1997leipolarimetry

8/18/2019 1997LeiPolarimetry

1/80

COMPTON POLARIMETRY IN GAMMA-RAY ASTRONOMY

F. LEI, A. J. DEAN and G. L. HILLS

Department of Physics and Astronomy, University of Southampton Southampton, SO17 1BJ, U.K.

(Received 14 October, 1997)

Abstract. The analysis of compact astronomical objects has generally dealt with the physical prop-erties of the source within a two-parameter space, which is dened by the spectral characteristicsand time variability. This approach often leads to the situation whereby two or more very differ-ent models can explain the observations successfully. Polarimetric observations have the diagnosticpotential to discriminate between the different compact source models and can offer a unique insightinto the geometrical nature of the emission zones. To date, however, no polarization observation inthe gamma-ray energy domain has been successfully performed, due to the difculties in makingpolarimetric measurements in this high-energy region of the spectrum. In this paper the polarizedgamma-ray emission mechanisms are reviewed with the emphasis on their detectable characteristics.Potential astronomical sites in which these emission mechanisms may be at work are discussed.

Observational results obtained in other wavebands and theoretical predications made for some of the most likely astronomical sources of polarization are reviewed. Compton polarimetry has longbeen used in the eld of nuclear gamma-ray spectroscopy in the laboratory. The operational principlebehind all generations of nuclear gamma-ray polarimeters has been to measure the asymmetry inthe azimuthal distribution of the scattered photons. However none of the polarimeters designed forlaboratory experiments will be sensitive enough to observe even the strongest astronomical source.In the past few years there have been a number of innovative developments aimed at the construc-tion of astronomical gamma-ray polarimeters, either as dedicated experiments or in missions withpolarimetric capability. The designs of all the polarimeters are based on either discrete or continuousposition sensitive detector planes. In this paper the data analysis techniques associated with this typeof polarimeter are discussed as well as methods of removing some of the systematic effects introducedby a non-ideal detector response function and observation conditions. Laboratory tests of these newpolarimetric techniques are reviewed. They demonstrate the feasibility of building a suitably sensitiveastronomical gamma-ray polarimeter. Optimization of the design of pixellated detector array basedpolarimeters is also addressed. The INTEGRAL mission, which is to be launched by ESA in the year2001, is the most likely telescope to perform the rst successful gamma-ray polarization observation.The polarimetric characteristics of the two main instruments on board INTEGRAL are evaluated andtheir sensitivities to a wide range of potentially polarized gamma-ray sources are estimated.

Table of Contents

1. Introduction2. Polarized Gamma-Ray Emission Mechanisms

2.1. Magneto-Bremsstrahlung Radiation2.1.1. Cyclotron Emission2.1.2. Synchrotron Emission2.1.3. Curvature Radiation

2.2. Bremsstrahlung Radiation2.3. Compton Scattering2.4. Magnetic Photon Splitting

3. Potential Astronomical Sites of Polarized Gamma-Ray Emission

Space Science Reviews 82: 309–388, 1997.c 1997 Kluwer Academic Publishers. Printed in Belgium.


2/80

310 F. LEI ET AL.

3.1. Gamma-Ray Bursts3.2. Pulsars3.3. Solar Flares3.4. Other Possible Sites for Polarized Emission

3.4.1. Crab Nebula3.4.2. AGNs3.4.3. Galactic Black Hole Candidates

4. A Review of Gamma-Ray Polarimetric Instrumentation4.1. Theory of Compton Polarimeters4.2. Laboratory Polarimeters4.3. Astronomical Polarimeters

4.3.1. COMPTEL4.3.2. Proposed Future Missions4.3.3. X-ray and High-Energy Polarimeters

5. Computer and Laboratory Tests of Novel Polarimetric Techniques

5.1. Polarization Dependent M-C Code5.2. Polarization Data Analysis

5.2.1. The Moving Mask Technique (MMT)5.2.2. The Radial Bin Technique (RBT)

5.3. Systematic Modulation Effects5.3.1. Effect of Non-Uniform Polarimetric Response5.3.2. Effect of Off-Axis Incidence5.3.3. Effect of Background Noise5.3.4. Effect of Pixellation

5.4. Laboratory Tests with Pixellated Detector Arrays5.5. The Geometrical Optimization of a Pixellated Planar Polarimeter

6. Gamma-Ray Polarimetry with INTEGRAL6.1. IBIS as a Gamma-Ray Polarimeter6.2. SPI as a Gamma-Ray Polarimeter6.3. Polarization Sensitivity of INTEGRAL

7. Conclusions

1. Introduction

For the most part, the analysis of compact X-ray and gamma-ray sources hasbeen conned to spectral characteristics and time variability. However, this ana-lysis often allows two or more very different models to successfully explain theobservations. In order to discriminate between the various models, the number of observational parameters should be increased. It is possible to double the numberof observational parameters through measurements of the polarization angle anddegree of linear polarization of the source emission. Polarimetric measurements inother wavebands have been extremely valuable in determining which mechanisms


3/80

COMPTON POLARIMETRY IN GAMMA-RAY ASTRONOMY 311

and physical conditions are responsible for the emission. For example, the radio toX-ray emission from the Crab nebula was unambiguously attributed to synchrotronradiation after consistency in the polarization was found (Velusamy, 1985; Smithet al., 1988; Weisskopf et al., 1978). Astronomical measurements of polarizationhave never been performed at photon energies greater than 10 keV, due to thedifculties in making polarimetric measurements at high energies. However in thisarticle we review such a possibility with COMPTEL and other opportunities withfuture planned missions.

This paper begins with a detailed review of emission mechanisms capableof generating polarized gamma rays. The emission mechanisms leading to theproduction of gamma rays are mainly non-thermal and operate far from equilibriumconditions. Beams of highly energetic particles in extremely strong magnetic eldsare a prime example. Almost all of these emission mechanisms lead to the creationof polarized gamma rays with little or no need for specialised source geometriesor physical conditions, and the high levels of polarization expected give strong

justication to the potential diagnostic power of polarimetric observations.Section 3 deals with some potential astronomical sites of polarized gamma-ray

emission. For example polarization levels of up to 80% are expected from theCrab pulsar. The detection of polarization at gamma-ray energies could prove tobe important in differentiating between rival models of gamma-ray production inpulsars, and it is clear that this technique offers a great diagnostic power in awide range of studies. Although a wide range of possible sources and processeshave been suggested, the origin of Gamma-Ray Bursts (GRBs) remains a mystery,to the extent that it is impossible to say conclusively whether GRBs are a local,galactic, or cosmological phenomenon. The detection of polarization in a GRBspectrum could help identify the emission mechanism and therefore the correct

distance scale. Bremsstrahlung has been identied as an important mechanism forthe production of hard X-rays and gamma-rays in solar ares. Models of solarare emission predict large degrees of linear polarization, up to 75% at 100 keV. Asuccessful detectionwould provide an important conrmation of our understandingof solar ares.

In Section 4, gamma-ray polarimetric instrumentation is reviewed. The meas-urement of the degree of linear polarization was rst reported in 1950 by Metzgerand Deustch, when they exploited the Compton scattering process to measure theasymmetry in the azimuthal distribution of scattered gamma rays. Since then polar-imeters have been constructed with ever increasing sensitivities. Although severalX-ray polarimeters have been included on astronomical telescopes, to date no ded-icated gamma-ray polarimeter has been launched. However, the future prospectsfor gamma-ray polarimetry are good. Measurements are possible on non-dedicatedinstruments, such as COMPTEL, and will be possible on some of the next genera-tion of gamma-ray satellites such as INTEGRAL.

Section 5 reports on the recent development of astronomical gamma-ray polar-imetry techniques, in terms of both the data analysis and instrumentation. It starts


4/80

312 F. LEI ET AL.

with an example to show the importance in implementing a rigorous polarization-dependent Compton algorithm in the Monte-Carlo (M-C) code so as to accuratelyreproduce the experiment results. The development of data analysis techniquesassociated with non-rotational polarimeters is described. The validity of usingvarious techniques to analyse polarimetric distributions from a continuous detec-tion plane is shown by comparisonsbetween results obtained from M-C simulationsand analytical calculations. Methods of removing some of the systematic effectsintroduced by the non-rotational nature of the polarimeter are discussed. Polar-ization measurements from two different experiments, one based on a pixellatedCsI detector array and the other based on a Germanium Strip Detector (GSD), arereviewed to show the feasibility of constructing astronomical Compton gamma-raypolarimeters based on pixellated detector arrays in the energy range from some tensof keVs to a few MeVs. Optimization of the pixel geometry of a planar polarimeterto maximize the polarimetric sensitivity is described. The various issues relatingto the creation of the optimum polarimeter design are discussed and the optimiza-

tion of the pixel geometry is conducted by considering the scintillator depth, pixelcross-section and low-energy threshold.

There are a number of existing or proposed astronomical telescopes that arecapable of performing polarimetric observations in the medium energy gamma-ray range (100 keV to 10 MeV). Among them the INTErnational Gamma RayAstrophysics Laboratory (INTEGRAL) is the most likely mission to make the rstbreak through in polarimetric observation at gamma-ray energies. In Section 6 thepolarimetric characteristics of the two main instruments on board INTEGRAL areevaluated and their polarimetric sensitivities at various incident photon energiesare calculated. The sensitivities of INTEGRAL to a selection of potential polarizedgamma-raysources such as GRBs, the Crab pulsar, and solar ares are investigated.

