THE GALACTIC GLOBULAR CLUSTERNGC 3201: PRIMORDIAL BINARIES

AND TIDAL DYNAMICS

By

Patrick Cote B.Sc.. ~LSc.

A TheJi"

Submitted to the Faculty of Graduate Studies

in Partial Fulfillment of the Requiremenf.,

for the Degree

Doctor of PhilOJophy

McMaster University

June 1994

(c) Copyright by Patrick Cote, 1994.

DOCTOR OF PHILOSOPHY (1994)

{.\STROPHYSICS)~[d1.-\STER t-~lVERSITY

Hamilton, Ontario

TITLE: The Galactic Globular Clustt'r :\GC 3201: Prllllordial Binariesand Tidal Dynamics

.-\t-THOR: Patrick CoteB.Sc. (l-niwrsity of \\'estern Ontario)~LSc, (~Ic~laster Cnh'ersity)

SCPER\lSOR: Dr. D. L. \Yekh

Nl"~lBER OF PAGES: xv, 125

ii

ACKNOWLEDGElVIENTS

I am grateful to ),Idlaster Cniversity and the Department of Physics £.: .-\5-

tronomv for continued fundin!! I and XSERC for cominued in:miration I. \Yithout. - . ...

),Iarg, Wendy. CheryL Rosemary and Jackie to guide me through the paperwork. I

might never have escaped the confines of graduate schooL ending up. instead. like

a fossil entombed in GH-llO. The entire ensemble of students \\-ith whom I ha';e

shared an office over the last four years - Ste\'e Butterworth. Pat DurrelL Phil Fis-

cher, Dave Fleming, Steve Holland. Dean ),IeLaughlin. Kanan Patel. Jeff Secke:- and

Mark \Valker - are hereby acknowledged for not just their counsel and tolerance

but also for their unwavering eagerness to "talk shop"'. Especially profound thanks

are reserved for Phil Fischer. who expertly served as a sounding board throughout

the preparation of tbs thesis. The continuous encouragement of my family has

helped to ease the pain that ine"-itably accompanies the pursuit of a career in as-

tronomy. Thanks to the astronomy staff at MdIaster - Bill Harris. Ralph Pudritz.

Peter Suthcrland~Doug \Velch and Christine \Vilson - for almost never reminding

me of the fine line between professor and student. And to Doug \Yelch - ad,,;sor

extraordinaire and contagious enthusiast of everything astronomical - my sincere

gratitude. But. most of all. thank you Abby for your constancy and understanding

in all things great and small.

iii

iv

For Abby

\Ve can conclude that a project as grand as the

scientific-mythical construction of victory over human limitation is not something

that can be programmed by science. Even more, it comes from the \;tal energies

of masses of men sweating within the nightmare of creation - and it is not even in

man's hands to program. \Vho knows what form the forward momentum of life \\;ll

take in the time ahead or what it will make of our anguished searching. The most

that anyone of us can seem to do is to fashion something - an object or ourselves

- and drop it into the confusion, make an offering of it, so to speak, to :he life

force.

- Ernest Becker

\'

v

TABLE OF CONTENTS

..\.bstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IX

List of Important Symbols.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Xl

List of ..\.cronyms xiii

List of Figures xiv

List of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. x'·

Section 1 Overture .

1.1 Astronomical Context and Division of Labour , .

1.2 Observational Basics 8

Section 2 The Detection of an Extended Moving Group Near the Galactic

Disk 12

2.0 .-\bstract 12

2.1 Introduction............ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12

') .) Ob . . 1"_._ servatlons . ..... . . . . .... . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _

2.3 Monte Carlo Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13

2.-1 Ta.....onomy and ~Io,;ng Group Parameters.. . . . . . . . . . . . . . . . . . . . . . . . . . .. l-l

2.5 Conclusions and Future \Vork '" 15

Section 3 A Search for Binaries in Globular Cluster NGC 3201 16

vi

:to Abstract , 16

3.1 Introduction.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16

:3.~ Ohsen<l.tions and Reductions 1j'

3.3 The Radial Velocities.......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19

3.-1 The Binary Candidates 35

3.5 )'lodeling the Binary Population. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39

