since these interchange processes are rather complicated, we could only follow the evolution of the ISM for ~ 109 yr in the paper by Ikeuchi et al. (1984). In the present paper, we simplify the fundamental processes by extracting the essential results from the preceding paper, and follow the evolution for 1.2 x 1010 yr.

We assume that a galax:y is composed of four components, which mutually inter-change by the following processes.

(1) Sweeping up of ambient medium(AM) by SNRs. (2) Evaporation of small clouds (SC), and ionization of SC by UV flux. (3) Formation of molecular clouds (MC) by mutual encounters of SCs. (4) Formation of MC by gravitational instability of AM. (5) Erosion of MC by newly born massive stars.



208 Y. D. TANAKA ET AL.

6

Fig. I. Four components in a galaxy and their interchange routes. Each process is explained in the text.

20r--.-Fi~g,2--~'-r--.--'---.--r--.--.---r--' i

a: >......

N U CL

IS

~IO %:

t!> <:> -' 5

L.s t!

i

i i.

! 1 ~ /1 I I i I /I I i I : I I I I I I i L.-.-._. L.m c i I \ I 1 I i 1,/ '7 -.-.-.-._._ I 1'. : r"'j: 'r.": r' I-T---i::---------·=-~:J I_~'i f'-l .-~ t. -. I ! I 1 1 I I. I' I! 'I I, \',. I, ii, ! I' I ' I " L.am I Iii ! i ! i !i U \. ~ \,.-'

°O~~~~~--~--~~~(~X--I~g~02-y-R~)~~~~~120

Fig. 2. A typical evolutionary result for (BURST) case. The surface density of each component is illustrated.

(6) Star formation from Me. (7) Inflow of gas. (8) Mass loss from stars, Summing up the above interchange processes, the time variations of abundances of

respective components are calculable. Since we suppose the initial mass function of newly born stars to be the Salpeter's one, we can calculate the number of massive stars and supernova explosion rate, consistently. As a criterion for the gravitational instability of AM (process No.4), we take the one proposed by Jog and Solomon (1984) as

Lgas> LR == KAV/.j3 nG,

where K is the epicyclic frequency, A and v are measures of the inhomogeneity of the

EVOLUTION OF DISK GALAXIES

20'--'--'-~~j~~--'--'---'--r--r--.--'

Lst :

~1 5 a:: >-

" '" u ... ~lO :<:

W <..0 o ...J 5

! / /

! /

//_._.-._._._.~:c_ . I // ! -._._.-.-.-._ 1 .1 ! .-.-._._ 1.1 i L sc . ~_Ir-------------___________________ _ ! / ! / Lam I:

°O~~~2~O~-L~4~O--~~.--L~~~-'~--~~120

a:: >-" N U ...

15

';;10 :E

l!)

o ...J 5

Fig. 3. The same as in Figure 2 but for (INSTA) case.

Ls t Lm e I .. .. ..:.. .. --: . -

Fig. 4. The same as in Figure 2 but for (NOSTAR) case.

209

disk and the random velocity of the gas component, respectively. Therefore, if the surface density of the gas exceeds the critical one, the instability produces abundant molecular clouds which leads to an efficient process of star formation . On the other hand, if the surface density of the gas is small, the formation of molecular clouds (and therefore, the formation of stars) is dominated by mutual collisions of small clouds. If the cloud density is very small, this collision time becomes too long to make molecular clouds. From this consideration, we can classify the evolutionary features into four types as summarized in the following:

NOSTAR: The case where the (surface) gas density is too small to make stars, because the collision time of clouds is longer than the lifetime of a galaxy. A typical result is shown in Figure 4, in which time variation of each component is illustrated.

210 Y. D. TANAKA ET AL.

SO: The case where the gas inflow rate has been so high that the star formation was active in the past, but it is inactive at the present epoch because of the deficiency of gas. A typical result is illustrated in Figure 5.

BURST: The case where the gas inflow rate is so high, even at present, that the star formation occurs recurrently, since the condition Lgas > LR is recurrently satisfied. A typical result is shown in Figure 2.

INSTA: The case where the condition Lgas > LR is always satisfied, because the gas inflow rate is so high and/or the critical surface density LR is so low. A typical result is shown in Figure 3.

20r-",-.!.-,\.-~r-.--'--.--''--.--.--.--;

i \

~15 0:: >.....

'"

i \ i \ i ' , ! Ls t Lmc' i \, _-----------! \ ,.---

u Co.

~IO l:

H

'" o

o i \\ I ~·i-------- .'. I r: Lsc ----_ '. I

...J 5 · I --" · : ----J I I • i : ! · I 1 !j Lam i

o !: . o

Fig. 5. The same as in Figure 2 but for (SO) case.

12Q

The above results would be applicable to the outer regions of our Galaxy (NOSTAR), the SO galaxies (SO), the burst-like star formation, or peculiarly blue, galaxies (BURST), and the active galactic nuclei (INSTA). The solar neighbourhood is between the BURST and INSTA cases, and observational data are well reproduced by the above model. The application of our models to various real galaxies will be presented in future.

References

Habe, A., Ikeuchi, S., and Tanaka, Y. D.: 1981, Publ. Astron. Soc. Japan 33, 23. Ikeuchi, S., Habe, A., and Tanaka, Y. D.: 1984, Monthly Notices Roy. Astron. Soc. 207, 909. Jog, C. J. and Solomon, P. M.: 1984, Astrophys. J. 276, 114.

ON THE EFFECTS OF COMPRESSION OF A GASEOUS DISC BY

THERMAL AND DYNAMICAL PRESSURES OF

INTERGALACTIC GAS*

YASUKI KUMAI and MAKOTO TOSA

Astronomical Institute. Tohoku University. Sendai. Japan


Abstract. We consider a galaxy moving in a cluster of galaxies and study the effects of compression of the gas disc by both thermal and dynamical pressures of intergalactic gas. As the result of compression, massive gas clouds are formed. They are not stripped by dynamical pressure of the intergalactic gas but stay in the galaxy until they are disrupted by formation of massive stars.

Many clusters of galaxies have a hot and rarefied intergalactic gas. For example, in the Coma cluster of galaxies, an extended hot gas whose density and temperature are 10- 3 cm - 3 and 108 K has been detected. A galaxy moving in such a cluster is strongly compressed by thermal and dynamical pressures of the intergalactic gas (intracluster gas). These pressures are strong enough to have a significant effect on the physics and stability of the gas disc of a galaxy. As a galaxy moves in a cluster, the external pressures exerted on the gas disc of the galaxy change according to variations of the velocity of the galaxy and the density of the intracluster gas. The change of the external pressures causes various phenomena in the gas disc. In this paper, we briefly discuss the effects of compression of a gas disc of a galaxy moving in a cluster.

We consider a galaxy moving in a Coma-like cluster of galaxies which has a hot intracluster gas. As a model of the gas disc of a galaxy we consider a gas layer embedded in the gravitational field of a galaxy. We assume that the parameters of the model are the same as those of our Galaxy.

In a cluster like Coma, a typical value of the thermal pressure is about 104 cm - 3 K. This value exceeds that of the thermal pressure of the diffuse interstellar gas in the Galaxy. According to the two-phase model of the interstellar gas (e.g., Field et al., 1968), diffuse HI intercloud gas changes to H I gas clouds, as a result of thermal instability, when its pressure exceeds a certain critical value. In our Galaxy, no intercloud gas is found with a pressure in excess of 3 x 103 cm - 3 K (Myers, 1978), so this value can be regarded as the maximum pressure of the intercloud gas. Therefore, thermal pressure of the intracluster gas alone can force the diffuse gas to take a form of H I gas clouds. This assists the development of a Rayleigh-Taylor instability as stated below.

As the galaxy moves toward the centre of the cluster, the ram pressure increases, because the velocity of the galaxy and the density of the intracluster gas increase toward the cluster centre. As the ram pressure increases, the galactic gas is pushed aside and



212 Y. KUMAI AND M. TOSA

ultimately the front interface between the intracluster gas and the interstellar gas passes beyond the midplane of the galaxy. Consequently a situation is realised where a heavy fluid (interstellar gas, whose mean density is about 1.0 cm - 3) is superposed over a light fluid (intracluster gas, whose maximum density is about 10 - 3 cm - 3 at most) under the gravitational field toward the plane. The Rayleigh-Taylor instability immediately develops in such a situation. As the instability grows, the intracluster gas pushes aside the interstellar gas, and at the same time the pushed interstellar gas drains downward to the plane along the interface. After the instability has fully developed, the interstellar gas is gathered and massive condensations of gas are formed on the plane. This occurs when the ram pressure exceeds 240 (km s I )2 cm - 3. The minimum growth time of the instability is several times 107 yr, and the corresponding wavelength is about 1 kpc. About 106 M 0 of interstellar gas is gathered to form a massive condensation of gas. Inside the condensation, self-gravitating molecular clouds with masses of 105 Mo will be formed (Blitz and Shu, 1980).

To sweep up such a molecular cloud, a ram pressure exceeding 104 (km Sl f cm - 3

is needed. Such a value is far greater than the ram pressure of intracluster gas, even at the center of the Coma cluster. Therefore, the formation of the massive clouds helps the galactic gas to stand the ram pressure and to stay in the galaxy. On the analogy of molecular clouds in our Galaxy, it is expected that these clouds will be disrupted by massive stars formed within them. The debris of massive clouds, which consists of small clouds and/or diffuse gas, will be swept away immediately by the ram pressure. Thus, just before the disruption of the molecular clouds, the galaxy will show an active formation of stars all over the disc. If the life time of molecular clouds is several times 107 yr (e.g., Bash, 1979), the galaxy loses its gas in a time-scale shorter than 108 yr, after the Rayleigh-Taylor instability is triggered.

If the galaxy is replenished with the interstellar gas from stellar mass loss when it moves out to the outer region of the cluster, the above processes can be repeated when the galaxy returns to the inner region of the cluster.

References

Bash, F. N.: 1979, Astrophys. J. 233, 524. Blitz, L. and Shu, F. H.: 1980, Astrophys. J. 238, 148. Field, G. B., Goldsmith, D. W., and Habing, H. J.: 1968, Astrophys. J. 155, Ll49. Myers, P.: 1978, Astrophys. J. 225, 380.

FORMATION OF COLLIMATED BEAMS*

MASAYOSHIYOKOSAWA

Department of Physics, Ibaraki University, Japan


Abstract. A mechanism is proposed for the formation of collimated beams in radio galaxies. Collimated flows are considered to be non-thermally driven by high energy particles and magneto-hydrodynamic (MHD) waves. The galactic nucleus is regarded as being surrounded by a cool gas. The cool gas accretes onto the nucleus, and then the high energy particles are completely locked to the MHD waves. When a quasi-radial magnetic field is embedded in the accretion flow, the resulting MHD wave packets are collimated into the direction of the symmetry axis of the galactic nuclear disc. The fluid around the nucleus is considered to be accelerated and heated by these MHD waves. The fluid beam is ejected along the symmetry axis.

The magnetic field in an axially-symmetric accretion into a Kerr black hole can be studied in this way. An exact, nonstationary solution for the variation of the magnetic field has been obtained (Yabuki et al., 1986). The magnetic field is considered as 'frozen' in the matter, and homogeneous at the initial moment. The flow, without taking account of the feedback influence of the magnetic field, is assumed to freely fall into the Kerr black hole. Matter falls from rest at infinity with zero angular momentum. The flow trajectory is then radial, in the sense that the latitude e of the falling matter remains constant for all values of e, though the azimuthal coordinate ¢ varies due to the dragging of the inertial frame. The initially homogeneous magnetic field increases with time, changing into a quasi-radial field. The azimuthal component of the field is generated by the rotating accretion matter.

Collimation of the flow energy and momentum may actually be caused in two ways. One is due to the action of MHD waves (Yokosawa, 1982). MHD wave packets propagate into the region where the Alfven velocity is small. The other is due to the geometry of the Kerr space-time. When light rays with an outward direction are emitted near a black hole, they are collimated into the direction of the symmetry axis of the Kerr space-time. The fluid can be accelerated by MHD waves, or radiation pressure.