2. Polarized Gamma-Ray Emission Mechanisms

This section discusses some of the justications for gamma-ray polarimetry andreasons why polarimetric observations can provide a unique insight into the geo-metries of gamma-ray emitting objects. The emission mechanisms leading to theproduction of gamma rays are mainly non-thermal and far from equilibrium, suchas beams of highly energetic particles in extremely strong magnetic elds. Many of these mechanisms can lead to high degrees of linear polarization that are dependentupon the exact source geometry.

The derivations contained in this section are based largely on those contained in Radiative Processes in Astrophysics by G. B. Rybicki and A. P. Lightman (1979)and High-Energy Astrophysics , Volumes 1 and 2 by M. S. Longair (1992 and 1994).Where additional material has been used, it is referenced directly in the text.


5/80


2.1. M AGNETO -BREMSSTRAHLUNG RADIATION

A charged particle moving at a velocity, v , in a constant magnetic eld, B , in theabsence of a static electric eld, experiences an external force given by

F =

Z e

c

v B : (2.1)

The force on the particle acts perpendicular to both v and B and if they arealso perpendicular to each other, then the particle will describe a circle around thedirection of the magnetic eld. If v and B are at an angle, , to each other, knownas the pitch angle, then the particle will precess along a helical path in the directionof the magnetic eld at the relativistic gyrofrequency,

r

,

r

=

Z e B

2 m c

c

; (2.2)

where c is the speed of light, Z is the charge on the particle, e is the elementarycharge, m

c

is the mass of the charged particle, and is the Lorentz factor, =

1 = q

1 , v 2 = c 2. Therefore, particles moving with a constant velocity, in a constantmagnetic eld, experience a constant acceleration and emit radiation at a rate of

,

d E d t

=

T

4

v

c

2c

2B

2 sin2 ; (2.3)

where T

= 8 Z e 4 = 3 m 2c

c

4 is the Thompson cross section.In the general case this is known as magneto-Bremsstrahlung radiation. There

are two special cases of interest. The non-relativistic case is known as cyclotronemission and the radiation is emitted in a dipolar form. The ultra-relativistic caseis known as synchrotron emission, here the transformation from the inertial frameof the particle to that of the observer is important. A special form of synchrotronemission, known as curvature radiation, is also of interest and arises from themotion of ultra-relativistic particles moving in a curved magnetic eld.

In most cases of astrophysical interest, the charged particles that emit magneto-Bremsstrahlung radiation are electrons, as, due to their low mass, electrons exper-ience much greater accelerations than their heavier counterparts. Therefore, theremainder of this section will be limited to the discussion of the radiation emittedby electrons.

2.1.1. Cyclotron EmissionIn the non-relativistic limit, where v c , = 1 and therefore Equation (2.3)becomes

,

d E d t

=

T

4

v

c

2c B

2 sin 2 : (2.4)


6/80

314 F. LEI ET AL.

Figure 2.1 . Polar diagram showing the dipole radiation emitted by an accelerated electron.

The electron emits in a dipolar form, as shown in Figure 2.1. The power radiatedper unit solid angle varies as sin 2 with respect to the acceleration vector, a , of the electron. Therefore no radiation will be emitted parallel to a and the intensitywill be greatest perpendicular to a . The emitted photon is polarized with its electriceld vector, " , lying in the plane described by the acceleration vector of the electronand the direction of the photon.

To a distant observer, when the magnetic eld is perpendicular to the line of sight, the acceleration vector will be seen to perform simple harmonic motion ina plane perpendicular to the magnetic eld. The photons detected by the observerwill be seen to be linearly polarized. However, when the magnetic eld is parallelto the line of sight, the acceleration is seen to rotate as the electron describes acircular orbit. Therefore, the radiation observed will be 100% circularly polarized.For an observation at an arbitrary angle, the polarization will be a combination of the two cases above and will be observed to be elliptically polarized.

For cyclotron radiation, the relativistic gyrofrequency simplies to

g

=

e B

2 m e

c

; (2.5)

where m e

is the mass of an electron. However, even for slowly moving electrons,not all the radiation will be emitted at the gyrofrequency because there are smallrelativistic effects that distort the observed angular distribution of the intensityfrom the sin 2 form. The observed polar diagram can be decomposed by Fourieranalysis into a sum of equivalent dipoles radiating at harmonics, l , of the relativisticgyrofrequency with intensities, I

l

,

I

l

v

c

2 l , 1 ; (2.6)


7/80


Figure 2.2 . The spectrum of emission of the rst 20 harmonics of a relativistic plasma, v = 0: 4 c (Befeki, 1966).

where l = 1 for the rst harmonic, l = 2 for the second harmonic, etc.The energy radiated in the high harmonics is thus small when the particle is non-

relativistic and only becomes important when v = c 0: 1. The Doppler correctionsto the observed frequencies also become signicant and a wide spread of emittedfrequencies is possible for the different pitch angles of the electrons. The resultis the broadening of the widths of the emission lines of the harmonics, and, forthe higher harmonics the lines become so broadened that the emission spectrumbecomes continuous. An example of the spectra of the rst 20 harmonics of amildly relativistic plasma emitting cyclotron radiation is shown in Figure 2.2.

It is useful to note that c

is only dependent on the magnetic eld strength, noton the energy of the electron, therefore Equation (2.5) can be expressed in termsof the magnetic eld strength required for the rst harmonic to produce a photonof the energy of E keV,

B T = 8 : 64 106 E keV : (2.7)


8/80

316 F. LEI ET AL.

Figure 2.3 . The dipole radiation emitted by a relativistic accelerated electron as transformed into theobserver’s frame of reference.

Magnetic elds of 10 9 T are believed to exist close to the surfaces of neutronstars (Shrader and Gehrels, 1995). These are the strongest magnetic elds found innature and thus cyclotron emission is likely to be limited to energies 100 keV.

2.1.2. Synchrotron EmissionOne of the most signicant features of synchrotron radiation is that the radiation isbeamed in the direction of motion of the electron. In the instantaneous rest frame of the electron radiation is emitted in the same dipole pattern as for cyclotron emissionshown in Figure 2.1. When transformed to the observer’s frame of reference theradiation becomes concentrated in the forward direction as shown in Figure 2.3.

Thus the angles = = 4, which correspond to the angles at which the

intensity of radiation falls to half of its maximum value in the instantaneous restframe of the electron, will be transformed to the angles 0 in the observers frame of reference. The resulting beam is therefore tightly conned to the forward directionand a signicant amount of radiation is only observed if the beam sweeps past theobserver.

Unlike cyclotron emission, the radiation produced from synchrotron emissionis not at discrete energies. The emission can be thought of as the relativistic limitof the process illustrated in Figure 2.2, in which all the harmonics are washed outinto a smooth continuum. To investigate the properties of synchrotron radiation, itis necessary to nd an expression for the spectral energy distribution.

It is possible to express the power emitted by synchrotron radiation from a

single electron at an angular frequency,!

, in terms of its components layingparallel, P k

! , and perpendicular, P ?

! , to the projection of the magnetic elddirection as seen by the observer,

P

?

! =

p

3 e 3 B sin 4 m

e

c

2 F x + G x ; (2.8)


9/80


P

k

! =

p

3 e 3 B sin 4 m

e

c

2 F x , G x ; (2.9)

where F x = x R

1

x

K 5= 3 z dz and G x = x K 2= 3 x , K 5= 3and K 2= 3 are mod-ied Bessel functions, x = 2!

r

r = 3c 3 and ! r

is the relativistic angular gyro-frequency and r is the radius of curvature for the electron, r = v = !

r

sin . It isconvenient to dene a critical angular frequency, !

c

,

!

c

=

3 c 3

2 r ; (2.10)

such that,

x =

!

!

c

(2.11)

and

!

c

= 2 c

=

32

c

v

3!

r

sin : (2.12)

Taking the limit v ! c and rewriting Equation (2.12) in terms of the non-relativistic gyrofrequency given by Equation (2.5),

c

=

32

2

g

sin : (2.13)

The total emitted power per angular frequency of a single electron is given by thesum of Equations (2.8) and (2.9),

P ! =

p

3 e 3 B sin 2 m

e

c

2F x (2.14)

and the form of Equation (2.14) is shown in Figure 2.4.As shown in Figure 2.4, the emission has a broad maximum centred at max =

0 : 29 c

. Therefore expressing Equation (2.13) in terms of the magnetic eld strengthrequired to produce a photon of E keV,

B T = 1: 99 107

2 sin E keV : (2.15)

To produce 1 MeV gamma rays in a magnetic eld of 10 4 T, a Lorentz factorof = 1411 is required, correspondingly for a eld of 10 9 T, a Lorentz factorof = 4: 46 is required. These correspond to electron energies of 721 MeV and2.28 MeV, respectively.

In the astronomical context, the energy spectra of electrons can often be approx-imated by a power-law distribution,


10/80

318 F. LEI ET AL.

Figure 2.4 . The form of the spectral energy distribution of a single electron by synchrotron radiation.