3.6 Discussion 40

3. j Summary 45

Section -l Dynamics of the Galactic Globular Cluster NGC 3201 4j

·4.0 .-\.bstract 48

4.1 Introduction 49

4.2 Observations and Reductions 51

·4.2.1 Surface Photometry and Star Counts 51

4.2.2 Radial Velocities 53

4.2.3 Structure in the Velocity Field....... . . . . . . . . . . . . . . . . . . . . . . . . . .. 54

4.3 Dynamical :\Iodels.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59

4.3.1 Single- and )'(ulti-Mass Models 59

4.3.1.1 Luminosity-to-Mass Ratios 62

4.3.1.2 Fitting the ~Iodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63

4.3.1.3 ~lonte Carlo Simulations 65

4.3.2 Xonparametric ).Iodels. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. 66

4.4 Results 68

4.4.1 Previous \Vork on NGC 3201 68

4.4.2 ~Iass-to-Light Ratios 69

4.4.3 )'lass Function Slope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69

4.4.4 .~nisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ;1

4.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ;2

vii

Section 5 Future \Vork 103

Section 6 Appendix: Radial Velocity Simulations 106

Section 7 References 1:?4

viii

ABSTRACT

1859 radial velocities (median precision ~ 1 km S-I) have been measured for

1318 stars in the direction of the Galactic globular cluster XGC 3201. Since the

systemic radial velocity for NGC 3201 is 494.2 km 5- 1 , the field and cluster samples

separate unambiguously into two distinct samples. Analysis of the radial velocities

and APMjCCD photometry for the 879 field stars in our sample has revealed the

presence of a probable mm-;ng group of'" 13 stars '\vith radial velocity 75 km S-1

at a distance of 6 - 12 kpc. For the cluster members, we have multiple velocities

for 279 stars (known photometric variables excluded) spread over a ma."cimum of six

years. Comparison of the observed velocities to simulated datasets containing knovm.

numbers of binaries has yielded u.pper limi~ to the true binary fraction (for binaries

with 0.1 ~ P ~ 5 - 10 years and mass ratios in the range 0.1-1.0) of 0.06-0.10

(circular orbits) and 0.15-0.18 (eccentric orbits), consistent with the corresponding

incidence among nearby solar-type stars and among a sample of six other Galactic

globular clusters with measured binary fractions. NGC 3201 appears to be rotating

with an apparent projected rotation amplit11de of 1.22±0.25 km S-I. The observed

increase in ostensible rotation amplitude with distance from the cluster core may,

however, be due to either the projection of the cluster space velocity onto the

plane of the sky, or the preferential stripping of stars on prograde orbits near the

limiting radius due to the disk-shocking instability identified by Oh and Lin (1992).

BV CCD images have bef:n used to derive cluster surface brightness profiles which

extend out to ~ 18'. These profiles and the 399 mean radial velocities for non­

variable cluster members have been analysed using both single- and multi-mass

King-Michie models and nonparametric techniq~es. Both methods suggest that

the cluster mass-to-light ratio is relatively fiat in the range 1.5 - 10 pc: M/Ls ~

ix

~I!L\.. = 2.0±0.2 in solar units. The best-fit mass function has a spectral index of

I :::: 0.75 ± 0.25, consistent \\;th recent findings that the fomi of the mass function

depends on the position relative to the potential of the Gala.'\."}o.

x

a

B j , B. 1,J.~ R, I

c

e

ErB- V)

E

1J

[Fe/HI

f(E,J)

I(e)

G

£3

MB

Mv

(m.M}o

(m.M)\!

M/L

[O/Fe]