We have investigated the wave conditions around such a galactic nucleus. If high energy particles are generated in an accretion disc rotating around the proposed black hole, they travel through a magnetized plasma, and generate MHD waves. When the travel velocity of the high energy particles is greater than the Alfven velocity, MHD waves are rapidly enhanced by particle-wave resonance. The MHD waves are damped by the collisions of protons and hydrogen atoms. Resistive and viscous damping also occur. lfthe net damping rate r d becomes much larger than the growth rate r c' the MHD waves are rapidly damped, and cannot scatter the high energy particles. The high energy particles freely stream, and do not transfer their energy and momentum to the



214 M. YOKOSAWA

ambient matter. The region in which this process occur is called the 'free zone'. In the contrary case, r c > r d' high energy particles are completely locked to the waves. This interacting region would then be called the 'wave zone'. When a wave zone is formed around the galactic nucleus, and the mean free path of the MHO waves is comparable to, or longer than, the collimation scale of the flow, the MHO waves can contribute to flow collimation.

We can now investigate a galactic nuclear region which is surrounded by accreting matter. For a reasonable set of parameters, the mean free path can be taken as I ~ 0.1 pc.

A complete set of hydrodynamic equations which describe the energy transfers of high energy particles and MHO waves has been obtained. The high energy particles are assumed to be completely coupled to waves, and supply the energy of the MHO waves. The MHO waves are then damped by thermal gas, and their energy and momentum are transferred to the gas flow. The equation for the gas motion can be expressed as an exact equation of motion averaged over the random phases of the waves.

We have investigated one-dimensional flows which expand toward the symmetry axis of the galactic nuclear disc. The cross-section of the flow is determined by the condition that the expanding flow must maintain its pressure in equilibrium with the pressure of the surrounding matter. It is assumed that the MHO waves and the high energy particles

Fig. I. Schematic illustration of the formation of a collimated beam. High energy particles which are represented by the symbol Ef) are generated in the galactic nuclear disc. Magnetohydrodynamic (MHD) waves are enhanced by the high energy particles. The propagations of the MHD wave packets are displayed by the wavelike lines. The quasi-radial magnetic field which is displayed by the dash-doted lines is formed around galactic nucleus by the accretion flow. The wave zone, which is the dotted area, is confined by the accreting matter. The upper hatched area is the accreting matter region and the lower hatched area is the

disc region.

FORMATION OF COLLIMATED BEAMS 215

are confined within this fluid flow. The external magnetic field is taken to have a direction parallel to that of the flow velocity. We adopt the pressure distribution of the accretion flow for that of the surrounding matter.

The flow structures have been obtained by numerical calculation of the flow equations. The Mach number M is found to increase along the symmetry axis. The cross-section of the one-dimensional flow decreases when M < 1, and increases when M> 1. The MHD waves accelerate the flow and make the flow radius to become narrower in the supersonic region. When the wave pressure becomes stronger than the fluid pressure, the flow radius tends to be nearly constant. When a large amount of wave energy is transferred, therefore, collimated beams with high density and hypersonic velocity are formed.

The MHD waves act on the thermal gas not only as an external force, but also as a heat source. When the waves act on the fluid mainly as an external force, they effectively increase the momentum density of the fluid. In the contrary case, the fluid is heated and the cross-section of the flow becomes very large. The flow structures, therefore, depend on the wave conditions. When the Alfvenic Mach number of the flow is larger, the flow radius becomes smaller. In the case of a weak magnetic field embedded in the flow medium, a narrow beam can be formed. The damping length of the MHD waves varies along the flow. When this length becomes short at some region far from the ejection point, damping, due to the resistivity, becomes larger along the collimated flow, and the collimated beam re-expands broadly.

On this basis of a collimated beam driven by high energy particles, the morphology of extra-galactic radio sources can be discussed. In the case of a flow with very small damping rate due to the resistivity lJoule' the collimated beam may form the classical double radio source, because the collimated beam will interact with the intergalactic medium before the rate lJoule becomes very large. A small value of lJoule refers to a beam with a weak magnetic field or a hot gas. It is suggested that a beam from a hotter galactic nucleus would correspond to the classical double radio source, while that from a cooler galactic nucleus would form the 3C31 type radio source.

References

Yabuki, Y., Yokosawa, M., and Ishizuka, T.: 1986, in preparation. Yokosawa, M.: 1982, Astrophys. Space Sci. 84,225.

ELECTRON-POSITRON PAIRS IN A MILDLY RELATIVISTIC

PLASMA IN ACTIVE GALACTIC NUCLEI*

FUMIO TAKAHARA

Nobeyama Radio Observatory, Tokyo Astronomical Observatory, University of Tokyo, Nobeyama, Minamimaki, Nagano, Japan

and

MASAAKI KUSUNOSE

Department of Astronomy, University of Tokyo, Bunkyo-ku, Tokyo, Japan


Abstract. We investigate the electron-positron pair concentration in an optically thin mildly relativistic plasma which is supposed to exist in active galactic nuclei. Firstly the equilibrium concentration is calculated when copious soft photons are supplied through the cyclotron higher harmonics. It is shown that the attainable states of the plasma are strongly restricted. Secondly we examine the pair production in a hot accretion plasma around a massive black hole, comparing relevant time scales. We find that significant pair production occurs when the accretion rate is moderately high and the infall velocity is slow compared to the free fall.

1. Introduction

Recently relativistic and mildly relativistic plasmas have received much attention in connection with active galactic nuclei (see the references). It is recognized that electron-positron pair production strongly affects the thermal and dynamical properties of such plasmas. In this report we discuss the pair concentration in an optically thin, mildly relativistic plasma with magnetic fields, where hard photons are produced by the unsaturated Comptonization of soft photons, which are supplied by the cyclotron higher harmonics.

2. Equilibrium Pair Concentration

The equilibrium pair concentration, for a static, homogeneous plasma of a finite size, may be calculated by equating the pair creation rate to the pair annihilation rate. Parameter values such as the electron temperature T * == kTelmec2, the proton number density N, the pair free optical thickness to the Thomson scattering 'N == NaTR and the strength of the magnetic fields B are initially given. We assume the charge neutrality. To obtain the pair concentration we must determine the photon spectrum simultaneously. As for the photon processes we take into account bremsstrahrung, cyclotron higher harmonics and Compton scattering.

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984


218 F. TAKAHARA AND M. KUSUNOSE

4

1/4

3 112

>. 01 2 0

2

3

0

-3 -2 -1 0 log TN

Fig. I. Equilibrium pair concentration y == n _ IN as a function of TN for constant T * in the case of B = 104 G and N = 1011 cm - 3. Here n - denotes the number density of electrons.

4

3

>. en 2 0

o -1

LN = 103

o log T",

Fig. 2. Different representation of the same result as Figure I.

ACTIVE GALACTIC NUCLEI 219

Examples of some numerical results are shown in Figures 1 and 2 for N = 1011 em - 3

and B = 104 G. Compared to the results for B = 0, the maximum value of T * decreases from 1.6 to 0.3 for TN = 1 and the maximum value of TN decreases from 4 to 1 for T * = ~. The luminosity is smaller than ~ 1044 erg s - 1 for T * > ~ and N = 1011 em - 3. There also exists a maximum for the strength of the magnetic fields, which turns out to be 1.4 x 104 G for T * = ~, TN = 1, and N = 1011 em - 3. These restrictions imply that we cannot take arbitrary values of T * and TN in fitting observed hard X-ray spectrum to a theoretical spectrum based on unsaturated Comptonization.

3. Pair Production in an Accretion Plasma

When a hot plasma is produced as a result of accretion onto a massive black hole, the plasma is swallowed into the hole in a finite lifetime. In order to obtain significant pair production, we require that the time-scale of pair production tcr should be shorter than that of infall tfall . We assume that the released gravitational energy is first converted to the thermal energy of ions, and then transferred to electrons. The pair creation rate strongly depends on the number density of hard photons, which can create pairs through photon-photon collisions. Ifbremsstrahrung is the only photon source tcr is longer than tfall , unless the accretion rate is near Eddington's critical rate and the infall velocity is as small as 0.1 times the free fall velocity.

However, if copious soft photons are supplied, and hard photons are produced by the unsaturated Comptonization, the essential condition turns out to be that the time scale of Comptonization is shorter than tfall . This condition can be realized for a moderately high accretion rate (~0.05 ~ 0.2 times the critical rate) and slow infall velocity (~0.1 ~ 0.2 times the free fall velocity). These conditions are easily satisfied in popular models of two temperature accretion disks.

References

Kusunose, M. and Takahara, F.: 1983, Prog. Theor. Phys. 69, 1443. Kusunose, M. and Takahara, F.: 1985, Prog. Theor. Phys. 73, 41. Lightman, A. P.: 1982, Astrophys. J. 253, 84. Svensson, R: 1982, Astrophys. J. 258, 335. Svensson, R: 1984, Monthly Notices Roy. Astron. Soc. 209, 175. Takahara, F. and Kusunose, M.: 1984, Proceedings of 'Plasma Astrophysics; Course and Workshop', held at

Varenna, Italy, 28 Aug.-7 Sept., 1984, p. 209.

SIMULATION OF COMPACT GROUPS OF GALAXIES*

TOSHIAKIISHIZAWA

Department of Astronomy. University of Kyoto. Kyoto. Japan


Abstract. Self-consistent simulations of seven groups of galaxies with halos have been performed to find a constraint upon the size of missing halos around spiral galaxies. An initial galaxy, which consists of 100 superstars, has half-mass radius 41 kpc and central velocity dispersion 235 km s - I. The simulations start from the epoch of maximum expansion. The initial conditions involve a variety of spatial distributions of galaxies, and the velocity dispersion of galaxies as would be permitted for maximum expansion. Dense groups having collapse times shorter than (~)Ho- 1 are shown to form multiple mergers in a Hubble time Ho- I.

From a comparison of the frequencies of cD galaxies, or multiple mergers, in observed and simulated groups, it is concluded that the effective radius of missing halos is less than 41 kpc.

1. Introduction

The 'missing halo' hypothesis (Ostriker and Peebles, 1973; Einasto et at., 1974; Ostriker et ai., 1974) has achieved a great success in stabilizing disk galaxies for bar-like deformations, producing flat rotation curves of spiral galaxies and stabilizing groups and clusters of galaxies. However, we know little about the structure of missing halos surrounding spiral galaxies. The only available structural parameter is the (three dimensional) velocity dispersion (J, which is related to the rotational velocity Vrot by the formula Vrot = $. At present we have no information upon the size of missing halos.

In some self-consistent simulations of groups of galaxies, Carnevali et al. (1981) and Ishizawa et al. (1983) have shown that in a Hubble-time huge cD galaxies can be formed in groups slightly denser than the average, if the member galaxies have extended halos. In this paper we further probe this problem to obtain a constraint on the size of missing halos.

2. Simulations

It is assumed that galaxies in a group have already been formed at a phase of maximum expansion. We run simulations of seven groups of galaxies A, B, C, D, E, F, and I. Groups except group I contain 10 galaxies. Group I contains 50 galaxies, Groups A, B, C, and D collapse from the state of maximum expansion with low-velocity dispersions. To see the effects oflarger velocity dispersion (Merritt, 1984), we add Groups E, F,and I. As the initial conditions of group F, we adopt the second maximum-expansion phase of a 10-body collapsing system indicated by a minimum of the velocity dispersion. The same is also done for group I. The physical parameters of the seven groups are given



TA

BL

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The

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ram

eter

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ups

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ies

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atio

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to

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ses.

Rt

" th

e vi

rial

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ius

defi

ned

by R

t, =

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2 /(

-2E

J).

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the

vel

ocity

dis

pers

ion

defi

ned

by V

J =

(

-2E

J/M

)1/2

. T

/, t

he c

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e de

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d by

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=

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in

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10

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49

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I w

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= 0.

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N

N

~ '" :r: N

;,. ::E ;,.

SIMULATION OF COMPACf GROUPS OF GALAXIES 223

R E F

:-.. ' . • .~

T·O. !: .''t ... ToO. o ' ~

T-O. ." • ' .. . "'-)0; .. '

." r",: , ~ T-16 . .' T=20 . T~ 16 . ~

.,,,, ...:.' - :,,:C •

~, .......

To3B . • 1=35 . T= 3~ . :It, "

Fig. I. Projected views of groups A, E, and F at the maximum expansion (t = 0) and at the present times for h = 0.8 and 0.5, All stars are plotted in the left hand of each figure. Only 'core' stars are plotted in the right-hand side figure. The core is defined by the ten most strongly bound stars of the original members of

each galaxy.

I

. ~~'"

Fig. 2. Projected views of group I at the maximum expansion (t = 0), at the present time for h = 0.8, and at the last computed time. The others are the same as in Figure I.

m Table 1. Units of mass, length, velocity, time are 1.4 x 1012 Mo, 100 kpc, 245 km s - I, 4.0 X 108 yr. The initial galaxy has a half-mass radius 0.41 (41 kpc) and central velocity dispersion 0.96 (235 km s - 1). The latter corresponds to the rotational velocity of a spiral galaxy of some 190 km s - 1. The Hubble constant is expressed as Ho = lOOh km s - IMpc - 1. It is assumed that 0.5 :::; h :::; 0.8.