N E d E = E , dE ; (2.16)

where and are constants. The emitted power in the frequency range to + d can be shown to follow the form:

P d , , 1 = 2 (2.17)

and therefore the observed photon energy spectrum will also be a power-law.The other major characteristic of synchrotron radiation is its polarization. The

radiation from a single electron is typically elliptically polarized but will tendtowards linear polarization as the energy of the electron increases. This is because,as shown in Figure 2.3, signicant amounts of radiation are only seen when theemission beam points towards the observer. For an electron with a pitch angle of 90 , the emission will be linearly polarized as the projection of the accelerationvector will be seen to remain in the same orientation while the emission beam isvisible. However, for other pitch angles, the acceleration vector will be seen torotate through a small angle as the emission beam sweeps past the observer. Thisintroduces a circular component to the polarization and the resulting polarizationwill be elliptical. As the electron energy increases, the emission beam narrows andthus the acceleration vector rotates less in the time that it is visible, therefore thepolarization appears more linear in nature.

For the case of many electrons, where there is a distribution in the pitch angles,all the electrons with beams within an angle , 1 to the line of sight will contribute


11/80


to the observed intensity. The net polarization is found by integrating over all of the electrons which contribute to the intensity. Because the elliptical componentseither side of the line of sight occur in opposite directions, they cancel and theresultant polarization is linear.

The linearly polarized component of the radiation can be found from the aver-ages of P

k

and P ?

by neglecting their time variance through the pulse. For a singleelectron the fractional degree of linear polarization, , is dened to be,

=

P

?

! , P

k

!

P

?

! + P

k

!

: (2.18)

Inserting Equations (2.8) and (2.9) into Equation (2.18),

=

G x

F x

: (2.19)

For a power-law distribution of electron energies, the fractional polarizationbecomes,

=

1

Z

0

G x x

, 3 = 2 d x

1

Z

0

G x x

, 3 = 2 d x

; (2.20)

therefore,

=

+ 1 +

73

: (2.21)

For the observed range of power-law indices from 1.5 to 5.0 for astrophysicalsynchrotron radiationsources, the observeddegree of linearpolarization is expectedto range from approximately 65% to 80%.

Equation (2.21) relates to the maximum degree of linear polarization and anyinhomogeneities in the structure of the magnetic eld will result in the degree of linear polarization being reduced.

2.1.3. Curvature RadiationAn electron moving in a non-uniform magnetic eld will tend to drift in thedirection of the eld lines. If the radius of curvature is small, signicant amountsof magneto-Bremsstrahlung radiation will be emitted. In the relativistic limit theequations relating to curvature radiation can be generated by replacing the gyrationradius, r , by the radius of curvature of the eld lines, R

c

, therefore,


12/80

320 F. LEI ET AL.

c

=

3 c 4 R

c

3: (2.22)

As r is dependent upon and R c

is not, the emitted power from curvature radiationwill be a factor of greater than that from synchrotron radiation. The polarizationcharacteristics of curvature radiation are similar to those for synchrotron radiation,except that the polarization vector of synchrotron emission will be orthogonal tothe local magnetic eld vector, while the polarization vector of curvature radiationwill be parallel to the magnetic eld vector.

2.2. B REMSSTRAHLUNG RADIATION

Bremsstrahlung or free-free emission, is the radiation associated with the acceler-ation of a charged particle in the electrostatic eld of an ion or the nucleus of anatom. It is indicative of a hot gas and is produced wherever there is an adequate

density of free electrons. As for the case of magneto-Bremsstrahlung emission theenergy loss due to Bremsstrahlung radiation is more important for electrons thanfor heavier particles because they experience greater acceleration due their smallermass. However, for certain systems such as solar ares, the emission from heavierions may become signicant.

The maximum energy of a photon emitted from Bremsstrahlung radiation, forany two charged particles, is given by (Heristchi, 1986),

E max = m

z

E 1

m 2 + m 1 + E 1 , M cos ; (2.23)

where E 1, M , and m 1 are the kinetic energy, momentum, and rest mass of the

incident particle respectively, m 2 is the rest mass of the target particle and isthe emission angle measured from the incident particle’s direction. Figure 2.5shows the variation in the maximum emitted energy with the angle of emissionfor electron-proton (where the electron is the incident particle accelerated by thetarget proton) and proton-electron Bremsstrahlung for various proton and electronenergies. For the gamma-ray energy range, where the hot gas is optically thin tothe emission, the emitted power is only weakly dependent upon the frequency andproduces a continuous spectrum of the form (Robson, 1996),

P d : (2.24)

The degree of linear polarization of the emission from electron-proton Brems-strahlung radiation, is given by (Gluckstern et al., 1953; Gluckstern and Hull,1953),

=

m

e

c

2E z D 0 , 2m 3

e

c

6

E

2 0 , m e c

2E 0 + 2m 3

e

c

6; (2.25)


13/80


Figure 2.5 . The variation of the maximum energy (in units of m e

c

2) of emitted photons fromelectron-proton (dashed lines) and proton-electron (solid lines) Bremsstrahlung with the directionof emission for various incident particle energies. The lines correspond to equivalent electron andproton velocities (Heristchi, 1986).

where E is the energy of the emitted photon,

0 = E e , M cos ; (2.26)

and E e

is the initial total energy of the electron (rest mass + kinetic energy). A plotof the variation of the degree of linear polarization with the emitted photon energyfor an initial electron energy of E

e

= 6m e

c

2 is shown in Figure 2.6 for variousemission angles.

The polarization vector tends to be parallel to the direction of acceleration andthe photons tend to be emitted perpendicular to the electron’s plane of motion. Thedegree of linear polarization can reach high levels of the order of 80% and reaches


14/80

322 F. LEI ET AL.

Figure 2.6 . The variation of the electron-proton Bremsstrahlung cross-section (lower gure) and thedegree of linear polarization (upper gure) with the emitted photon energies for E

e

= 6m e

c

2 andvarious photon emission angles (Gluckstern and Hull, 1953).

a maximum for a scattering angle which is dependent upon the incident electronenergy.

2.3. C OMPTON SCATTERING

Compton scattering involves the collision between a photon and an electron inwhich there is a transference of energy and momentum. In theastrophysical context,there are two instancesof interest.Therst is thegeneral caseofCompton scatteringand regards the collision of a high-energy photon with a free electron. Generally,the photon energy is sufciently high that any electron binding energies can beneglected, and the electron can therefore be assumed to be free. Figure 2.7 shows aschematic view of the Compton scattering processes.The second case, involves thescattering of low-energy photons off relativistic electrons and is known as inverseCompton scattering. The average energy of the scattered photons is given by


15/80


16/80

324 F. LEI ET AL.

Figure 2.8 . The degree of linear polarization of scattered photons created by a non-polarized incident

beam.

" =

E

0

E 0=

11 + E 0 = m e c 2 1 , cos

: (2.30)

The degree of linear polarization of the scattered photons is given by,

U = sin 2

" + "

, 1, sin2

(2.31)

and is shown in Figure 2.8 for various energies and scattering angles.For a polarized photon beam, the azimuthal distribution of the scattered photons

is no longer isotropic, but is related to the electric vector of the incident photons.The Klein–Nishina differential cross-section for a free electron at rest becomes,

d KN ; Pd

=

12 r

20 "

2 " + "

, 1, 2sin 2 cos 2 ; (2.32)

where is the azimuthal scattering angle, which is dened as the angle betweenthe polarization unit vector of the incident photon, P 0, and the plane of scattering.

The degree of linear polarization of the scattered photons is given by

P = 2 1 , sin2 cos 2

" + "

, 1, 2 sin cos

(2.33)

and is shown in Figure 2.9 for photons scattering at right angles to P 0.

For both the polarized and non-polarized incident beams, the polarization unitvector, P , of the polarized fraction of the scattered photons, is given by (Angel,1969),

P =

1j P j

P 0 D D ; (2.34)


17/80


Figure 2.9 . The degree of linear polarization of scattered photons, at = 90 , created by a 100%polarized incident beam.

where D is the direction vector of the scattered photon. Compton and inverseCompton scattering are very important astrophysical mechanisms and can bothproduce polarized photons from an initially unpolarized ux. However, scatteringis also responsible for the depolarizing of polarized beams, and thus an originallypolarized ux undergoing multiple scattering will have a substantially reduceddegree of linear polarization.

The degree of linear polarization observed from Compton and inverse Comptonscattering is dependent on the vectors of the incident photons being aligned. For anisotropic distribution of incident photons the scattered beam will be composed of polarized components from all incident directions, these components will cancelleaving a completely non-polarized beam.

2.4. M AGNETIC PHOTON SPLITTING

In an extremelystrongmagnetic eld where B approaches a fraction of thequantumcritical eld:

B

c r

=

m

2e

c

3

e h

= 4 : 413 1013 G ; (2.35)

magnetic photon splitting ! , as predicated by quantum electro-magneticdynamics, can be a dominant production mechanism of low-energy gamma-rays(Mitrofanov, 1986; Baring, 1993, 1995). It has a similar effect to ! e , e + paircascade in reprocessing high-energy gamma rays down to low-energy gamma rays.Baring (1995) has shown that the emerging photons from the ! cascade arestrongly polarized (20–30%) with a reverse in polarization angle at the peak of theemerging spectrum. Neutron star sources such as pulsars, soft gamma-rayrepeaters


18/80

326 F. LEI ET AL.

Figure 2.10 . An example of the ! ; cascade emerging spectra in terms of ? and k components.Also plotted is the polarization P " showing the reversal of the polarization angle and the zero break at the peak of the emission spectrum (Baring, 1995).