p

II,E),Z

LIST OF IMPORTANT SYMBOLS

Amplitude of Projected Rotation Curve

Orbital Semi-:"lajor Axis

Right Ascension

Broadband Photometric ~Iagnitudes

Concentration Parameter

Surface Brightness uncertainty

Anisotropy ~'Ieasure

Declination

Eccentricity

Colour Excess in B- V

Ellipticity

Dimensionless Velocity Dispersion

Logarithmic Iron-to-Hydrogen Abundance

Distribution Function

Eccentricity Distribution

Gra\;tational Constant

Scale Luminosity

Absolute Blue Magnitude

Absolute Visual Magnitude

Reddening-Corrected True Distance Modulus

Apparent Visual Distance ~Iodulus

Mass-to-Light Ratio

Surface Brightness

Degrees of Freedom

Logarithmic Oxygen-to-Iron Abundance

Orbital Period

Velocity Components in Galactic Rest Frame

xi

r

Po

Ph

Pt

til

trO

trh

Td,O

< v~ >1/2

Vrot

'Wo

x

Position Angle

Nwnber of Stars per l7 nit ~lass

S~condary-to-Primary :Mass Ratio

Stellar Radius

Galactocentric Distance

Solar Radius

Projected Radius

Anisotropy Radius

Scale Radius

Tidal Radius

Central }.-Iass Density

Mean Density within Half-Mass Radius

Mean Density within Tidal Radius

Luminosity Density

Velocity Uncertainty; Core Velocity Dispersion

Cluster Disruption Timescale

Central Rela."<ation Time

Half-Mass Relaxation Time

Central Binary Disruption Time

Central rms Velocity

Mean Cluster Radial Velocity

Projected Rotation Velocity

Scale Velocity

Dimensionless Cluster Potential

Mass Function Spectral Index

Binary Fraction

Perpendicular Distance from Galactic Disk

xii

AAS

ADU

APM

AU

AGB

CCD

CMD

CTIO

HB

HST

lAS

IAU

IMF

lRAF

LMC

LSR

NLTT

QERGB

SBP

VDP

LIST OF ACRONYMS

American Astronomical Society

Analog-Digital Conversion ("nits

Automatic Plate )"Ieasuring

Astronomical Unit

Asymptotic Giant Branch

Charge Coupled De,,;ce

Color ~lagnitude Diagram

Cerro Tololo Inter-American Observatory

Horizontal Branch

Hubble Space Telescope

Institute for Advanced Study

International Astronomical 'Union

Initial Mass Function

Image Reduction and Analysis Facility

Large Magellanic Cloud

Local Standard of Rest

New Luyten Two Tenths

Quantum Efficiency

Red Giant Branch

Surface Brightness ProfilE'

Velocity Dispersion Profile

,j'

xiii

LIST OF FIGURES

Figure 1.1 BV Transmission Curves and Stellar Spectrum 11

Figure 2.1 Radial Velocity Histogram 13

Figure 2.2 Field Star Distribution 1-1

Figure 2.3 Field Star C~ID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. H

Figure 3.1 Radial Velocity Histogram 18

Figure 3.2 Photographic C~ID. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19

Figure 3.3 Binary Probabilities.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38

Figure 3.4 NGC 3201 C~ID 38

Figure 3.5a Finder Chart for 20 Candidate Binaries. . . . . . . . . . . . . . . . . . . . . .. -11

Figure 3.5b Finder Chart for Outermost Binary Candidate.. . . . . . . . . . . . . .. 42

Figure 3.6 Dependence of Red Giant Radii on Luminosity 43

Figure 3.7 Model Velocity Distributions (Circular Orbits) 4-l

Figure 3.8 Model Velocity Distributions (Eccentric Orbits)... . . . . . . . . . . . .. 45

Figure 3.9 Radial Distribution of Candidate Binaries. . . . . . . . . . . . . . . . . . . . .. 45

Figure 4.1 Orientation of CCD Fields............ . . . . . . . . . . . . . . . . . . . . . . . .. 93

Figure 4.2 Radial Velocity versus Position Angle/Projected Radius 94

Figure 4.3 Cluster Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 95

Figure 4.4 Vrot./u versus ellipticity for Galactic Globular Clusters 96

Figure 4.5 Location of Cluster Members on the Plane of the Sky. . . . . . . . .. 97

Figure 4.6 BV Surface Brightness Profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98

Figure 4.7 Velocity Dispersion Profile 99

Figure 4.8 Mass Density and M/Lv Profile " 100

Figure 4.9 Mass Function Slope vs Position Relative to Galactic Potential 101

Figure 4.10 Mass Function Slope vs Disruption and Rela.'Ction Timescales 102

xiv

LIST OF TABLES

Table 2.1 Candidate Mo";ng Group Members 13

Table 3.1 Log of Observations IS

Table 3.2 Radial Velocities for NGC 3201 Photometric Variables. . . . . . . . .. 20

Table 3.3 Radial Velocities for NGC 3201 Member Stars 21

Table 3.4 Radial Velocities for NGC 3201 Field Stars 36

Table 3.5 Candidate Binaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39

Table 3.6 Velocity Differences ~ (8, 10) km s-1 Per Artificial Data Set. 43

Table 3.7 KoImolgorov-Smirnov Probabilities For Model Acceptance 44

Table 4.1 General Cluster Parameters 79

Table 4.2 BV Surface Brightness Profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80

Table 4.3 Ellipticities for Galactic Globular Clusters. . . . . . . . . . . . . . . . . . . . .. 83

Table 4.4 Dependence of Apparent Rotation on Sample Size 84

Table 4.5 Adopted Mass Bins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85

Table 4.6 V-Band Fitted Parameters 86

Table 4.7 B-Band Fitted Parameters ,. . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. 87

Table 4.8 V-Band Derived Parameters 88

Table 4.9 B-Band Derived Parameters 89

xv