224

1000

LOGV

100

0 . 1

T.ISHlZAWA

1

LLlGRH Fig. 3. Virial diagram for Geller-Huchra's (1983) groups. The ordinate is the three dimensional velocity dispersion in km s - '. The abscissa is the virial radius in Mpc, multiplied by h = Ho/IOO. The virial radius is twice the mean harmonic radius defined by Huchra and Geller (1982). The loci of groups A, E, F, and I are obtained from the projected positions and line-of-sight velocities of galaxy cores at 13:S; t :s; 14, 10 :s; t :s; 11, 9 :s; t:S; 10, 9 :s; t:S; 10, respectively. The loci of poor cD clusters are also plotted. The data for MKWIs, AWMI, AWM7, MKWI, MKW4, MKWI2, AWM3 (0) are taken from Beers, Geller, Huchra,

Latham and Davis (1984). The data for A2666 (6) are obtained from Hintzen's (1980) redshift data.

The dynamical evolution of the groups are followed from maximum expansion (t = 0) to the present time (t = Ho- 1 - T c*/2) using Aarseth's (1972, 1979) N-body code. Here Tc* is the collapse time for a group whose galaxies are assumed to be point masses. Figure 1 shows the projected views of groups A, E, and F at t = 0 and at the present times for h = 0.8 and 0.5. Figure 2 shows the projected views of group I at t = 0, at the present time for h = 0.8, and at the last computed time. Only 'core' stars are plotted in the right-hand side of each figure. The core is defined by the ten most strongly bound stars of the original members of each galaxy. It is regarded as the luminous part of the galaxy. The merging criterion is that both the distance and the relative velocity of two galaxy cores are less than unity in our units. If h ::; 0.8, the denser groups A, C, D, E, F, and I form multiple mergers in a Hubble time as shown in Figures 1 and 2. Table I gives the epoch of merger formation tm and the elapsed time from the 'Big Bang' to the formation of a multiple merger T~ /2 + tm .

In Figure 3 we plot the virial diagram for Geller-Huchra's (1983) groups. The loci of groups A, E, F, and I are plotted on the same figure. All of them fall along a line of constant density 3Tj2 = Ho-I. Therefore, almost all compact groups with 3 Tc/2 ::; Ho I

SIMULATION OF COMPACT GROUPS OF GALAXIES 225

are expected to form multiple mergers in a Hubble time. This implies that mUltiple mergers or cD galaxies are common in dense groups.

The loci of poor cD clusters are also plotted in Figure 3. It can be seen that these poor clusters occupy the denser region 3 Tel2 :::; Hr; 1. This clearly indicates that violent virialization is essential to the formation of a cD galaxy in a group (Ishizawa et al., 1983). However, Geller-Huchra's groups contain three poor cD clusters (A2666, MKWlO, MKW12), each as a subgroup in a larger group. Probably the frequency of cD galaxies in the region 3Tc/2 :::; Ho- 1 and M:::; 10 14 Mo would be 7% or so. It seems that 'cD galaxies form by some process involving a large element of chance' as suggested by Merritt (1984). This scarcity of cD galaxies requires us to reduce the implied highmerging rate by decreasing the size of halos. Thus, the effective size of missing halos should be less than 41 kpc. Rood (1981) has pointed out that there is the same puzzle about the existence of binary supergiant galaxies at the centers of rich clusters like the Coma cluster, and the survival of galaxies in very compact groups of galaxies.

3. Conclusions

Assuming that 50 km s - 1 Mpc - 1 :::; Ho :::; 80 km s - 1 Mpc - 1, that galaxies in groups have been formed at the phase of maximum expansion with not a large velocity dispersion, and that the central velocity dispersion in the missing halo of an average galaxy is 235 km s - 1, the effective radius (half-mass radius) of missing halos should be less than 41 kpc.

Acknowledgement

We would like to express our appreciation to Dr Sverre J. Aarseth for kindly making his N-body code available to us and for his overemphatic advice.

References

Aarseth, S. 1.: 1972, in M. Lecar (ed.), 'Gravitational N-body Problem', IAU Colloq. 10,373. Aarseth, S. 1.: 1979, in V. G. Szebehely (ed.), Instabilities in Dynamical Systems, D. Reidell Pub!. Co.,

Dordrecht, Holland, p. 69. Beers, T. C, Geller, M. 1., Huchra, 1. P., Latham, D.W., and Davis, R J.: 1984, Astrophys. J. 283, 33. Carnevali, P., Cavaliere, A., and Santangelo, P.: 1981, Astrophys. J. 249,449. Einasto, 1., Kaasik, A., and Saar, E.: 1974, Nature 250, 309. Geller, M. 1. and Huchra, 1. P.: 1983, Astrophys. J. Suppl. 52, 61. Hintzen, P.: 1980, Astron. J. 85, 626. Huchra, J. P. and Geller, M. 1.: 1982, Astrophys. J. 257,423. Ishizawa, T., Matsumoto, R, Tajima, T., Kageyama, H., and Sakai, H.: 1983, Publ. Astron. Soc. Japan 35,

61. Merritt, D.: 1984, Astrophys. J. 289, 18. Ostriker, J. P. and Peebles, P. 1. E: 1973, Astrophys. J. 186,467. Ostriker, 1. P., Peebles, P. 1. E., and Yahil, A.: 1974, Astrophys. J. 193, LI. Rood, H. 1.: 1981, Rep. Prog. Phys. 44, 1077.

MOTION OF QUASAR IMAGES BY GRAVITATIONAL LENS

GALAXIES*

M. FUJISHITA

International Latitude Observatory of Mizusawa, Mizusawa, Iwate, Japan


Abstract. Rotational motions of twin quasar images due to the motion of a gravitational lens galaxy are studied. A weak gravity field and a point mass lens are assumed. Twin images of a quasar appear and rotate when a lens galaxy passes near a straight line connecting the observer with the quasar. The positions and velocities of the quasar images are calculated using various sets of parameters.

Conclusions: (1) Quasar images move a few hundred milli-arc-seconds per year or more, if the lens galaxy passes within a thousandth parsec from the line connecting the observer with the quasar, (2) the distance between the galactic center and the quasar images is about ten kilo-parsec at the most.

As an example, the velocities of 0957 + 561 A, Bl and B2 are calculated. Even the fastest case, they are 1.5,1.8, and 1.6 x 10- 5 milli-arc-second per year, respectively.

1. Introduction

The accuracy of position determinations of celestial radio sources has become the order of a milli-arc sec (mas) using a very long baseline interferometer (VLBI). The reference coordinate system composed of pertinently selected quasars is quasi-inertial. The stability of the positions of quasars, observed with a VLBI, was discussed from the standpoint of structural variations of radio sources (Fujishita, 1983). In the meantime, twin images of a background quasar appeared symmetrically positioned around a galaxy, whose gravitational lens action was studied under the assumption that the galaxy is a point mass. As the galaxy moves near the straight line connecting an observer with the quasar, these images may rotate. In this paper, the apparent motions of quasar images due to a moving gravitational lens are studied from the viewpoint of maintaining a radio reference coordinate system for quasars within a mas accuracy. The positions and velocities of the quasar images are calculated using various sets of parameters.

2. Equations and Characteristics of the Image Motions

The following basic equation is obtained under the assumption of weak gravity in the relativistic theory:

()= 4GM c2 (r' - r)

(1)

where () is the deflection angle; G, the gravitational constant; M, the lens mass; c, the light velocity; and r' - r the impact parameter (see, for example, Peacock, 1983). Figure 1 shows the coordinate system and geometric relations. An x - y plane is



228 M. FUJISHITA

y Q

x

Fig.!. The coordinate system and parameters D, d, M, and (x, y). D indicates the distance between the quasar and the observer. The x - y plane is perpendicular to the straight line connecting the observer with the quasar, and contains the lens galaxy. The origin of the coordinate system in the x - y plane is on the line QO. d is the distance between the observer and the origin. (x, y) is the position of the galaxy with

massM.

perpendicular to the straight line connecting an observer with a quasar. The origin of the coordinate system in the x - y plane is on this straight line. The coordinates (x, y, 0) indicate the position of the centre of the lens galaxy. This galaxy, with mass M, can have some movement in the x - y plane. Any motion of the galaxy in the direction of the observer or the quasar will be disregarded here, because it is not important to our purpose. We take the x-axis to lie along the projection of the galaxy's motion in the x - y plane. d is the distance between the observer and the origin of the coordinate system. D is the distance between the observer and the quasar. Using Equation (1), with the coordinate system and parameters of Figure 1, the following positions and velocities of the twin images are derived:

where

GMd(D - d) A= ,

c2 D(x2 + y2)

B = )1 + 16A.

Y 8y = - (1 ± B) , 2d

(d/dt) x

d

MOTION OF QUASAR IMAGES 229

The characteristics of velocity and position of quasar images may be summarized as

follows (Fujishita, 1984): (1) Any lens motion in the direction of the observer or the quasar has almost no effect on the velocity of the quasar images. (2) The distance

between the observer and the quasar also has almost no effect. (3) The velocity of the quasar images is approximately in proportion to JMjd. (4) If the closest distance between the galaxy and the line connecting the observer with the quasar is less than one tenth parsec, the quasar images move faster than 1 mas yr - J. (5) The mass of the galaxy has an important effect upon the length of the impact parameter. (6) The longest impact parameter occurs when the lens galaxy is halfway between the observer and the quasar. (7) The longest impact parameter is about twelve kiloparsecs.

3. The Velocities of 0957 + 561 A, Bl, and B2

As an example, the velocities of 0957 + 561 A, B 1, and B2 which are known to be images formed by the gravitational lens effect are calculated. The following parameter values have been used:

D = 7.67 X 1025 m, d = 4.26 X 1025 m ,

x = 0.0 m + 8 x 104 m s - 1 t, y = - 4.97 X 1020 m ;

together with the following image positions:

A = (0.0, 2.93) , B 1 = (0.0, - 3.44) , B2 = (0.0, - 3.09) ,

where the unit is arc sec. These values are slightly changed from 'GI only' modes (Young et al., 1980). The calculated velocities of A, B1, and B2 are 1.5, 1.8, and 1.6 x 10 - 5 mas yr - 1, respectively. A clockwise rotation of B around G appears noticeable between radio maps of 1980 (Greenfield et al., 1980) and of 1982 (Burke et al., 1983) by the Very Large Array (VLA) of the National Radio Astronomy Observatory. But such a rotation seems to be not real when set against the above calculation, and taking into account the limit of the VLA resolution.

4. Conclusions

Possible variations of position of quasar images seem to be detectable by current VLBI techniques. But the probability that a galaxy passes sufficiently near the line connecting the observer with the quasar is minimal - quasar images would have to be very close to the galactic center. Thus the galactic gravitational lens effect is not important in maintaining the radio reference coordinate system with mas accuracy, if quasars are selected as fiducial points.

References

Burke, B. F., Roberts, D. H., Hewitt, 1. N., Greenfield, P. E., and Dupree, A. K.: 1983, Quasars and Gravitational Lenses, Univ. Liege, Liege, p. 203.

230 M. FUJISHITA

Fujishita, M.: 1983, Pub!. Int. Latit. Obs. Mizusawa 17, 13. Fujishita, M.: 1984, Pub!. Int. Latit. Obs. Mizusawa 18, 19. Greenfield, P. E., Burke, B. F., and Roberts, D. H.: 1980, Nature 286, 865. Peacock, J. A.: 1983, Quasars and Gravitational Lenses, Univ. Liege, Liege, p. 86. Young, P., Gunn, J. E., Kristian, J., Oke, J. B., and Westphal, J. A.: 1980, Astrophys. J. 244, 736.

OPTICAL IDENTIFICATION OF QSOs WITH FLAT RADIO

SPECTRUM*

YAOQUAN CHU, XINGFEN ZHU

Center for Astrophysics. University of Science and Technology of China. China

and

H.BUTCHER

Kitt Peak National Observatory. Tucson. Arizona. U.S.A.


Abstract. Preliminary results of a program to identifY optically a sample of flat spectrum radio sources are described. The identifications are based only on positional coincidences, and have yielded at least one object with a very high redshift.