(SGRs) and possibly gamma-ray bursts (GRBs) provide excellent candidates forastrophysical sites where photon splitting may operate. Polarization studies would

be the most effective method for conrming the action of !

reprocessing ingenerating the source spectra.

The derivation of the splitting rate and the solutions of the kinetic equationsof the magnetic photon splitting process are beyond the scope of this paper anddetailed descriptions and treatments can be found in Baring (1993, 1995) andHarding et al. (1997). As an example, the solutions of the polarization dependentkinetic equations are depicted in Figure 2.10 for the case of B = B

c r

wherethe photon propagation angle relative to the eld is = = 2 and the emissionregion is of the size of R = 2 106 cm (Baring, 1995). In the gure one cansee that the individual polarization component spectra are very similar and thepolarization P " = j n

?

" , n

k

" = n

?

" + n

k

" j is strong (20–30%). However,as photons of perpendicular polarization component are preferentially destroyed athigher energies and created at lower energies, i.e., below the peak, this behaviourgeneratesa zero in thefunction P " and a reversal in thepolarizationangle betweenenergies below and above the peak energy point in the emission spectrum. This is aprominent feature of photon splitting that could distinguish it observationally frompolarized synchrotron radiation.


19/80


3. Potential Astronomical Sites of Polarized Gamma-Ray Emission

As demonstrated in Section 2, almost all emission mechanisms that lead to the

creation of gamma rays will produce polarized photons with little or no needfor specialized source geometries or physical conditions. Thus, many gamma-rayemitting astronomical objects are expected to be sources of polarized emission.

Polarimetric observationshave the ability to provide a unique insight into astro-nomical objects where several models may t the observed data equally well. Bysuccessfully identifying the correct emission mechanism, many models may beeliminated and valuable information can be gained about the emission regions.

3.1. G AMMA -RAY BURSTS

After more than 20 years of study the origin of GRB remains a mystery. It is evenimpossible to say whether they are a local, galactic or cosmological phenomena.Recent advances in GRB observations, those carried out by BATSE (see Fishamnet al. (1992) for the description of the instrument and Kouveliotou et al. (1995)for a review of the observations) in particular, do provide some well denedcharacteristics of GRBs. They can be briey summarised as below:

(1) They are isotropicaly distributed but bound in radial direction.(2) Their light-curve spans time scales ranging from 0.1 s to 100 s, with

sub-millisecond structures.(3) Their spectra are hard, in single or multiple power-law forms. Energy

ranging from keV to GeVs.(4) Absorption cyclotron features have been reported in GINGA observations

(Murakami et al., 1988).The implied luminosities, the observed sub-millisecond scale variability and the

possible cyclotron features suggest a neutron star (NS) or black hole (BH) origin.Although a wide range of sources and processes have been proposed, only threepossible source distributions can satisfy the stringent isotropic source conditionimposed by the BATSE results: heliospheric shells, extended galactic halos orcosmological sources.

Although the local Oort cloud could produce the required GRB distribution,heliospheric shells are unlikely to be the source of GRBs, as there are no knownmechanisms that can create intense gamma-ray ashes without the signicantproduction of radiation at other wavelengths.

Galactic models have effectively been ruled out by the isotropic nature of theBATSE data. Only the extended galactic halo model with a population of oldmagnetized neutron stars is still a possibility (e.g., Brainerd, 1992; Li and Dermer,1992). Harrison et al. (1993) have suggested that neutron stars born in the halo witha signicant velocity may form an extended halo. Radio observations of high birthvelocity radio pulsars (e.g., Lyne and Lorimer, 1994) do suggest the existence of


20/80

328 F. LEI ET AL.

a very large spherical halo of old neutron stars that is consistent with the BATSEobservations.

Cosmological models (e.g., Pacz ýnski, 1992; Fenimore et al., 1993) are becom-ing increasingly popular, as sources at cosmological distances naturally producean isotropic distribution and the geometry of an expanding universe could causea reduction in the number of fainter, and therefore, more distant bursts. Cosmolo-gical models do have their own problems however, most notably is that they mustbe signicantly more energetic to produce the intensity of gamma-rays observed.Another problem arises due to the presence of GeV photons in the spectra of someGRBs as it is difcult to avoid pair production attenuation in the source. The smallsource size implied by the short time scale variations in the GRB light-curves(Bhat et al., 1992; Ryan et al., 1994), results in high photon densities leading tophoton-photon pair production at energies above m c 2. For isotropic emission froma stationary source, the burst must be within a few kpc to avoid this attenuation(Schmidt, 1978). Bursts may occur at greater distances if the emission is aniso-

tropic, as the pair production threshold increases for smaller angles between thephotons. At cosmological distances, to avoid attenuation of GeV photons, the con-straints on the emission are quite severe and imply strong beaming of the emittedphotons.

One possible model that meets the observational criteria involves the mergingof two compact objects, such as neutron stars, at cosmological distances (Moch-kovitch et al., 1995). Mergers would result in the generation of over 10 53 ergs,predominately in the form of neutrinos. To account for the observed burst bright-ness, only 0.1% of the energy must be converted into gamma-ray photons, which ispossible through neutrino–antineutrino annihilation. However, problems do arisewith baryonic pollution and the expected merger rate in galaxies not matching the

observed frequency of bursts (Sommer et al., 1994).Shaviv and Dar (1995) proposed that GRBs can be generated by inverseCompton scattering from highly relativistic electrons in transient jets. Such jetsmay be produced along the axis of an accretion disk formed around stellar black holes (BH) or neutron stars (NS) in BH–NS and NS–NS mergers and in accretioninduced collapse of magnetized white dwarfs (WD) or neutron stars in close binarysystems. Such events may produce the cosmological GRBs. Transient jets formedby single old magnetized neutron stars in an extended galactic halo may produce alocal population of GRBs. These two distinct sources of highly relativistic jets mayexplain the existence of the two populations of GRBs, the long duration popula-tion ( 1 s) and the short duration ( 1 s) population, respectively. Shaviv and Darhave demonstrated that jet production of GRBs by inverse Compton scattering canexplain quite simply the striking correlations that exist between various temporalfeatures of GRBs, their duration histogram, the power spectrum of their complexmulti-peak light curves, their power-law high-energy spectra and other features of GRBs.


21/80


Figure 3.1 . Average polarization of long-duration GRBs as a function of their duration.The maximumaverage polarizaffonoccur fordurations of about 5 s where the average polarization is nearly complete(Shaviv and Dar, 1995).

Figure 3.2 . Histogram of the expected polarizations (4% bins) calculated for GRBs (Shaviv and Dar,1995).

One of the predication of the Shaviv and Dar jet model is the polarization char-acteristic of GRBs. As discussed in Section 2, Compton scattered radiation froma highly relativistic jet is partially polarized with the direction of the electric eldperpendicular to the jet axis. Figure 3.1 shows the expected polarization of long-duration GRBs as a function of their duration, t . As can be seen, the polarizationhas a maximum for t of the order of 5 s. At maximum, the gamma rays are almost


22/80

330 F. LEI ET AL.

completely polarized. The polarization is not a unique value for a given durationhowever, even without dispersion, because the bursts are generated at differentredshifts. Hence if one wants to compare the predicted average polarizations withobservations, a histogram of polarization as shown in Figure 3.2 may be moreuseful.

So far no polarimetric study of GRBs has been performed successfully. Hills(1997) has performed polarimetric analysis on the COMPTEL/CGRO data of GRB910503 and GRB 940217. As will be shown in Section 5 the COMPTEL telescopecan be operated as a gamma-ray polarimeter with a modest sensitivity. COMPTELobservations of GRB 930131 and GRB 940217 should be sensitive to a minimumdetectable degree of linear polarization, at the 3 level in the 750 to 1125 keVenergy range, of 9.6% for both sources. Thus, COMPTEL should be sufcientlysensitive to place important constraints on the emission mechanisms leading to theproduction of GRBs.

The analysis of the real GRB 910503 data, for both with and without the inter-

peak region is consistent with the hypothesis that the emission is unpolarized.When t to a cos 2 distribution, the analysis of the real data does, however, revealextremely high Q factors indicating polarization levels of over 600%. In both casesP

2) is extremely high and indicates that the modulation is due to a systematicerror rather than to random errors.

The analysis of the real GRB 940217 data also appears to contain a modulationthat has arisen due to an unknown systematic error rather than due to a polarizedresponse and is not consistent with either a straight line ar a cos2 distribution.

Several possible sources for this systematic error have been eliminated includingvarying thresholds in the various COMPTEL modules, the non-operating modulesthat were awaiting out-gassing and selection effects in the data lost from the

telemetry buffer.

3.2. G AMMA -RAY PULSARS

The rst pulsar was discovered in 1967 (Hewish et al., 1968) as a series of radiopulses with a period of about 1.33 s. Since then over 500 radio pulsars have beenfound, with an average period of just under 1 s and ranging from 1.5 ms to nearly5 s. Pulsars are believed to be rapidly rotating neutron stars where the magneticaxis is at an angle to the rotational axis. Emission occurs continuously into twoconical beams above the magnetic poles and a pulse of photons is therefore onlyobserved every time one beam points towards the observer.

Only seven gamma-ray pulsars are known to exist, including the two mostprominent gamma-ray galactic point sources, the Crab and Vela pulsars (Nel et al.,1996). Six of these also emit at radio frequencies, but the Geminga pulsar is theonly known radio-quiet pulsar. The radio emission amounts to a trivial fraction(typically 10 , 5) of the total energy loss, with most of the energy emitted in theX-ray and gamma-ray ranges.


23/80


Figure 3.3 . The variation in the intensity of the optical Crab pulsar emission during one cycle (Smithet al., 1988).

Table 3.1Summary of the polarization measured for the mainpulse and the secondary pulse of the optical Crab pulsaremission (Smith et al., 1988)

Degree of linear Polarizationpolarization angle

Main pulse 8.4% 112

Secondary pulse 8.1% 116

Information on the polarization characteristics of gamma-ray pulsars is rareand it is difcult to collect. One of the best studies currently available relates tothe optical polarization of Crab pulsar by Smith et al. (1988). Observations of thepolarization of the pulsed optical emission from the Crab pulsar show that boththe angle and the degree of polarization change during the period of the pulses.Figures 3.3, 3.4, and 3.5 show the intensity, polarization angle, and degree of linearpolarization of the optical Crab pulsar emission during one cycle.

Table 3.1 contains a summary of the polarization angle and degree of linearpolarization measured at the peak of the main pulse and the interpulse (Smith et al.,1988). The similarities in the polarization characteristics indicate that the pulsesoriginate from two separate sources with the same emission mechanism.

Theoretical models to explain the production of gamma-rays by isolated pulsarsfall into two general categories. In polar capmodels (Daugherty andHarding,1982),


24/80

332 F. LEI ET AL.

Figure 3.4 . The variation of the polarization angle of the optical Crab pulsar emission during onecycle (Smith et al., 1988).

Figure 3.5 . The variation in the degree of linear polarization of the optical Crab pulsar emissionduring one cycle (Smith et al., 1988).


25/80


charged particles are accelerated in the electric elds that develop near the polarcaps of the neutron stars. The primary particles induce electromagnetic cascadesthrough thecreation of electron-positron pairs by eithercurvature radiation (Daugh-erty and Harding, 1982, 1994, 1996) or inverse-Compton radiation (Sturner andDermer, 1994). Magnetic photon splitting can be the alternative photon attenuationmechanism. Harding et al. (1997) have shown that there is a strong polarizationeffect both in the energy of the spectral cutoffs and the spectral shape just below thecutoffs when photon splitting process is involved in their polar cap model. Whilethe emission involving only the pair production attenuation mechanism has muchless distinctive polarization features.

In the outer gap models (Cheng et al., 1986), the particle acceleration takes placein charge depletion regions much further from the magnetic poles and gamma-rayemission is either by synchrotron emission or inverse Compton scattering by theaccelerated e beams. Since the magnetic elds in the outer gaps are too lowto sustain one-photon pair production cascades, it must rely on photon-photon

pair production of gamma-rays, interacting with either non-thermal X-rays fromthe gap or thermal X-rays from the neutron star surface, to initiate pair cascades.The modied version of the outer gap model (Chiang and Romani, 1994; Romaniand Yadigaroglu, 1995) successfully accounted for the radio to gamma-ray pulseoffsets of the known pulsars, as well as the shape of the high-energy pulse proles.In the case of Crab pulsar this model naturally reproduced the double sweep inthe polarization position angle as observed in optical wavelengths (see Figure 3.2above and Figure 5 of Romani and Yadigaroglu, 1995).

It is clear that polarization studies in the gamma-ray energy range could playan important role in determining the nature of pulsar emission. For example, thesimilarities in the radio, optical, and gamma-ray spectral indices, have suggested

that the radiation originates from the same emission mechanism. This could beconrmed if the optical and gamma-ray polarization angles were found to bealigned (M ész àros et al., 1988). Polarization could also be the key to differentiatingbetween polar cap models and outer gap models.

3.3. S OLAR FLARES

Solar ares areclosely associated with thephenomenaof sunspotsandaregenerallyfound near the larger more complex groups of spots. They are a sudden andshort-lived brightening of the chromosphere. Flares are normally viewed with H spectroheliograms, as they are only occasionally bright enough for wide bandoptical detection. Several ares a day may occur within the more active regionsof sunspots. The lifetime of a are may vary from about 20 min to over 3 hoursfor the bigger ares. Flares are typically 20 000 to 40 000 km across with a totalenergy emission between 10 23 and 10 25 J. Besides optical emission, ares producecomplex radio, ultraviolet, X-ray, and gamma-ray emissions. Flares also produce


26/80


27/80


Figure 3.7 . The degree of linear polarization vs viewing angle for four heights in the coronal loopand the whole loop for a collimated electron beam (Leach and Petrosian, 1983).

line emission and are thought to be emitted solely by electron Bremsstrahlung(Petrosian et al., 1994).

It is unlikely that the nuclear line emission is in itself polarized, however, the

emission from electron Bremsstrahlung (Gluckstern and Hull, 1953) and proton-electron Bremsstrahlung (Heristchi, 1987) can be highly polarized. Leach andPetrosain (1983) have predicted the degree of linear polarization to be expected insolar ares at hard X-ray energies from 30 to 100 keV. Figures 3.7 and 3.8 showthe variation in the degree of linear polarization with the polar angle, where 0

is away from the photosphere, for various heights within a coronal loop and forthe whole loop at photon energies of 16 and 102 keV. Figure 3.7 corresponds toa model with a strongly collimated beam of electrons and shows a high degreeof polarization, especially higher in the loop and at angles perpendicular to theelectron beam. The degree of linear polarization for the whole loop reaches 20 to25% for both energies. Figure 3.8 corresponds to an electron model with isotropicpitch angles and shows a lower degree of polarization. However, the polarizationof the whole loop can still reach 10 to 15% for both energies. For both energies,curve 1 corresponds to the top of the loop, curve 5 to the centre of the loop andcurves 7 and 9 to the chromosphere at two column depths.

Attempts to measure the hard X-ray polarization of solar ares have been besetby instrumental difculties (Nakada et al., 1974; Tindo and Shuryghin, 1976;


28/80

336 F. LEI ET AL.

Figure 3.8 . The degree of linear polarization vs viewing angle for four heights in the coronal loopand the whole loop for isotropic electron angles (Leach and Petrosian, 1983).

Tramiel et al., 1984) and no attempts have been made to measure the gamma-raypolarization. The Tramiel et al. (1984) measurement of polarization at 20 keV,showed the polarization to be much lower than predicted by Leach and Petrosain

(1983). This was attributed to the pollution of the Bremsstrahlung spectrum bythermally generated photons from close to the photosphere and the fact that theinstrument had no spatial resolution. Therefore it could not discriminate betweenphotospheric emission from the are and hard X-ray emission from the otherregions of the Sun (Leach et al., 1985).

It can be seen from the discussion in this section that polarization resolvedobservations of gamma-ray emission could be important to the further understand-ing of the emission mechanisms and thus the nature of the primal accelerationmechanisms in solar ares. However, at lower energies the hard X-ray continuumis contaminated by thermal emission and above 1 MeV the gamma-ray emission isdominated by lines. This leads to the conclusion that the best area for polarimetricinvestigation is in the 0.1 to 1 MeV energy range.

Any measurement of the polarization of the continuum emission will placeimportant constraints on the emission models. For instance a large degree of linearpolarizationwill be difcult to reconcilewith pion decay models. Polarizationcouldalso be a good diagnostic as to the level of beaming of the accelerated chargedparticles which produce the Bremsstrahlung emission.


29/80


Table 3.2Polarimetric measurements of the Crab nebula at opticaland X-ray wavelengths (Smith et al., 1978; Weisskopf et al., 1978)

Wavelength Polarization/% Polarization angle/

Optical 8.1 152X-ray 19 : 22 0: 92 155 : 79 1: 37

3.4. O THER POSSIBLE SITES FOR POLARIZED EMISSION

Many gamma-ray emitting objects are of little interest in the context of polarimetricobservations as, their emission mechanisms will lead to the production of unpolar-ized photons. These include supernovae and the Al 26 galactic background, whichboth produce nuclear line radiation, as well as the diffuse galactic centre emissionwhich is primarily annihilation line radiation. It is impossible to fully catalogue themyriad of astronomical objects that may produce polarized gamma-ray emission,but a few other objects of interest are briey covered in this section.

3.4.1. The Crab NebulaThe Crab nebula supernovae remnant (SNR) was created in 1054 AD and takes theform of an expanding cloud of gas powered by a central pulsar. The Crab nebulaemits at almost all wavelengths from the radio to the gamma-ray region. Polariza-tion measurements of the Crab nebula have been performed at radio wavelengths(Velusamy, 1985) and show strong local variations in both the degree of linearpolarization and the polarization angle which map out the lamentary nature of the

nebula. The degree of linear polarization reaches up to 30% in the northern jet.Polarimetric measurements have also been made at other wavelengths includingthe optical (Smith et al., 1988) and X-ray (Weisskopf et al., 1978) regions. Thepolarimetric properties of the Crab nebula at these wavelengths are shown inTable 3.2.

The consistency in the polarization angle at optical and X-ray wavelengths,shown in Table 3.2, suggests that a singlemechanismis responsible forthe emission.The only known mechanism that can produce polarized emission over such awide energy range is synchrotron radiation. The detection of polarized gamma-rayemission from the Crab nebula would provide a useful insight as to the whethergamma-ray production was linked to the emission at other wavelengths.