Most strong flat-spectrum ac(S!, S2) (= -In(SdS2)/ln( vdv2);:S + 0.5) radio sources can be identified with star-like optical objects. As a part of a program to study the optically faintest quasars, we have identified the objects associated with a selection of previously 'empty field', flat spectrum radio sources from the CHJ sample (Condon et aI., 1977), in which sources stronger than 0.5 Jy at 2700 MHz in the declination ranges - 30 0 < (j < - 4 0 and + 4 0 < (j < + 50 0 are given. Thirty-five 'empty fields' have been studied, by using TV and CCD cameras at the Kitt Peak National Observatory's (KPNO) 4 m telescope. Based on close radio-optical position coincidence, 29 sources have been identified with stellar objects. These identified objects have a steeper radio-optical spectrum index acRO' The statistical results suggest a correlation of radio and optical luminosity.

Seventeen of the new identifications have been studied spectroscopically with the CCD spectrograph on the KPNO 4 m telescope. Seven of them have been confirmed to be quasars. Our identifications do not rely on colour or morphology and, as a consequence, are free from some of the biases of optical quasar searches. This becomes important at large redshifts. One of our new identifications, PKS 0335 - 122 (Condon et al., 1978), has a high redshift Z = 3.45. Figure 1 shows the spectrum of this object, covering the range from about 4500-8000 A at a resolution of ~ 15 A. It clearly shows strong emission features of .4.5412 and .4.6887, the latter being much weaker and broader than the former. These lines have been identified with Lac .4.1216 and CIV .4.1549 with redshift Z = 3.45.



232 YAOQUAN CHU ET AL.

, Ly-a

Ny SilY [NIY] CIY NIY .,. , • * t

4542 4942 5342 5742 6142 6542 6942 7342 7742

o Wavelength ( A )

Fig.!. The optical spectrum of PKS 0335 - 122.

References

Condon, J. J., Hicks, P. D., and Jauncey, D. L.: 1977, Astron. J. 82, 692. Condon, J. J., Jauncey, D. L., and Wright, D. E.: 1978, Astron. J. 83, 1036.

UNITED KINGDOM SCHMIDT TELESCOPE (UKST) OBJECTIVE

PRISM SEARCH FOR QUASARS*

ANN SAVAGE

Royal Observatory, Edinburgh, Scotland, U. K.


Abstract. Several optical techniques are being used to find quasars using UKST direct and objective prism plates. Six already much-s'tudied fields are proposed as 'standard fields' for the comparison of techniques. The completeness of objective prism samples, and their applicability to studies of three-dimensional quasar clustering, are discussed.

1. Introduction

In recent years UKST visual searches for quasars on objective prism plates have yielded more quasar candidates than other methods, because of the large area covered. Candidates are selected both by their ultraviolet excess, as evidenced by their long continuous spectra on the plates, and by virtue of the emission lines seen in their spectra. However, any single optical QSO search technique suffers from subjective and systematically varying selection criteria, which may cause the resulting samples to be up to 50 % incomplete. This results in their limited applicability for studies of red shift cutoffs, cosmology and the collective properties of quasars.

2. Standard Fields

Both Smith (1983) and Veron (1983) advocated that all workers in this field should concentrate their different search techniques on the same areas of sky, so that some of the selection effects could be quantified. Table I provides a list of 6 UKST fields which have been studied extensively for many diverse projects which are suited for further QSO research.

3. Objective Prism Spectra

Savage et at. (1985) have compiled a list of over 100 UKST objective prism selected quasar candidates with slit spectra. Such UKST samples are limited to the magnitUde range 17~ 5 < B < 19~ 5, because of the small dynamic range on the limiting exposure prism plates. For about 60% of the UKST quasar candidates red shifts can be estimated



234 A. SAVAGE

TABLE I

SGP F297 F197 F927 F864 Savage Nl

0053 - 2803 0144 - 40 0200 - 50 1040 + 05 1340 + 00 2203 - 1855

Photoelectric Reid and Hawkins a Savage Peterson Tritton sequence Gilmore a (1978) and Ellis a et al.

(1984) uvx search Campusano Savage and Savage and

and Torres Bolton Bolton (1983 ) (1979) (1979)

Shanks el al. (1983)

Multicolour, Reid and Shanks multiobject Gilmore a el al.

(1983)a Proper motion Murray a Murray Visual prism Clowes and He el al. Savage and Cannon Savage and

search Savage (1984 ) Bolton and He a Bolton (1983) (1979) (1979)

AQD and PRS Clowes Hewett Clowes Clowes Hewett el al. el al. el al. el al. el al. (1984) (1984)a (1984)a (1984)a (1985)

Hewett et al. (1984)

Other 'prism' Tololo CHFT CHFT plates Prism and Grens Grens

Grism Slit redshifts 16 in 2~6 30 in 1 ~23 30 < I ~O 8 in < I ~O Full plate ~35 ~30 ~ 15 ~40 ~20

Variability Clowes and Smith and Savage a Savage a Hawkins a Hawkins a

Galaxy survey Bean el al. Bean el al. (1983) ( 1983)

Various radio Condon Condon Savage Condon Wall el al. Condon survey el al. el al. (1978) el al. (1971 ) el al.

VLA b VLA b VLA b Downes VLA el al. Wall el al. (1985) (1982) VLA Downes (1985) el al.

(1985) VLA (1985)

a Unpublished. b Planned.

UKST SEARCH FOR QUASARS 235

from the emission lines seen in the prism spectra. A comparison can be made between these red shifts and those from the slit spectra; although our slit spectra sample is a very inhomogeneous selection of candidates, and any inferences made should be treated with caution. For 71 candidates with prism redshifts 75% were found to have z> 1.6 and 25 % with z < 1.6. For 22 candidates, where we could not estimate a prism red shift, the slit spectra showed that 28% hadz > 1.6 and 75% hadz < 1.6. Thus 40% of our sample have z < 1.6.

A comparison can be made with the red shift-magnitude tables of Cheney and Rowan-Robinson (1981). In the magnitude range where the UKST samples are most complete, 60% of quasars are predicted to have z < 1.6. Therefore, the UKST searches may have missed one third of such objects. Although such red shift incompleteness hampers studies of the quasar luminosity function, the UKST samples are still well suited to 3D clustering studies, where systematic redshift incompleteness is not a bar.

Figure 1 shows the detailed distribution of red shift differences between prism and slit spectroscopy. Two regions are indicated in this figure: (i) the scatter expected in the red shift differences due to the limited accuracy of red shifts on the prism plates (wavelength errors ± 100-150 A), and (ii) the accuracy needed for valid clustering studies to be made on the 50 Mpc scale (corresponding to lOon the sky; or Az = 0.07 atz = 2,forqo = 0 andHo = 100). The larger differences are due to inherent inaccuracies of assessing the position of the emulsion cut-off, which is used as the wavelength reference point. In some cases this was systematically set some 200 A to the red, giving redshift estimates low by Az ~ 0.25. Some 20% of the redshifts are completely wrong, because an incorrect line identification has been made. However, these prism redshifts can still be used for 3D clustering studies on the 100-500 Mpc scales.

Lya Lya elv ellI] Lya

not not not not not

15 HP MglJ Mgll MglJ elv

10

(prism - slit) redshift difference within prism measurement errors of 150 of z = 2 I I

-0.12 0.12

- 0.15

Accuracy required for 10 Mp, clustering of z = 2

- 0.03 0.03

o Redshift difference

Fig. 1.

0.15

elV Mgll

not not

Lya Lya

0.3

236 A. SAVAGE

4. 3D Clustering Studies

The UKST prism plates cover 40 square degrees, although visual searches are usually restricted to the central 25 square degree area to exclude any effects due to telescope vignetting (Dawe, 1984). At a red shift of 2 this corresponds to a 300 Mpc by 300 Mpc area on the sky. The most effective redshift range is 1.6 < z < 2.8, where we can most easily estimate prism redshifts and where we confirm the candidates as quasars. Over this range we can cover 2000 Mpc in depth, without the vignetting or edge effects suffered by such studies covering similar areas with many plates. The surface density of quasars in this magnitude and red shift range obtained with only prism red shifts (4-8/square deg) is large enough to provide a statistically useful sample. A preliminary 3-dimensional clustering analysis has been applied to the quasars with red shift values obtained from the prism plates in a field at 0112 - 35 (Savage et ai., 1984), in order to search for structure in the Universe with scales of order 100-500 Mpc.

The three coordinates of each quasar are inferred from its right ascension, declination and redshift. k is the reciprocal of the wavelength of the spatial sinusoids employed in the analysis, and Q' gives the strength of any structure. For a perfectly random Poisson process Q' should equal unity, whereas clustering is revealed by high values of Q', falling to unity as k increases (see Webster, 1976). This sample of quasars appears to exhibit clustering with a characteristic cluster dimension of 100-200 Mpc and an average of about 1.5 quasars per 'cluster'.

5. Conclusions

With both low and medium dispersion prisms on the UKST, and utilising IIIa-J and IIIa-F emulsions, we now have the potential to cover a redshift range from 0.3 to 4.7.

2

Q'

o Fig. 2.

UKST SEARCH FOR QUASARS 237

Problems with the variable sensitivity response with wavelength of the IIIa-F emulsion (Simkin, 1984; Savage and Peterson, 1983) can be overcome using automated quasar detection techniques. Such techniques, developed at ROE (Clowes et at., 1984) involving the COSMOS measuring machine and the Starlink computer system can be used to select the quasar candidates from many fields, so that the surface and redshift depths are comparable for the clustering analyses. The future plans for a fibre optic system (Dawe and Watson, 1984) on the UKST provide an ideal widefield capability to give us spectra of 50-100 such candidates a night. Slit spectra obtained in this way will enable clustering analyses to be extended down to the 50 Mpc scales with a higher degree of statistical significance due to the tenfold increase in red shift precision.

Acknowledgements

I would like to thank the UKST staff for taking the superb plate material without which this research would not have been possible.

References

Bean, J., Estathiou, G., Ellis, R. S., Peterson, B. A., Shanks, T., and Zou, Z.-L.: 1983. in G. O. Abell and G. Chincharini (eds.), 'Early Evolution of the Universe and Its Present Structure', TAU Symp. 104,175.

Campusano, L. E. and Torres, c.: 1983, Astron. J. 88, 1304. Cheney, J. E. and Rowan-Robinson, M.: 1981, Monthly Notices Roy. Astron. Soc. 195,497. Clowes, R. G. and Savage, A.: 1983, Monthly Notices Roy. Astron. Soc. 204, 365. Clowes, R. G., Cooke, J. A., and Beard, S. M.: 1984, Monthly Notices Roy. Astron. Soc. 206, 99. Dawe, J. A.: 1984, in M. Capaccioli (ed.), 'Astronomy with Schmidt-Type Telescopes', IAU Colloq. 78, 193. Dawe, J. A. and Watson, F. G.: 1984, in M. Capaccioli (ed.), 'Astronomy with Schmidt-Type Telescopes',

[AU Colloq. 78, 181. Downes, A. J. B., Peacock, J. A., Savage, A., and Carrie, D.: 1985, Monthly Notices Roy. Astron. Soc. (in

press). He, X.-T., Cannon, R. D., Peacock, J. A., Smith, M. G., and Oke, J. B.: 1984, Monthly Notices Roy. Astron.

Soc. 211,443. Hewett, P. c., Irwin, M. J., Bunclark, P. Bridgeland, M. T., Kibblewhite, E. J., He, X.-T., and Smith, M.

G.: 1985, Monthly Notices Roy. Astron. Soc. 213, 971. Savage, A.: 1978, Ph.D. Thesis, Univ. Sussex, Sussex. Savage, A.: 1983, Monthly Notices Roy. Astron. Soc. 203, 181. Savage, A. and Bolton, J. G.: 1979, Monthly Notices Roy. Astron. Soc. 188, 599. Savage, A. and Peterson, B. A.: 1983, in G. O. Abell and G. Chincharini (eds.), 'Early Evolution of the

Universe and its Present Structure', IAU Symp. 104,57. Savage, A., Clowes, R. G., Cannon, R. D., Cheung, K., Smith, M. G., Boksenberg, A., and Wall, J. V.: 1985,

Monthly Notices Roy. Astron. Soc. 213, 485. Shanks, T., Fong, R., Green, M. R., Clowes, R. G., and Savage, A.: 1983, Monthly Notices Roy. Astron. Soc.