3.4.2. Active Galactic NucleiActive Galactic Nuclei (AGNs) are thought to be massive black holes at the centresof galaxies that emit large amounts of high-energy radiation by the accretion of material from the surrounding galaxy. AGN manifest themselves as the distant andcompact quasars andas a variety of peculiar galaxies,such as Seyfertsand BL Lac’s.


30/80

338 F. LEI ET AL.

They are typically characterized by the copious emission of lines in the optical andultraviolet from the highly ionised elements that surround the AGN. However, ithas been shown that the majority of their power is emitted in the medium energygamma-ray band (Bassini and Dean, 1983). Emissions from quasars and BL Lac’s objects are closely associated with their relativistically beamed electron/positron jets, as shown in radio and some optical observations. Polarimetry studies in radioand optical wavelengths also revealed that most of them are highly polarizedsources, an expected result as both radiations are most likely due to synchrotronemissions. As for the hard X-ray and gamma-ray emission from AGNs, almostall theories associate it with electrons in either the accretion disk or the jets.In both cases the highly ordered geometric conditions of the production regionscan naturally lead to highly polarized emissions for all the possible underlyingproduction mechanisms.

Sunyaev and Titarchuk (1985) have calculated the degree of linear polarizationexpected from low-energy photons, inverse Compton scattered up to hard X-ray

energies by multiple scattering off hot electrons in an accretion disk surroundinga compact object. This is believed to be the situation found in both AGN andgalactic black hole candidates. They nd that the degree of linear polarizationof the subsequent radiation is dependent on the optical depth of the accretiondisk, 0. For optically thick disks, 0 1, the degree of polarization is highlydependent on the angle of emission with respect to the plane of the disk and thenumber of scatters undergone by the photons in escaping from the disk. For a disk with 0 = 2, the maximum polarization of the escaping radiation after 5 scatters is9.5% for an emission region on the centre line of the disk and for radiation escapingperpendicular to the plane of the disk. Figure 3.9 shows the variation in the degreeof polarization with the viewing angle for an accretion disk in the hard X-ray band

for the optical thick case. Figure 3.10 shows the same calculation for the opticallythin case. It can be seen that very high degrees of linear polarization are possible inthe hard X-ray band in the optically thin limit. Thus, the detection of a high degreeof polarization could prove to be a direct probe of the physical conditions presentin the centres of AGNs.

Skibo et al. (1994) proposed that the hard X-ray and soft gamma-ray emissionfrom Centaurus A is beamed radiation from the active nucleus that is Compton-scattered into our line of sight. They successfully used a model of highly beamedincident power-law photon source, scattered off a cold electron cloud moving withbulk relativistic motion along the jet axis, to t the OSSE observational data (seeFigure 3 of Skibo et al., 1994).One of the main predicationsof this model is that thegamma-ray emission from Centaurus A is highly ( 60%) polarized for energiesbelow 300 keV, but the polarization falls rapidly to zero above this energy.

3.4.3. Galactic Black Hole CandidatesSeveral X-ray binary objects have been identied in which one of the componentsis massive enough to be considered as a black hole candidate (McClintock, 1992).


31/80


Figure 3.9 . The degree of linear polarization vs viewing angle for accretion disks with various opticaldepths, 0, in the optically thick limit (Sunyaev and Titarchuk, 1985).

Figure 3.10 . The degree of linear polarization vs viewing angle for accretion disks with variousoptical depths, 0 in the optically thin limit (Sunyaev and Titarchuk, 1985).


32/80

340 F. LEI ET AL.

One of the best candidates is Cygnus X-1 which is also the brightest X-ray objectin the sky. The Sunyaev and Titarchuk (1980, 1985) inverse Compton model of hard X-ray emission for compact objects can be readily apply to Cygnus X-1. Asshown in the last section a high degree of polarization is expected in the hard X-ray,gamma-ray emission.

In a different model, the gamma-ray emission from Cygnus X-1 is thought to bedominated by thermal Bremsstrahlung radiation from a cloud of electron-positronpairs surrounding the black hole (Laing and Dermer, 1988) with a characteristictemperature of k T 400 keV. The accretion disk surrounding the black hole isthought to be optically thick with 0 2. Laing (1990) has suggested that thereis also a transition region from the disk to the pair cloud with a mean temperatureof k T 240 keV. Therefore polarization resolved observations should show alow degree of linear polarization from the disk, a higher polarization from theinverse Compton scattered emission of the optically thin transition region and alow polarization from the unscattered thermal Bremsstrahlung emission from the

pair cloud. With a sensitive spectro-polarimeter, it should be possible to resolve thevarious components of the emission and test the validity of the model.

The degree of linear polarization and the direction of the polarization vector of emission from an accretion disk surrounding a black hole may be strongly inu-enced by general relativistic effects due to the intense gravitational eld (Connorsand Stark, 1977). They predict that the degree of linear polarization and the orient-ation of the polarization vector will change signicantly depending on the energyof the emitted radiation from the accretion disk. Although the change in the degreeof polarization can be explained by other means, the change in the orientation of the polarization vector is less easily explained in the context of inverse Comptonscattering. If such a variation was observed, it could conrm the presence of black

holes.Therecentdiscovered galactic jet sources (i.e., 1E 1740 , 2942, GRS1758 , 258)and superluminal jet sources, GRO J1655 , 40 and GRS 1915 + 105, are all believedto be harbouring stellar type black holes. The analogy to AGNs in morphologyindicates that similar emission mechanisms are at work but in smaller scales.Hence they are potentially excellent candidates for polarization studies.

4. A Review of Gamma-Ray Polarimetric Instrumentation

The measurement of the degree of linear polarization of was rst reported in 1950by Metzger and Deustch, when they exploited the Compton scattering processto measure the asymmetry in the azimuthal distribution of scattered gamma-rays.Since then polarimeters have beenconstructed with ever increasing sensitivities.Asshown in Section 2, a wide range of astrophysical production mechanisms of X-rayand gamma-rays will produce polarized emission. Several X-ray polarimeters havebeen included on astronomical telescopes, but to date no dedicated gamma-ray


33/80


polarimeter has been launched. However, the prospects for gamma-ray polari-metry are good. Measurements are possible on non-dedicated instruments, such asCOMPTEL, and will be possible on some of the next generation of gamma-raysatellites such as INTEGRAL.

In this section, the theory of Compton polarimeters is reviewed rst. Thenpolarimeters used in nuclear spectroscopy are reviewed and the concepts behindthe construction and optimization are discussed. In the second part of this section,the use of COMPTEL as a polarimeter is considered in some detail and severalother future astronomical polarimeters are reviewed.

4.1. T HEORY OF COMPTON POLARIMETERS

The differential Compton cross-section, d , is the probability that a photon of energy E will suffer a collision with an electron in a medium in which the electrondensity is 1 cm , 3. If the scattered photon emerges with an energy E 0 within a solid

angle d

, and is so polarized that its electric vector

0

makes an angle

with theelectric vector of the incident photon, then the Compton polarimetric differentialcross-section may be expressed as (Heitler, 1954),

d d

=

r

20 "

2

4

1"

+ " , 2 + 4cos

; (4.1)

where " = E 0 = E = 1= 1 + 1 , cos , = E = m e

c

2 and r 0 is the classicalelectron radius, m

e

is the massof an electronand is the angle between the incidentphoton direction and the scattered photon direction. The geometrical arrangementused in thederivation is shownin Figure4.1. However, knowledge of the orientationof the scattered photon’s electric vector is not needed to determine the polarization

angle of the incident photons. Thus, after averaging over the electric vector of thescattered photon, the differential cross-section can be rewritten as (Evans, 1955),

d d

=

r

20 "

2

2

1"

+ " , 2sin 2 cos 2

; (4.2)

where is the azimuthal angle of the scattered photon with respect to the electricvector of the incident photon. It can be seen from Equation (4.2) that, for a xedscattering angle, the cross-section will be at a maximum for those photons scatteredat right angles to the direction of the electric vector of the incident photon. This willlead to an asymmetry in the number of photons scattered in directions parallel andorthogonal to the electric vector of a beam of photons incident on some scatteringmedium. By a suitable arrangement of detector elements this asymmetry can beused to determine the direction and degree of polarization of the beam. This processmay be exploited in a Compton polarimeter such as that shown in Figure 4.2.

The detector at A is used to scatter photons from the source into a detector at B.Detector B is rotated about until a maximum is found in the coincidence countsbetween A and B.


34/80

342 F. LEI ET AL.

Figure 4.1 . The geometrical setup used for the cross-section equations.

Figure 4.2 . Basic principle of operation of a Compton polarimeter.

To assess the relative effectiveness of any arrangement of detectors as a polar-imeter, the response of the polarimeter to a 100% polarized beam of photons ismeasured or calculated. This response is known as the Q polarimetric modulationfactor and is given by Suffert et al. (1959) as,

Q =

N

?

, N

k

N

?

+ N

k

; (4.3)

where N ?

and N k

are the count rates in orthogonal detectors in the X Y plane.For point scattering and point detection, the expected count rates are given by thedifferential cross-sections at = 90 and = 0 and the Q factor is therefore,


35/80


Figure 4.3 .Q

factor vs scatter angle for point scatter and detection for various incident photonenergies.

Q =

d = 90 , d = 0 d = 90 + d = 0

; (4.4)

thus,

Q =

sin2 "

, 1+ "

, sin 2 : (4.5)

A plot of the Q factor vs is shown in Figure 4.3. For increasing photon energy,

the maximumQ

factor is achieved at progressively lower

. Futhermore, photonsscattered directly forward ( = 0 ) or directly backwards ( = 180 ) carry noinformation about the degree of polarization of the incident photon beam.

The scattering angle for which the Q factor is at its maximum is plotted inFigure 4.4 and the value of the maximum Q factor for energies up to 10 MeV isshown in Figure 5, where it can be seen that the maximum Q factor decreases frmunity at low energies to zero at high energies.

Equation (4.1) can be re-written in terms of "

= A , 2 B cos2 ; (4.6)

where

A =

r

20

" 2Z

" 1

1"

+ " d " (4.7)

and


36/80

344 F. LEI ET AL.

Figure 4.4 . Scattering angle for the maximum Q factor vs energy for point scatter and detection.

Figure 4.5 . Q max vs energy for point scattering and detection.

B =

r

20

" 2Z

" 1

1 , 1 + 2

2+

2 1 + "

2,

1"

2

2 d" : (4.8)

The theoretical form of the Q factor at an angle with respect to the X -axis,for a given polarization vector angle with respect to the X -axis, , is

Q ; =

, , 90 , , , , 90 + ,

; (4.9)


37/80


38/80

346 F. LEI ET AL.

Figure 4.7 . The two-element polarimeter of Bass et al. (1972).

yields and a better linearity between the energy deposited and the light output.Their high atomic numbers and densities also result in high interaction probabil-ities. Inorganic scintillators suffer from relatively slow response times but usuallythe detection of polarized emission is not time dependent. Semiconductor detect-ors have the advantage of superior energy resolution, but come in smaller sizes.

Most of them need to be cryogenically cooled. Semiconductor polarimeters havebeen extensively used in nuclear physics experiments to identify quantum spinstates where good energy resolution is required to correctly select specic nucleartransitions (e.g., Butler et al., 1973).

Several polarimeters have been reported that have essentially the same geomet-rical layoutas Metzger and Deustch but use inorganic scintillatorsor semiconductordetectors to improve their polarimetric sensitivity. Suffert et al. (1959) have usedNaI scattering and detection elements, Butler et al. (1973) have used Ge(Li) ele-ments and Ohya et al. (1989)haveuseda mixture ofSi(Li) as the scattering elementsand Ge as the detection elements. The POLALI (von der Werth et al., 1995) is oneof the latest realisations of the Metzger and Deustch type of polarimeter. It consistsof ve high purity (HP) Ge detectors, with the centre one being optimized as thescatter and the other four arranged in two pairs orthogonal to each other serving asthe absorbers (analyzers).

A different geometrical setup, whereby only two detectors are used, may beseen in Figure 4.7 (Bass et al., 1972). In this arrangement, the degree of linearpolarization of the beam of photons, , is determined by comparing the ratio of


39/80


coincidence counts in the detectors, i.e., the number of events where the gamma-rayscatters from one crystal to the other, N 1, to the total number of single interactionsin both detectors, N 2, at angles of 0 and 90 with respect to the polarization vectorof the incident beam. Thus,

=

1Q 100

N , 90 , N N , 90 + N

; (4.11)

where in this case,

N =

N 1

N 1 + N 2 ; (4.12)

is the angle about which the detectors are rotated and Q 100 is the Q factorexpectedfor 100% polarized photons. This arrangement has the advantage that the whole of the sensitive area of the polarimeter is used, therefore giving the instrument betterdetection sensitivity than the shielded types.

The use of two Si(Li) detectors side by side in a manner similar to the Bass et al.(1972) type has also been described by Ljubicic and Logan (1971). The use of silic-on as the scattering material has advantages for lower energy gamma rays becauseof its high Compton cross-section compared to its photoelectric cross-section forenergies down to 50 keV. However, Si(Li) detectors must be cryogenically cooledwith liquid nitrogen.

A segmented Ge(Li) crystal can also be used as a polarimeter (Simpson et al.,1983). The single Ge(Li) crystal is electrically divided into eight segments and isused in a similar way to the two element Bass et al. (1972) instrument describedabove. This detector arrangement has a good Q factor due to the small angular

size of the segments and again has the advantage that the whole of the sensitivearea of the detector is used as a polarimeter, thus increasing its overall sensitivity.Recent variations of this type of design based on the use of HP-Ge detectors havebeen reported in Schlitt et al. (1994), Sareen et al. (1995), and von der Werth et al(1995).

Ljubicic and Logan (1972) have described the use of a single planar NaI(Tl)crystal as a polarimeter. In this arrangement, seen in Figure4.8, the crystal is rotatedabout its diameter and the photo-peak count rates with its diameter at 0 and 90 tothe electric vectorof the gamma-ray beam are compared. The thinness of the crystaland the small variance in the photo-peak count rate, means that this setup has botha low detection efciency and a poor Q factor, resulting in sensitivities typicallyan order of magnitude lower than conventional polarimeters. However, this designdoes have the benet of being extremely simple and Ge based polarimeters of thistype will be useful when very accurate energy resolution is required (Twin, 1972;Filevich et al., 1977).

A good review of various type of Compton gamma-raypolarimetersemployed innuclear spectroscopycan be found in Sareenet al. (1995). Here thekey performance


40/80

348 F. LEI ET AL.

Figure 4.8 . Ljubicic and Logan’s (1972) single NaI(Tl) crystal polarimeter.

parameters of these polarimeters and a few more recent ones are summarised inTable 4.1.

4.3. A STRONOMICAL POLARIMETERS

Although the polarimeters discussed in the previous section have reasonable Q factors over a wide energy range, none of them will be suitable for use in theastronomical context because their sensitive areas are generally too small to allowfor efcient observation of the relatively small number of photons from cosmicsources. Using many detectors, each requiring shielding elements would be aninefcient use of available detector mass; a quantity always at a premium in bothsatellite and balloon-borne experiments. The requirement of all the ‘classical’polarimeters for rotation about their axis also restricts the use of such detectorsto rotating spacecraft, which might be incompatible with other instruments on thepayload, or requires the addition of complex mechanisms on three axis stabilisedspacecraft.

Polarimeters have been constructed for use in the X-ray (1 to 30 keV) bandfor astronomical observations, but no dedicated instrument has yet been built foruse in the low-energy gamma-ray range (l00 keV to 10 MeV). However, somegamma-ray telescopes, such as COMPTEL and the INTEGRAL are capable of


41/80


Table 4.1A summary of Compton gamma-ray polarimeters which have been developed and used in nucleargamma-ray spectroscopy in the laboratory

Reference Polarimeter Modulation Modulation Efciencytype factor factor

(lowest energy) (at 1 MeV)

Ewan (1969) 1 planar Ge(Li) 0.13/480 keV 0.13Logan (1971) 1 Si(Li) 0.59Lubicjc (1971) 2 Si(Li) 0.17/121 keV 2.2% @ 122 keVHardy (1971) 2 planar Ge(Li) 0.58Bass (1972) 2 Ge(Li) 0.61/198 keV 0.21Bass (1972) 2 NaI 0.24/470 keV 0.2Butler (1973) 3 Ge(Li) 0.58/417 keV 0.33 0.3% @ 1.33 MeVAsible (1975) 3 Ge(Li) 0.25/1.4 MeV 0.25 1.5% @ 1.33 MeVAoki (1975) sectored planar Ge(Li) 5% @ 0.5 MeVFilevich (1977) 1 planar Ge(Li) 0.15/480 keV 0.152Ishii (1979) 2 HPG planars 0.7/190 keV 0.3Khan (1980) 2 HPG planars 0.74/91.4 keV 0.29 0.2% @ 100 keVMatsuzaki (1981) 2 HPG planars 0.71/197 keV 0.29 5% @ 511 keVIshii (1982) 4 HPG planars 0.8/102 keV 0.325 3.4% @ 511 keVSmith (1982) 1 planar + 2coax HPG 0.24/428 keV 0.16 0.49% @ 1.33 MeVSimpson (1983) sectored coax Ge(Li) 0.3/328 keV 0.26 0.5% @ 300 keVSchlitt (1994) sectored coax HPG 0.21/512 keV 0.18Sareen (1995) sectored planar HPG 0.31/80 keV 0.25 0.6% @ 1.0 MeVWerth (1995) sectored planar HPG 0.2/80 keV 0.08Werth (1995) 5 coax HPG 0.8/300 keV 0.4

polarimetric observations. In addition, there are several proposed future missionsof either dedicated polarimeters or telescopes with good polarimetric sensitivity. Inthis section, the performance of COMPTEL as a polarimeter is reviewed in detail,as it is the only instrument own that may be able to perform polarimetry study, theability of proposed future telescopes to detect polarized emission is also discussedand as well as some dedicated X-ray polarimeters. The INTEGRAL mission willbe discussed in Section 7.