203, 181. Simkin, S. K.: 1983, AAS Photo-Bulletin, No. 33, 9. Smith, M. G.: 1983, Proc. 24th Liege Int. Astrophys. Colloq. p.4. Tritton, K. P., Savage, A., and Morton, D. c.: 1984, Monthly Notices Roy. Astron. Soc. 206, 843. Veron, P.: 1983, Proc. 24th Liege Int. Astrophys. Colloq. p.210. Wall, J. V., Shimmins, A. J., and Merkelijn, J.: 1971, Australian J. Phys. Astron. Sup pI. 19, I. Wall, J. V., Savage, A., Wright, A. E., and Bolton, J. G.: 1982, Monthly Notices Roy. Astron. Soc. 200, 1123. Webster, A. S.: 1976, Monthly Notices Roy. Astron. Soc. 175, 61.

OPTICAL IDENTIFICATIONS OF RADIO SOURCES WITH

ACCURATE POSITIONS USING THE UNITED KINGDOM

SCHMIDT TELESCOPE (UKST) IIIA-J PLATES*

ANN SAVAGE

Royal Observatory, Edinburgh, Scotland, U.K.


Abstract. Several programmes are making use of UKST Sky Survey plates to identify southern radio sources. The fine-grain modern plates and accurate radio positions give a much improved identification rate. It seems that it will very soon be possible to determine whether or not there is a quasar redshift cut-off at z - 4. There is an urgent need for more accurate fundamental reference star positions in the South.

1. Introduction

Radio source identification programmes are described which are based on radio samples which have radio positions known to better than 2 arc sec r.m.s. Optical identifications are being made on the basis of radio-optical positional coincidence alone, without regard to colour or morphology, using the UKST IIIa-J sky survey which has a limiting magnitude of22. 5. The use of such radio selected samples circumvents worries about completeness in optical searches for quasars.

2. The Optical Identification Programmes

The Parkes 2.7 GHz selected regions are one complete sample that is being studied (Downes et al., 1985). This comprises six areas of6.5 degrees square surveyed to 0.1 Jy at 2.7 G Hz (Wall et aJ., 1971). This survey contains 178 sources, and our optical identification programme to date has been made using the Palomar Observatory Sky Survey (POSS); John Bolton's Palomar B/UV; and existing UKST equatorial zone J and R plates. Extensive radio observations have been made with the VLA, so that our knowledge of the radio structure is very detailed and we were able to define the expected positions for the optical counterparts to within an arcsec in most cases. 100 sources (56%) have been identified to V;;;; 21; and some 30 CCD frames have been attained on the remaining blank fields. The fraction of sources predicted by the models of Peacock and Gull (1981) to be at z > 3 to 0.1 Jy at 2.7 GHz (Figure 1 of Peacock, 1983) is about 50 %. The importance of the optical data is clear; we only need to show that ;;;; 5 % of the objects have z > 3 and this would immediately indicate a sharp depression of density



240 A. SAVAGE

by a factor ~ 3 from that expected via extrapolation of existing data; if quasars at z ~ 4 exist we should find them; if not, we should have demonstrated conclusively that there is a cutoff in the number density. Already our high identification success rate is an indication that most objects cannot be as distant as predicted. Most identified quasars in this sample have redshifts which are less than 3.

A second programme using accurate positions has been a full sky VLBI survey (Jauncey et al., 1985). Radio positions were measured from the observed delay and fringe rate at 2.29 GHz on an Australia to South Africa baseline. Optical identifications were again based on positional coincidence and were measured from the UKST IIIa-J deep-sky survey plates. The nuclei of extragalactic radio sources are suitable objects to define a precision radio reference frame, since their radio positions may ultimately be determined to milliarcsecond accuracy. Such objects are usually identified with quasars, whose stellar appearance makes them particularly valuable in relating the extra-galactic radio reference frame to the optical reference frames. A candidate list of sources with radio positional accuracy of 0.01 arc sec has already been compiled in the north (Argue et al., 1984). We have selected a grid of 63 sources with correlated flux densities greater than 0.3 Jy at 2.3 GHz as potential candidates for the extension of the list south of declination - 40 0 •

Fig. 1.

Figure 1 shows (as asterisks) our sources on an Aitoff equal area projection of the northern sources. These sources provide an inertial reference frame against which the motions of the Earth, solar system, galactic objects, and spacecraft may be measured.

During the course of the optical position measurements it became clear that the observed SAO star residuals showed a marked dependence on both declination and plate epoch.

OPTICAL IDENTIFICATIONS OF RADIO SOURCES 241

TABLE I

A comparison of observed SAO star residuals as a function of declination for both the POSS and UKST sky survey plates

Dec. 00to-34° -34°to-40° -400to-50° -50 0 to-60° -60 0 to-70° -70 0 to-90°

POSS 0.85(10) UKST 1.21(10) 1.13(9) 0.86(17) 0.94(9) 1.51(12) 2.02(14 )

It can be seen that, over the common declination range (0 ° -t - 34 0), and for the same stars, the POSS residuals are significantly lower than for the UKST plates. This appears to result from the smaller time base over which unmeasured or incorrectly measured proper motions are applied. The UKST residuals increase significantly with declination, rising to 2.02 arc sec south of the declination - 70 ° .

The Tidbinbilla Interferometer (Batty et ai., 1982) is being used to position all the Parkes 2.7 GHz sources south of declination - 30°. First results (Jauncey et ai., 1982) showed that these positions and the UKST plates are well matched for the identification of such sources. The zone - 30° to - 35° has been completed with an identification rate of 65 % which corresponds to a doubling of the identification rate from the original Parkes identifications on the POSS prints. 10% of the Parkes identifications have been found to be incorrect.

For compact sources the ability to identify such radio sources on the basis of positional coincidence alone, without recourse to colour or morphology, is an important feature of radio identification programmes. Identification criteria such as ultraviolet excess and morphology have, in the past, provided serious bias in the resulting red shift distributions. High red shift (z> 2.1) quasars appear red, and have a galaxy type morphology on POSS plates (Savage, 1983). The presence or absence of the strong emission lines, L:x in particular, has a significant effect on the quasar colours and image structure. This is compounded by the presence of the L:x absorption forest and also by any Lyman limit absorption. The density of absorption lines increases with increasing redshift (Peterson, 1983), with the result that the integrated continuum magnitudes on either side of the La emission line differ significantly. For PKS 2000 - 330 these broad band colours show a 1 n; 7 difference. Thus, the most liminous quasar appears as a 17n; 3 object in the red but drops to 19n:5 on the 'blue' UKST IIIa-J plates. Thus we might expect quasars with z> 3.5 to appear ~ 20n;0 rather than 18n;0 on those plates.

A significant fraction of the QSOs identified with flat spectrum radio sources continue to be found at redshifts above 3. PKS 1935 - 692 with a redshift of 3.170 continues the trend, found for the other z > 3 radio QSOs, of having a peaked radio spectrum in the range 1 to 10 GHz (Jauncey et al., 1983). Radio identification programmes based on accurate radio and optical positions form a reliable method for finding more of these, and for determining their spatial and luminosity distributions.

242 A. SAVAGE

3. Conclusions

The three accurate radio positioning programmes described here, and the subsequent optical identification programmes undertaken on the UKST IIIa-J plates, have demonstrated: (i) An improvement in the identification rate afforded by identification by positional coincidence techniques alone on the deeper, finer resolution plate material provided by the UKST. (ii) The potential of medium depth radio surveys to establish the reality of a z ~ 4 cut-off. (iii) The need for fundamental star positions in the Southern Hemisphere.

Acknowledgements

I would like to thank the staff of the UKST for taking the superb plate material without which this research would not have been possible. I would also like to thank my many colleagues, including Anne Downes, John Peacock, and Dave J auncey, for allowing me to summarize results here prior to pUblication. The VLBI and Tidbinbilla programmes are supported by NASF-lOO and the observations are made with the assistance of the staff of NASA's Deep Space Network.

References

Argue, A N., de Vegt, C, Elsmore, B., Fanselow, J., Harrington, R., Hemenway, P., Johnston, K. 1., Kuhr, H., Kumkova, I., Neill, A. E., Walter, H., and Witzel, A.: 1984, Astron. Astrophys. 130, 191.

Batty, M. J., Jauncey, D. 1., Rayner, P. T., and Gulkis, S.: 1982, Astron. J. 87, 938. Downes, A J. B., Peacock,J. A., Savage, A., and Carrie, D.: 1985,Monthly Notices Roy. Astron. Soc., in press. Jauncey, D. L., Batty, M. J., Gulkis, S., and Savage, A.: 1982, Astron. J. 87, 763. Jauncey, D. L., Batty, Savage, A., and Gulkis, S.: 1983, Proc. 24th Liege Int. Astrophys. Colloq. 59. Jauncey, D. L., Savage, A., Morabito, D. D., and Preston, R. A.: 1985, in preparation. Peacock,1. A.: 1983, Proc. 24th Liege Int. Astrophys. Colloq., p. 272. Peacock, J. A. and Gull, S. F.: 1981, Monthly Notices Roy. Astron. Soc. 196,611. Peterson, B. A.: 1983, in G. O. Abell and G. Chincarini (eds.), 'Early Evolution of the Universe and

Its Present Structure', IAU Symp. 104, 349. Savage, A.: 1983, Astron. Astrophys. 123, 353. Wall, J. V., Shimmins, A. J., and Merkelijn, K. J.: 1971, Australian J. Phys. Astron. Sup pl. 19, 1.

FORMATION OF A VOID AND GALAXIES IN A

NEUTRINO-DOMINATED UNIVERSE*

MASA YUKI UMEMURA

Department of Physics. Hokkaido University. Sapporo. Japan

and

SATORU IKEUCHI

Tokyo Astronomical Observatory. University of Tokyo. Mitaka. Tokyo. Japan


Abstract. The recent discovery of the large 'honeycomb' structure of the Universe has triggered many models of the Universe dominated by dark matter. The neutrino-dominated universe is a favorable model for explaining the size of the large-scale structure and the dark matter of the larger scale than the galactic one. Our calculations on the evolution of density perturbations in a two-component universe composed of neutrinos and dissipative gas on a spherically-symmetric model have shown that the galactic scale does correlate the scale of a void of galaxies: if a neutrino has the mass of some tens e V, galaxies of the typical size form surrounding a typical void.

Recently a number of observations on the distribution of galaxies have revealed the large 'honeycomb' structure of the Universe which consists of voids where few galaxies are observed and surrounding sheets or filaments of galaxies. This discovery has stimulated many works on the growth of density perturbations in an expanding universe. Especially, much attention has been paid to explanation of the typical size of the honeycomb -namely, 20-100 h - 1 Mpc in linear dimension - where h is the present Hubble constant in units of 100 km s - 1 Mpc - 1. For such a purpose the perturbation of massive neutrinos is surprisingly successful, because the scale of the first growing perturbation of neutrinos having the mass mv is

;'W1I = 41(mj30 eV)-1 (1 + Z)-1 Mpc,

and it has been reported by Lyubimov et al. (1980) that mv ranges from 20 to 40 eV. Furthermore, the average mass density of neutrinos is presently

Q v = 0.3(mj30 eV)h- 2 ,

in units of the closure density Pc = 3HJ/8nG = 2 x 10 - 29 h2 g cm - 3, so that neutrinos can be a candidate for the 'dark matter' suggested by mass to light ratios of a greater scale than the galactic one.

The nonlinear evolution of density perturbations of such collisionless particles as neutrinos was numerically calculated by means of three-dimensional N-body methods by Centrella and Melott (1983) and Frenk et at. (1983). The numerical results by Centrella and Melott showed that sheets and filaments of collisionless particles form



244 M. UMEMURA AND S. IKEUCHI

in interconnecting dense regions, and spherically symmetric low-density regions also form. It is worthy of note that the high-density regions exhibit more complicated features, while the low-density regions, which originate from negative density perturbations of collisionless particles, appear in simple spherical shapes. These calculations have neglected the effect of the dissipation of baryons, which should actually constitute the luminous matter of galaxies. We can readily include the dissipative effect with a simple one-dimensional model without losing generality, if we concentrate our attention on a spherically symmetric low-density region, namely a void.

The authors (Ikeuchi and Umemura, 1984) have examined the nonlinear evolution of negative density perturbations of a two-component system composed of collisionless particles (neutrinos) and dissipative gas (baryons) by means of a spherically-symmetric model for two cases, that is, an Einstein-de Sitter universe with Qv = 0.9 and Qb = 0.1 and an open one with Qv = 0.1 and Qb = 0.05, where Q's are present values. At the recombination epoch, taken as the initial epoch, the density perturbation of baryons can be assumed to be zero, because of frequent collisions with isotropic photons prior to and during the recombination, as discussed by Bond et al. (1980). Since the region of a negative density perturbation of neutrinos expands faster than the Hubble flow, a void and a surrounding ridge of neutrinos form, and baryons are forced to gather into the ridge by the gravitational force of the neutrinos. Before long a dissipative separation between neutrinos and baryons occurs and a dense shell of baryons forms within the extended neutrinos. After that, the expansion of the dense shell agrees with the self-similar evolution investigated by Bertschinger (1984). We have found the relations between the epoch of formation of a baryon dense shell Zc and the initial amplitude of a neutrino density perturbation ev as

and

1 + Zc = 7.9 X 102 e~·9 for Q v = 0.1 and Qb = 0.05.

Now we are interested in the mass accumulated into a dense shell, and the mass of a fragment formed by the gravitational instability of the dense shell. The former is presently

or

where Rvo is the present radius of a void. The latter can be estimated in terms of the energy principle that a 'pancake' cut out of the dense shell should be unstable if it has negative total energy. The mass of the most unstable pancake is, with the same dependence upon R Vo as M bs '

Mb = 1.8 x x 1011 (RvPO MpC)3 h- 1 Mo (in baryons),

NEUTRINO-DOMINATED UNIVERSE

or

Mv = 1.7 x x 1012 (RvPO MpC)3 h- I Mo (in neutrinos),

which is almost independent of when the fragmentation occurs.

245

These masses are very attractive, in the sense that they correspond to the typical masses of a supercluster and a galaxy, respectively, when a void with a few of tens megaparsecs in radius forms. The minimum mass of an unstable pancake depends upon the temperature of intergalactic gas heated by dissipation as

T[G(z) = 5 x 105(R vo/20 MpC)2(1 + zf/(1 + ZJ2 K

and is

Mb , min ~ 108 - 9(R vo/20 MpC)3 h - 1 M 0 in baryons,

which is comparable to the mass of a La cloud seen in QSO light. In what state is such an intergalactic cloud in the hot intergalactic gas? For cases without dark matter, the evolution of intergalactic clouds was investigated by Umemura and Ikeuchi (1984) and Ikeuchi and Ostriker (1984) with a neutrino-dominated case. The physical states of intergalactic clouds within dark matter has been extensively examined by Umemura and Ikeuchi (1985a, b).

From a statistical point of view, as for the distribution of galaxies, a neutrino-dominated universe tends to produce a stronger correlation of galaxies and Let absorbers than is observed in a supercluster scale. In order to obtain the statistical distribution by means of such a numerical study as the above, it is necessary to calculate the gravitational interaction of some dense shells. Our basic claim here, however, is that the galactic scale does correlate to the scale of the large 'honeycomb' structure of the Universe. The statistical feature may be reproduced by such versions on the collapse of a superc1uster as proposed by Dekel and Aarseth (1984) and Umemura and Ikeuchi (1985c).

References

Bertschinger, E.: 1984, Astrophys. J. Suppl. 58, I. Bond, J. R., Efstathiou, G., and Silk, J.: 1980, Phys. Rev. Letters 45, 1980. Centrella, J. and Melott, A. L.: 1983, Nature 305, 196. Deke1, A. and Aarseth, S. J.: 1984, Astrophys. J. 283, I. Frenk, C. S., White, S. D. M., and Davis, M.: 1983, Astrophys. J. 271,417. Ikeuchi, S. and Umemura, M.: 1984, Prog. Theor. Phys. 72,216. Ikeuchi, S. and Ostriker, J. P.: 1984, Astrophys. J. (submitted). Lyubimov, V. A., Novikov, E. G., Nosik, V. Z., Tret'yakov, E. F., and Kozik, V. S.: 1980, Phys. Letters B94,

266. Umemura, M. and Ikeuchi, S.: 1984, Prog. Theor. Phys. 72,47. Umemura, M. and Ikeuchi, S.: 1985a, Astrophys. J. 299 (in press). Umemura, M. and Ikeuchi, S.: 1985b, Astron. Astrophys. (submitted). Umemura, M. and Ikeuchi, S.: 1985c, in preparation.

DARK MATTER AND THE FORMATION OF LARGE-SCALE

STRUCTURE IN THE UNIVERSE*

LI Z H I FAN G, S H 0 U PIN G X I A N G, SHU X I A N LI, Y A 0 QUA N C H U, and XlNGFEN ZHU

Center for Astrophysics. University of Science and Technology of China. China


Abstract. A new scenario of clustering in a two component dark matter universe is discussed, from which we would expect the difference between the distributions of quasars and galaxies on the scale of 10-100 Mpc and the difference between the distributions of quasars with Z > 2 and Z < 2. Several analyses on quasars distribution are in good agreement with these predictions.

Most of the matter in the Universe is invisible. Such 'dark matter' plays an important role in the formation of large scale structure in the Universe. Several lines of evidence show that there are at least two kinds of dark matter: one is a dominant component with a large velocity dispersion, such as massive neutrinos; the other, lesser, component is more weakly interacting, and corresponds to more massive particles with a smaller velocity dispersion (inos). We discuss the scenario of clustering in a two component dark matter universe, by which one can explain that the distribution of dark matter might be more uniform than that of visible objects.

The new scenario is different from both the isothermal and adiabatic scenarios, from which we would predict:

(1) The distribution of quasars should be different from that of galaxies by no strong inhomogeneity on the scale of 10-100 Mpc.

(2) The distribution of quasars with Z> 2 and Z < 2 should be different from each other, in the sense that there should be no large scale structure in the former, but there should be such structure in the latter.

These predictions have been tested by a Nearest Neighbour Test (NNT) to the Savage-Bolton's quasar sample (Savage and Bolton, 1979; Chu and Zhu, 1983). The results for one of the two fields (02h , - 50 0 ) are shown in Figure 1. The observed nearest neighbour distances for quasars with Z < 2 deviate obviously from those of a MonteCarlo sample (random distribution) on the scale of 50-100 Mpc. It means that the distribution of Z < 2 quasars does have ~ 100 Mpc clustering.

The distribution of quasars with Z > 2 does not show any difference from that of a random sample. Similar results have been obtained for the field (22\ - 18 0 ).

From the same point of view, we can explain various other statistical results of quasar distributions; for example, the clustering of quasars in the sample of Shanks et al.



248 LIZHI FANG ET AL.

2~ ~ ______ ~Z~<_2~ ____________ ~ __________ Z_7_2 __________ -rv

15 15

10

5 5

o 150 jOO

tJ ( ;·ipc) (:.oc)

Fig. 1. The distribution of nearest neighbour distance D for quasars in the field (02\ - 50°) for the Savage-Bolton sample. Solid lines correspond to the distribution of the observed quasar sample. Dashed

line histograms are the mean values from ten Monte-Carlo simulation samples.

(1983), in which quasars identified by the UBV colour method show Z < 2. Similarly, no evidence of clustering has been found from a Cerro Todolo Interamerican Observatory (CTIO) sample (Osmer, 1981), in which most of the quasars have Z> 2.

References

Chu, Y.-Q. and Zhu, X.-F.: 1983, Astrophys. J. 267, 4. Fang, L.-Z., Li, S.-X., and Xiang, S.-P.: 1984, Astron. Astrophys. 140, 77. Osmer, P. S.: 1981 , Astrophys. J. 247, 761. Savage, A. and Bolton, J. G.: 1979, Monthly Notices Roy. Astron. Soc. 188,599. Shanks, T., Fong, R., Green, M. R., Clowes, R. G. , and Savage, A.: 1983, Monthly Notices Roy. Astron. Soc.

203, 181.

X-RAY DETECTION OF THE MONOCEROS SUPERNOVA

REMNANT*

D. A. LEAHY**

Dept. of Physics. University of Calgary. Canada

S. NARANAN and K. P. SINGH

Tata Institute for Fundamental Research. Bombay. India


Abstract. The Monoceros nebula is seen in the optical and in radio as a 3 ~ 5 degree diameter ring. It is believed to be an old supernova remnant. Here is reported the detection of X-rays from the Monoceros nebula, confirming its supernova remnant nature. Einstein imaging proportional counter observations 0[0.2 to 5 keY X-rays were analyzed to produce a surface brightness map. Preliminary modeling of the Monoceros supernova remnant yields an age of 50 000 years. A large age is expected for such a large remnant. However, the remnant is found to still be in the adiabatic blast wave stage of evolution.

1. Introduction

The Monoceros nebula was first recognized as a possible supernova remnant from radio observations (Davies, 1963). Further radio observations of the nebula have since been made by Holden (1968), Milne (1970), and Dickel and DeNoyer (1975). The Monoceros nebula is visible at optical wavelengths as a bright ring of emission north of the even brighter Rosette nebula. The diameter of the ring is 3': 5 and the center is at right ascension 6h 37m , declination 6°. The optical emission has 2 components - a fine filamentary structure and a more extended diffuse emission (Davies et al., 1978; Kirshner et al., 1978). Here we report initial results of X-ray observations of the Monoceros nebula taken by the Einstein observatory.

2. Observations

The Monoceros region was observed with the imaging proportional counter (Ipe) on board the Einstein observatory during September, 1979, and March and April, 1980. The instrument was described by Giacconi et al. (1979). A total of 15 observations were taken, each covering a 1 by 1 degree field of view, with approximately a 1 arc min resolution. Because of the large area of the Monoceros nebula, the coverage is not complete. All the data have undergone the standard reprocessing at the Harvard

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held n Kyoto, Japan, between 30 September-6 October, 1984. ** Present address: Institute for Space and Astronautical Science, Tokyo.


250 D. A. LEAHY ET AL.

6h40m 6h30m Fig. I.

Smithsonian Center for Astrophysics to improve the quality (e.g., better detector calibration, rejection of data including the sunlit Earth in the field of view). To construct the image of the region the 15 fields were background subtracted, then imbedded in a larger image array. The image array was corrected for varying exposure due to the different observation times of each field and also due to the decreasing effective area within each field away from the center. Due to the low intensity of emission from the Monoceros nebula, and resulting large statistical fluctuations within each bin of the image array, the image array was smoothed with gaussian smoothing functions of FWHM 80, 160, and 320 arc sec.

3. The Monoceros Supernova Remnant

The X-ray image of the Monoceros supernova remnant and surrounding region is shown in Figure 1. This is the image smoothed with the 320 arc sec gaussian. The zero contour

MONOCEROS SUPERNOVA REMNANT 251

6h40m 6h30m Fig. 2.

level corresponds to the boundary of the fields of view of the IPC, including blockage by the window support ribs. The other contour levels are at 0.5, 1.0, and 1.5 x 5.63 x 104 counts per second per square arc min. This map shows the large scale X-ray emission but suppresses any small scale detail. However, there are three point sources visible in Figure 1: at 6h29m16~4, 4°58'32"; 6h34m42~4, 6°10'39"; and 6h33m16~3, 7°57'44".

The radio and optical map of the Monoceros region (from Davies et al., 1978) is shown in Figure 2. The radio-emission at 2650 MHz is shown by the contours, while the optical emission is shown by shading (for the diffuse component) and by short line segments (for the sharp filaments). The X-ray emission correlates with the radio emission well. The Rosette nebula, however, is bright in radio, and does not show up strongly in the X-ray map, except for the central region. The diffuse optical emission extends around the entire ring, but the optical filaments are limited to regions which are also bright in X-rays. The optical filaments and the X-ray emission are indications of the shock wave in the supernova remnant.

We finally applied a Sedov model to the Monoceros remnant, assuming a distance of

252 D. A. LEAHY ET AL.

1600 pc. The shock radius is then 49 pc. We assume a temperature of 0.2 keY, comparable to other old supernova remnants, and find an age of 49 000 years and shock velocity of 390 km s - '. The time calculated for radiative cooling to become important (Cox. 1972) is found to be approximately 100000 years, so that the remnant should still be in the adiabatic phase.

Acknowledgement

Support for this work comes from NSERC grant No. 69-0366 to D. Leahy.

Cox, D.: 1972, Astrophys. J. 178, 159. Davies, R. D.; 1963, Observatory 83, 172.

References

Davies, R. D., Elliot, K. K., Goudis, c., Meaburn, J., and Tebbutt, N. J.: 1978, Astron. Astrophys. Suppl. 31, 271.

Dickel, J. R. and De Noyer, L. L.: 1975, Astron. J. 80, 437. Giacconi, R. et al.: 1979, Astrophys. J. 230, 540. Holden, D. J.: 1968, Monthly Notices Roy. Astron. Soc. 141, 57. Kirshner, R. P., Gull, T. R., and Parker, R. A. R.: 1978, Astron. Astrophys. Suppl. 31,261. Milne, D. K.: 1970, Australian J. Phys. 23,425.