4.3.1. COMPTELThe Imaging Compton Telescope COMPTEL is one of four instruments whichcomprise the Compton Gamma Ray Observatory (CGRO) and was launched on5 April, 1991. COMPTEL operates in the 0.75 to 30 MeV energy range with a1 steradian eld of view, to image the gamma-ray sky using the kinematics of the Compton scattering process. COMPTEL has a 1 angular resolution imagingcapability of approximately 1 and an energy resolution of better than 10% FWHM(Sch önfelder et al., 1993).


42/80

350 F. LEI ET AL.

A schematic view of COMPTEL with the principle of measurement is shownin Figure 4.10, where it may be seen that the upper layer contains seven cylindricalmodules of a low Z liquid scintillator each of which are viewed by eight pho-tomultiplier tubes. This allows centroiding techniques to be used to determine theposition of interaction to between 1 and 2 cm. Each of the upper layer modules are28 cm in diameter and 8.5 cm thick giving an area of 4188 cm 2.

The lower layer, situated 1.5 m below the upper layer, consists of fourteencylindrical NaI(Tl) crystals each of which is viewed by seven photomultipliertubes. This arrangement allows a positional resolution of between 1.5 and 3 cmdepending on the photon energy. Each of the lower layer modules are 28 cm indiameter and 7.5 cm thick giving an area of 8620 cm 2.

Despite the layers having a large detection area, the kinematics of the eventsare such that there is a low probability that a scattered photon will be detected in alower detector. Therefore, the combined effective sensitive area is only a fractionof the total area. For photons in the energy range from 1 to 5 MeV, the full-energy

effective area varies between 10 and 20 cm 2 (Sch önfelder et al., 1993).In theDoubleScatter Mode (DSM), which is thenormal imaging mode, a gamma

ray is rst scattered in an upper layer module and then undergoes photoelectricabsorption in a lower layer module. For each event, various parameters are recorded,the locations and energy deposits of the two interactions, the upper layer interactionpulse shape, the absolute time of the event and the time of ight of the scatteredphoton. From this data, many of the background events can be suppressed by theplacement of a suitable time of ight window, while neutron induced events can beremoved by pulse shape analysis.

If the incident photons are polarized, the azimuthal distribution of the DSMevents should show some degree of asymmetry and follow the shape of a cos 2

function, as described by Sch önfelder et al. (1993) and Lei et al. (1995). ThusCOMPTEL may be operated as a gamma-ray polarimeter. However whereas itmay be sensitive to polarized emission, COMPTEL was not optimized to operateas a polarimeter. Consequently, COMPTEL suffers from several adverse factorsthat reduce its polarimetric sensitivity (Lei et al., 1996). For example the largeseparation of 158 cm between the upper scattering plane ( D 1) and the lowerabsorbtion plane ( D 2), results in photons being only detected at relatively smallscattering angles. As shown in Figure 4.3, the Q factor varies with the scatteringangle and if the scattering is conned to small angles, the measured Q factor atlower energies will be signicantly reduced from the theoretical maximum. It hasalso been shown that there is a strong variation in the efciency of detecting thescattered photons at different azimuthal angles due to the geometrical congurationof the detectors. This is a problem of particular concern as any polarization of theincoming photons is revealed by an asymmetry in the azimuthal distribution of thescattered photons. Off-axis source incidence is another major problem encounteredin using COMPTEL as a polarimeter since this will introduce extra systematicmodulation in the azimuthal distribution of the scattered photons. The solution


43/80


Figure 4.9 . The imaging Compton telescope COMPTEL (Sch önfelder et al., 1993).

to both problems is to calibrate COMPTEL for each given source position andspectral shape by means of M-C simulations, as demonstrated in Lei et al. (1996)and will be further discussed in Section 5.

To operate COMPTEL as a polarimeter, themost important parameter that needsto be evaluated is the modulation factor as a function of incident photon directionand energy as well as the polarization angle (Lei et al., 1996). The Q values as afunction of the incident zenith angle are plotted in Figure 4.10. It shows that Q ishigher at larger incident angles. This can be explained by the fact that in the caseof a large incident angle, a greater number of large angle scattered photons are


44/80

352 F. LEI ET AL.

Figure 4.10 . Left : Q as a function of incident angle. The azimuthal angle of the incident photons isset to zero relative to COMPTEL x -axis. The polarization angle is also assumed to be zero and theenergy of the incident photon is 1 MeV. Right : Q as a function of incident photon energy. The gureis for normal incidence and the polarization angle is zero relative to the COMPTEL x -axis (Lei et al.,1996).

detected. These events contain more information on the polarization of incidentphotons.

The evaluated Q values plotted as a function of the incident photon energies arealso shown in Figure 4.10. Normal incidence is assumed and the polarization angleis zero degrees with respect to the COMPTEL x -axis. As expected COMPTEL hashigher Q values at low energies. It has also been shown in Lei et al. (1996) thatthe Q value of COMPTEL is independent of the polarization angle of the incidentphotons, and in all cases the polarization angle can be correctly located within a

few degrees to the assumed position.Based on the results of Leiet al. (1996)andtheCOMPTEL in-ight performance

data (Sch önfelder et al., 1993), Hills (1997) has evaluated the polarization sensit-ivity of COMPTEL, in particular to strong GRBs and the Crab source. Figure 4.11,shows the photon energy spectrum of the total Crab emission, with comparison tothe minimum ux levels required to detect 100% linearly polarized emission at the3 level in a 14-day observation with COMPTEL.

COMPTEL will be sensitive to the total Crab emission, across the energy range750 keV to 1.5 MeV. The minimum detectable degree of linear polarization froma 1 Crab source and the minimum source ux required to detect 100% polarizedemission in COMPTEL, for a 3 detection in a 14-day observation over variousincident photon energy bands is shown in Table 4.2.

COMPTEL will be thus sensitive to 29.5% linear polarization from a 1 Crabsource, or to 100% polarized emission from a 295 mCrab source, for a 3 leveldetection in the 750 to 1125 keV energy range in a 14-day observation. COMPTELwill not be sensitive enough to perform polarimetric studies of Crab pulsar (Hills,1997).


45/80


Figure 4.11 . Thephoton energyspectrum of thetotal Crab emission, with comparison to theminimumux levels required to detect 100% linearly polarized emission with COMPTEL at the 3 level in a14-day observation.

Table 4.2The sensitivity of COMPTEL for a 3 detection in a 14-day observation forvarious incident photon energy bands (Hills, 1997).

Energy range/keV Minimum detectable Minimum ux to detect 100%polarization/% polarization/mCrab

750–1125 29.5 295750–1500 58.6 586

1000–3000 200.0 2000

GRBs are ideal polarization study candidates. Their short duration and intenseux implies that the collected data will be less affected by temporal systematicerrors and background noise. Figure 4.12, shows the photon energy spectrum of a strong burst (GRB 930131) detected within the eld of view of COMPTEL,compared to the minimum ux levels required to detect 100% linearly polarizedemission at the 3 level in a 1 s observation.

As shown in the gure, COMPTEL will be sensitive to a burst of this type,across the energy range 750 keV to 3 MeV. The minimum detectable polarizationat the 3 level in the COMPTEL data from GRB 930131 in the 750 to 1125 keVenergy range should be 9.6%. Hills (1997) has performed similar analysis to GRB940217, another strong burst detected by COMPTEL, and found that the minimumdetectable polarization at the 3 level in the 750 to 1125 keV energy range shouldbe 9.6%. However the analysis of the real GRB 910503 data, revealed that onlyabout 160 GRB events were recorded, this was far less than the number of counts


46/80

354 F. LEI ET AL.

Figure 4.12 . The photon energy spectrum of GRB 930131, with comparison to the minimum uxlevels required to detect 100% linearly polarized emission with COMPTEL at the 3 level in a 1 sobservation (Hills, 1997).

expected from the spectrum shown in Figure 4.10. This loss is caused by the factthat COMPTEL can only handle a very small count rate in its imaging modeand a lot of the GRB events have been lost due to the overow of the eventbuffer. Nevertheless, Hills (1997) performed the polarization analysis with theavailable data and found that the distribution is consistent with a straight line andtherefore with the hypothesis that the emission unpolarized. However when t to acos2 function, the analysis of the real data does reveal extremely high Q factors

indicating unrealistic polarization levels of over 600%. In both cases,P

2

isextremely high and indicates that the modulation is due to a systematic error ratherthan to random errors. The analysis of the real GRB 940217 data also appears tocontain a modulation that has arisen due to an unknown systematic error ratherthan due to a polarized response and is not consistent with either a straight line ora cos2 distribution. Several possible sources for this systematic error have beeneliminated including, varying thresholds in the various COMPTEL modules, thenon-operating modules that were awaiting outgassing and selection effects in thedata lost from the telemetry buffer (Hills, 1997).

Solar ares represent another possible source of polarized gamma rays. Fig-ure 4.13 shows the photon energy spectrum of the 04/06/80 solar are, as comparedto the minimum ux levels required to detect 100% linearly polarized emission atthe 3 level in a 100 s observation with COMPTEL.

As shown in Figure 4.13, COMPTEL will be sensitive to solar are emissions,across the energy range 750 keV to 2 MeV. The minimum detectable degree of linear polarization for a 3 level detection in 10 and 100 s for various incidentphoton energy bands is shown in Table 4.3.


47/80


Figure 4.13 . The photon energyspectrum of the04/06/80 solar are, with comparison to the minimumux levels required to detect 100% linearly polarized emission with COMPTEL

1997leipolarimetry

Documents