ALIGNMENT OF SPIRAL GALAXIES IN THE LOCAL

SUPERCLUSTER*

H. T. MacGILLIVRAY

Royal Observatory Edinburgh. Scotland. U.K.

and

R. J. DODD

Carter Observatory, Wellington, New Zealand


Abstract. Evidence is presented indicating the non·random alignment of spiral galaxies in the Local Supercluster. The form ofthis effect is such that the spin angular momentum vectors of intermediate-type spirals are coherently aligned in space. The results suggest the formation of galaxies in the Local Superduster according to the fragmentation hypothesis.

1. Introduction

Observations of the geometrical properties (e.g., orientations and shapes) of galaxies in clusters and superclusters can provide important clues for helping with an understanding of the formation of such systems in the early Universe. We are at present engaged in studies of this nature, mainly from the use of objective means.

The local supercluster (LSC) is the nearest large-scale structure (within which we ourselves are situated) and is, therefore, a valuable starting point for a study of the global properties of superclusters. In a recent investigation (MacGillivray et al., 1981), in a sample of 727 galaxies (selected on the basis of radial velocity and brightness criteria, and thought to be representative of the LSC as a whole), a small preference was found for the galaxies to be aligned along the plane of the LSC. This alignment effect was found to be most pronounced for galaxies outside the plane of the LSC and for those galaxies seen nearly edge-on. Recently, we have combined these results with the morphological information on the galaxies, and with the observations of Yamagata et al. (1981) of the spiral winding directions ('S' or 'Z') in a search for other systematic, non-random trends in the galaxy properties.

2. Current observations

The results of the present investigation can be seen in Figure 1 where we show: (a) the frequency of galaxies outside the LSC plane: the frequency of galaxies within the plane



254 H. T. MACGILLIVRAY AND R. J. DODD

(as a function of morphological type); (b) the frequency of galaxies aligned along the plane (small values of A SGPA): those at right angles to the plane; and (c) the frequency of galaxies of spiral winding direction'S': those of winding direction 'Z'.

Note that galaxies of type Sbc-Sc consistently show deviation from the random situation (broken-lines) in all cases, and this deviation is outside the statistical error bars. In other words: galaxies of type Sbc-Sc are less concentrated towards the plane of the LSC, and preferentially show the effect of alignment along the plane of the LSC and show a preponderance of winding direction'S' over 'Z'. (The last effect is in agreement with the findings of Borchkadze and Kogoshvili, 1976; and of Yamagata et al., 1981). Galaxies oftypes Sab-Sb also show a lower concentration to the LSC plane but a weaker alignment trend and no preference for winding direction.

f(lSGBJl

1.5

j--i __ ~ __ t--*J 1

0.5

a

fl~SGPAI

1--J--~--t--t--t 1.5

1

0..5

b

Hsorzl

1.5 t 0.5

-~-i-----tr-J

Sa Sab Sbc Sed Sdm Irr Sb Sc Sd Sm

TYPE

Fig. 1.

ALIGNMENT OF SPIRAL GALAXIES 255

Application of the X2 test to contingency tables, involving combinations of the parameters, reveals that: intermediate-type spirals (i.e., those of types Sab-Sc) are less concentrated towards the plane of the LSC on the 99.3 % confidence level, that these spirals are preferentially of winding direction'S' (92 % confidence level) and that the alignment effect is present for galaxies of both winding directions (98 % confidence level). Furthermore, when analysis is carried out on galaxies of type Sab-Sc alone, it is found that galaxies at southern supergalactic latitudes are preferentially of winding direction'S' while those at northern supergalactic latitudes are preferentially of type 'Z' (91 % confidence level).

3. Summary of Results

The results of our investigation can be summarised briefly: (1) There exists, within the LSC, segregation of spiral galaxies according to mor

phological type, spirals of intermediate types (i.e., Sab-Sc) being less concentrated towards the LSC plane than spirals of other types.

(2) These intermediate spirals preferentially show the effect of alignment along the LSC plane and have a preponderance of winding types'S' over 'Z'.

(3) These intermediate type spirals display a hemispherical dependence on winding direction, those at southern supergalactic latitudes being preferentially of type'S' while those at northern supergalactic latitudes are preferentially of type 'Z'.

(4) Spirals of both winding directions show the alignment effect.

4. Conclusions

We interpret these observations as indicating that the spin vectors of the intermediatetype spirals in the LSC are coherently aligned hoth with themselves and with the pole of the LSC, and that this is a reflection of early conditions which prevailed in the LSC. The segregation of spirals according to morphological type might be taken to indicate that in the collapsing proto-LSC, the intermediate spirals condensed out first and retained a better 'memory' of the early conditions within the LSC. This memory was erased for the formation of subsequent galaxies (possibly by means of dynamical encounters in the LSC; see MacGillivray and Dodd, 1985).

These observations cannot be reconciled with either the hierarchical clustering mechanism for galaxy formation (Peebles, 1974), nor with the adiabatic perturbation mechanism (Zel'dovich, 1978; Doroshkevich et al., 1978), both theories being unable to reproduce the form of the properties observed. These properties can, however, be interpreted in the context of the primeval turbulence mechanism (Ozernoy, 1978) for galaxy formation, according to which galaxies form from fragmentation of a collapsing protosupercluster and gain angular momentum from the parent body. In such a situation, the spin vectors of the galaxies would tend to be coherently aligned with themselves and with the spin vectors of the parent supercluster.

Clearly, further investigation (along similar lines) ofthe properties of galaxies in other

256 H. T. MACGILLIVRAY AND R. J. DODD

superclusters will be worthwhile and will help to determine whether the results obtained for the LSC are indeed a feature common to such systems.

References

Borchkadze, T. M. and Kogoshvili, N. G.: 1976, Astron. Astrophys. 53,431. Doroshkevich, A. G., Saar, E. M., and Shandarin, S. F.: 1978, in M. S. Longair (ed.), The Large Scale

Structure of the Universe', IA U Symp. 79, 423. MacGillivray, H. T. and Dodd, R. J.: 1985, in O. G. Richter and M. Tarenghi (eds.), The Virgo Cluster of

Galaxies, (in press). MacGillivray, H. T., Dodd. R. J., McNally, B. V., and Corwin, H. G., Jr.: 1982, Monthly Notices Roy. Astron.

Soc. 198, 605. Ozernoy, L. M.: 1978, in M. S. Longair (ed.), The Large Scale Structure of the Universe', IAU Symp. 79,

427. Peebles, P. J. E.: 1974, Astrophys. J. 189, L51. Yamagata, T., Hamabe, M., and lye, M.: 1981, Ann. Tokyo Astron. Obs. 18, 164. Zel'dovich, Ya. B.: 1978, in M. S. Longair (ed.), The Large Scale Structure of the Universe', IAU Symp.

79,409.

LOG N - LOG S OF RADIO SOURCES AT 10 GHz WITH FLAT

SPECTRA*

KO AIZU

Physics Department, Rikkyo University, Nishi-Ikebukuro, Toshima-ku, Tokyo, Japan

HIROTO TABARA, TATSUJI KATO

Faculty of Education, Utsunomiya University, Mine, Utsunomiya, Tochigi, Japan

and

MAKOTOINOUE

Nobeyama Radio Observatoryt, Tokyo Astronomical Observatory, Nobeyama, Minamimaki, Nagano, Japan


Abstract. A log N - log S relation at 10 GHz is constructed for sources with the flat spectra C(::;; 0.5 (flux density SIX v- a) from observations at NRO, MPIfR and others. Based on the source distribution on log (Luminosity) ~ volume plane we obtain an epoch-depending luminosity function, which explains the above relation.

1. Observations

In order to study the log N - log S relation at high frequencies such as 10 GHz, it is important to separate sources with flat spectra (mostly compact QSOs) and those with steep spectra (mostly radio galaxies). Figure 1 shows the differential log N - log S relation of flat spectrum sources. Here N I1S is the number of sources per steradian having flux densities between Sand S + I1S, and 'flat' means that the spectral index rx, between 1.4 and 5 GHz, is :s;; 0.5, where Soc v- "'. For sources with flux densities less than 0,63 Jy we used our measurements at Nobeyama Radio Observatory (NRO) (Tabara et al., 1984). For other sources we used mostly results by Kiihr et al. (1981a, b) and others, as shown in Table 1. The most important feature established here is the rapid decrease of numbers with decreasing flux densities below 0.5 Jy. The slope is 0.9 as compared with 0.75 in the range 0.1 mly < S < 100 mJy at 5 GHz (Fomalont et al., 1984). This is consistent with a fact, found before by us, that the fraction of sources with spectral index rx :s;; 0.5 decreases sharply with decreasing flux density at around 0.5 ly at higher frequencies (Kato et al., 1984). Also the rapid evolution from 5 ~ 1 Jy is remarkable.

* Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984. t Nobeyama Radio Observatory, a branch of the Tokyo Astronomical Observatory, University of Tokyo, is a facility open for general use by researchers in the field of astronomy and astrophysics.


258 K. AIZU ET AL.

TABLE I

Data on flat spectrum a sources

Flux density Sky region Solid Number of (Jy) (lbl> 10°) angle sources

(sr)

0.063 ~ 0.63 RA 7h04m ~ 17h S6m 0.069 47 Dec!. 34°09' ~ 35°51'

0.63 ~ 2.50 Decl. ~ 35° 2.081 104 (llb)

2.50 ~ 6.30 Dec!. ~ - 30° 7.63 49 (Sb)

a Spectral index Co( between 1.4 and 5 GHz is s 0.5, Sex v-~. b Observed by us at NRO, unpublished.

Observatory

NROc

NRAO-BONN (S4, SS) NRAO-PARKES

C Tabara et at. (1984). Note that sources were selected from NRAO fast survey (Owen et at., 1983 ).

TABLE II

Data on sources used for construction of luminosity function I b I > 10°; rx S 0.5

Declination Solid Smin Smin Number of sources angle at 5G at lOG with known z (sr) (Jy) (Jy)

A - 300 ~ 0° 2.63 1.0 1.58 24 B 00~35° 2.92 0.8 1.00 38 C 35°~90° 2.08 0.5 0.63 SO

2. Epoch-Depending Luminosity Function of Flat Sources

In order to explain these results, we construct an epoch depending luminosity function (EDLF) n(L, z), defined as the number density on the log L ~ V plane, where L is the luminosity and V is the co-moving volume (Arakelian, 1970). Table II shows three different samples A, B, and C used for this purpose. We compute the luminosity for each source with known red shift, and study the population statistics on the 10gL ~ V plane. After a partial correction for no red shift data, and smoothing by running averages over three meshes in the V direction, these statistics are converted to the population density in the form of the epoch-depending luminosity function. Here we used the standard 'big-bang' cosmology, with Ho = 75 km s - I Mpc - 1 and the deceleration parameter qo set at 0.02, 0.5, or 1.0. The mesh size depends on qo , and is 004 x 2 (Gpc3) for qo = 0.5. As the statistical fluctuation is large, we average the three samples. The result in the case qo = 0.5 is shown in Figure 2. Sources with L < 1033 erg s - 1 Hz - 1 were found to be galaxies, and have been excluded from the figure.

The large fluctuations permit us to construct only a crude luminosity function. The three EDLF's made for three ranges of V limited by 0, 4, 8, and 12 Gpc3 , which correspond to z = 0,0.96, lAS, and 1.90, respectively, are shown in Figure 3. The solid

log(f1NI ANo> 2

1

-1

RADIO SOURCES AT 10 GHz 259

o 1 log S(Jy)

Fig. 1. Log N - log S relation of flat spectrum sources at 10 GHz. The differential count ~Nis normalized by the uniform Euclidian count ~No = ~S - 2.5, S in Jy. See Table I for explanation of data. The solid line

is computed from Equation (I).

-1 -1) !ogl(ergs Hz

35

34

33

.046 f-

.12

1.25

1. 24 .I" , , ,

.15

.81

.?1 .52

o (O)

I , I 1.79 , L

.073

.16

1.18

I I I I I

.073 .025 .053 -

.25 .17 .26 .57 .40 _.20------------- ------

.87---.56- .39 .52 .33

I

10 (1.69)

V(Gpc 3 )

I I

--

20 (2.84)

Fig. 2. Population density n(L, z) on the log L ~ V plane. The size of a mesh is 0.4 x 2 (Gpc3). The unit of n(L, z) is Gpc- 3 . The case for qo = 0.5 is shown. The dashed line is a locus of S = 1 Jy. In the abscissae,

values of z are given in parenthesis under the corresponding V.

260

o

- I

- 2

K. AIZU ET AL.

z .0- .96

.96- 1.45

1.45 - 1.90

34 35 log L (erg S - I Hz ')

Fig. 3. Epoch-depending luminosity functions for the case of qo = 0.5. The solid line is a fit with a form aL - b exp( - Lie) for the case of 0 S z < 0.96.

curve gives an analytical expression for the range 0 .:::; V < 4 Gpc3 . The figure suggests that the evolution effect with z is not large, and does not change greatly the form of EDLF. We adopt an analytical expression for EDLF, of the form

n(L, z) = aL - b exp( - Lle)(l + z)M , (1)

where L is given in unit of 1033 erg s - 1 Hz - 1. The values of the constants a = 15.37, b = 0.845 and e = 69.24 for qo = 0.5 are determined from the data, but that of M cannot be determined with certainty. Here we regard the latter value as an adjustable parameter, to be determined by the source count results.

3. The log N - log S

In order to compute the log N - log S curve from Equation (1) we need a cut-off parameter Zc for the red shift. Although we have not yet made an extensive search for (M, zJ, the values around (4, 4) seem to give a modest fit to the observations, as shown by solid line in Figure 1. A closer agreement can be obtained with more sophisticated models, such as those given by Peacock and Gull (1981).

We conclude, for the EDLF: (1) The range of luminosity is small, namely, L min ~ 1033 and Lmax ~ sever

al x 1035 erg s - 1 Hz - 1.

RADIO SOURCES AT 10 GHz 261

(2) Evolution effect is slight; if it is expressed as a factor (1 + z)M in the EDLF, M is around 4, and does not exceed 6.

(3) The cut-off of z is also around 4, and does not exceed 6 in any case. (4) We do not insist on the particular density evolution considered. We used

Equation (1) only for simplicity. Finally, it must be noted that our results are preliminary and more extensive data and

more refined models are necessary. Computations were carried out with M200 at NRO and UllOO at Rikkyo University.

References

Arakelian, M. A.: 1970, Nature 225, 358. Fomalont, E. B., Kellermann, K. I., Wall, J. V., and Weistrop, D.: 1984, Science 225, 23. Kato, T., Tabara, H., Saito, 1., and Keino, S.: 1984, Bull. Faculty Education, Utsunomiya Univ. 35, 1 (in

Japanese). Kiihr, H., Witzel, A., Pauliny-Toth, 1. K K, and Nauber, V.: 1981, Astron. Astrophys. Sup pl. Ser. 45,367. Kiihr, H., Pauliny-Toth, 1. K. K, Witzel, A., and Schmidt, J.: 1981, Astron. J. 86, 854. Owen, F. N., Condon, J. J., and Ledden, J. E.: 1983, Astron. J. 88, I. Peacock, J. A. and Gull, S. F.: 1981, Monthly Notices Roy. Astron. Soc. 196,611. Tabara, H., Kato, T., Inoue, M., and Aizu, K.: 1984, Publ. Astron. Soc. Japan 36, 297.

ANNOUNCEMENT

Third Asian-Pacific Regional Meeting of the International Astronomical Union. Part 2. September 30- October 51984, Kyoto, Japan. Supplementary Issue.

Editors: M. Kitamura and E. Budding

Please note that a hardbound edition of this special issue of Astrophysics and Space Science, Vol. 119, No.1 (February 1986), is available from the publishers.

ISBN: 90--277-2210--2 Prices: Dfl.115,-/$49.00!£31.95

Astrophysics and Space Science 119 (1986) 262.

LIST OF UNPUBLISHED PAPERS

The following papers were presented at the Regional Meeting but are not published here. Most of them are expected to be published elsewhere in the near future.

Y. Suematsu: On the Motion of Spicules in Ha ± 0.7 A (Solar Phys.)

S. Enome, and L. E. Orwig: Relations between Narrow-Band Decimeter Wave Bursts and X-ray Bursts (Nature).

K. Kai, T. Kosugi, and N. Nitta: Hard X-ray and Microwave Flux Radiation of Solar Flares Observed with the HINOTORI Satellite (Publ. Astron. Soc. Japan).

I. Kawaguchi: Solar Cinematography in the Hida Observatory (Solar Phys.)

T. Maihara, K. Mizutani, N. Hiromoto, H. Takami, and H. Hasegawa: Near-Infrared Bailon Observations of the 1983 Solar Eclipse (IAU Colloq.85).

D. N. Dawanas, and R. Hirata: The Expanding Envelope ofHD 166596 (B2.5 II) (Publ. Astron. Soc. Japan).

D. W. Krutz: Recent Observations of Rapidly Oscillating Ap Stars.

H. Shibahashi: On the Excitation Mechanism ofthe Rapid Oscillations of Ap Stars (Astrophys. 1. Letter).

R. T. Stewart: Radio Mapping of Coronal Magnetic Fields in Stellar Systems (Monthly Notices Roy. Astron. Soc.).

K. Mitsuda, H. Inoue, K. Koyama, K. Makishita, M. Matsioka, Y. Ogawara, N. Shibazaki, K. Suzuki, Y. Tanaka, and T. Hirano: Energy Spectra of Low-Mass Binary X-ray Sources Observed from TENMA (Publ. Astron. Soc. Japan).

T. Ebisuzaki, D. Sugimoto, and T. Hanawa: An Indication for Ejection of a Hydrogen-Rich Envelope from the X-ray Burster MXB 1636-53 (Publ. Astron. Soc. Japan).

Y. Nakagawa: Magnetic Field Evolution and Electric Current (Astrophys. 1.).

U. Lee: Vibrational Stability of the S Scuti Stars Against Nonradial Modes with Low Degrees (Publ. Astron. Soc. Japan).

H. Saio, and H. Shibahashi: On the Oscillation Frequencies of the Rapidly Oscillating Ap Stars (Publ. Astron. Soc. Japan).

K. Sadakane, J. Jugaku, and M. Takada-Hidai: Resonance Lines of BII and BeII in Hg-Mn Stars (Astrophys. J.).

E. B. Fomalont: Scorpius X-I: Evolving Double Radio Source (Astrophys. J.).

I. Waki, H. Inoue, K. Koyama, M. Matsuoka, T. Murakami, Y. Ogawara, T. Ohashi, Y. Tanaka, S. Hayakawa, Y. Tawara, S. Miyamoto, H. Tsunemi, and I. Kondo: Discovery of Absorption Lines in X-ray Burst Spectra from X 1636-536 (Publ. Astron. Soc. Japan).

Y. Osaki: A Model for Superoutbursts and Superhumps in SU UMa Stars (Astron. Astrophys.).

S. Mineshige, and Y. Osaki: Propagation of Transition Waves in Dwarf Nova Accretion Disks (Publ. Astron. Soc. Japan).

M. Nakamura, and Y. Nakamura: On Evolutionary Types of Case A Mass-Exchange in Massive Close Bi·· nary Systems (Astrophys. Space Sci.).

J. Fukue, S. Kato, and R. Matsumoto: Compton Scattering Radiation Hydrodynamics in a Moving Plasma (Publ. Astron. Soc. Japan).

L. Bronfman: Molecular Clouds and Galactic Structure A CO Survey of the Southern Milky Way (Astrophys. J.).

T. J. Lee: The Discovery Map of Shocked Molecular Hydrogen in M 17 (Monthly Notices Roy. Astron. Soc.).

Ch. V. Sastry, and A. A. Deshpande: Observations on the Giant HII Region Complex W5I at Decameter Wavelengths(Monthly Notices Roy. Astron. Soc.).

G. S. Sundar, and R. K. Kochhar: On the Dynamical Evolution of a Cluster (Monthly Notices Roy. Astron. Soc. ).

K. Tatematsu, M. Nakano, S. Yoshida, S. D. Wiramihardja, and T. Kogure: CO Observations of the S147! S153 Complex (Publ. Astron. Soc. Japan).

M. Hayashi, T. Omadaka, T. Hasegawa, S. S. Hayashi, and R. Miyawaki: CO Observations of the Molecular Cloud Around S140 IRS (Publ. Astron. Soc. Japan).

K. R. Anantharamaiah, and V. Radhakrishnan: Recombination Line Observations of the Galactic Plane at 324 MHz.

N. Kaifu, T. Hasegawa, and S. S. Hayashi: Characteristics and Evolution of Protostellar Disks (Publ. Astron. Soc. Japan).

S. Sata, T. Nagata, T. Nakajima, M. Nishida, M. Tanaka, and T. Yamashita: Polarimetry of Infrared Sources in Bipolar Molecular Outflows (Astrophys. J.).

T. Ichikawa, M. Nakano, Y. D. Tanaka, M. Saito, N. Nakai, Y. Sofue, and N. Kaifu: CO Observations of a Spiral Arm in M3I with a High Spatial Resolution (Publ. Astron. Soc. Japan).

H. Kamahori, and M. Fujimoto: Velocity Dispersion of Stars and Giant Molecular Clouds (Publ. Astron. Soc. Japan).

A. Sakata, S. Wada, T. Tanabe, and T. Onaka: Infrared Spectrum of the Laboratory-Synthesized Quenched Carbonaceous Composite (QCC) : Comparison with the Infrared Unidentified Emission Bands (Astrophys. 1. Letter).

K. Ogura, and B. Hidayat: A Survey of Southern Bok Globules for Ha Emission Stars (Publ. Astron. Soc. Japan).

I. Hachisu, and Y. Eriguchi: Equilibrium Structures of Rotating Isothermal Gas Clouds (Astron Astrophys.).

Y. Yoshii, and H. Saio: A Fragmentation-Coalescence Model for the Initial Stellar Mass Function (Astrophys. 1.).

N. Nakai, M. Hayashi, M. Sasaki, T. Handa, Y. Sofue, and T. Hasegawa: CO Observations ofM 82 (Publ. Astron. Soc. Japan).

M. Inoue, F. Owen, C. O'Del. H. Tabara. and M. Ishiguro: 3C75 : Four Radio Jets from Two Necei (Astrophys. J.).

S. Kato, and T. Horiuchi: A Model of the Turbulent Magnetic Field in Differentially Rotating Disks (Publ. Astron. Soc. Japan).

S. Ichikawa, K. Wakamatsu, and S. Okamura: The Structure of Dwarf Galaxies in the Virgo Cluster (Astrophys. 1. Suppl.).

M. Watanabe, K. Kodaira, and s. Okamura: A Principal Component Analysis Applied to Extensive Samples of Galaxies (Astrophys. 1.).

B. A. Peterson: The Space Distribution of QSOs (Publ. Astron. Soc. Pacific).

M. S. A. Sastroamidjojo, and S. Wulandari: Spectral Analysis of the Sun During the Solar Eclipse of 11 June 1983.

H. Maehara: A Study of Carbon Stars in the Cassiopeia Region (Publ. Astron. Soc. Japan).

M. Kondo, and T. Noguchi: KUV543-209: An Eclipsing Binary with Emission Lines (Publ. Astron. Soc. Japan).

N. Kaifu, S. S. Hayashi, M. Ohishi, and T. Hasegawa: High-Resolution CO Observations of Protostellar Objects.

S. R. Kulkarni: Measurement of Spin Temperatures in a Rapidly Moving HI Shell.

T. Tsibaki, and A. Takeuchi: Periodic Oscillations Found in the Velocity Field of a Quiescent Prominence (Solar Phys.)

G. Srinivasan, D. Bhattacharya, K. S. Dwarakanath, and V. Radhakrishnan: On the Supernova Remnants Produced by Pulsars.

M. Morimoto, M. Ohishi, and T. Kanzawa: Strong New Mazer Lines of Methanol.

K. Akabane: A 6.5mm Continuum Map of Ori A (Publ. Astron. Soc. Japan).

K. Wakamatsu, and M. Hamabe: The Vertical Structure of the Bar in NGC 4762 (Astrophys. J. Suppl.).

L. Grimshaw-Walsh, A. Wilkinson, and R. A. James: Forty N-Body Ellipsoidal Galaxies and Their Relation to Observations.

D. S. Mathewson: The ANU 2.3m Telescope.

K. Ratnatunga: Field K Giants in the Outer Galactic Halo (Astrophys. J.).

X. T. He, and M. G. Smith: Detection of QSOs in a 40 Square Degree Field at 01h44m,-40000' (Monthly Notices Roy. Astron. SOc.).

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