NASA Technical Reports Server (NTRS) 20070013786: The Prospects for X-ray Polarimetry and its Potential use for Understanding Neutron Stars

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NASA Marshall Space Flight Center
The prospects for X-ray polarim
for understanding neutron stars
M. C. Weisskopfl, R. F. Elsner2, D. Hanna3, V. M.
B. D. Ramsey2
NASA Marshall Space Flight Center, VP60, Huntsville, AL 35812, US
NASA Marshall Space Flight Center, VP62, Huntsville, AL 358
McGill University Physics Dept., Rutherford Physics Building, 3
Penn State University, Dept. of Astronomy and Astrophysics, 525 Davey Laboratory, University Park, PA 16802,
Abstract. We review the state of the art for measuring 8, Weisskopf et al. (1976) confirmed this result with a
the X-ray polarization of neutron stars. We discuss how 19-0 detection (P = 19.2% f l.O%), thus conclusively
valuable precision measurements of the degree and po- proving the synchrotron origin of the X-ray emission from
sition angle of polarization as a function of energy and, this plerionic supernova remnant. Unfortunately, because
where relevant, of pulse phase, would provide deeper in- of low sensitivity of those experiments, only upper lim-
sight into the details of the emission mechanisms. We then its were found for polarization from other X-ray sources
review the current state of instrumentation and its poten- (e.g., 13.5%a nd 60% for accreting X-ray pulsars Cen X-3
tial for obtaining relevant data. Finally, we conclude our and Her X-1, respectively; Silver et al. 1979). Since that
discussion with some opinions as to future directions. time, although there have been several missions that have
included X-ray polarimeters such as the original Einstein
Observatory, and Spectrum-X, no X-ray polarimeter has
actually managed to be launched. We discuss this point
1. Introduction
in more detail in 55.
Here we discuss the history and the potential scientific im-
pact of X-ray polarimetry for the study of neutron stars. 3. Scientific basis for neutron-star X-ray
Despite major progress in X-ray imaging, spectroscopy, polarimetry
and timing, there have been only modest attempts at X-
3.1. Radio pulsars
ray polarimetry. Indeed, the last such dedicated experi-
-
ment, conducted by one of us over three decades ago, had Radio pulsars are isolated, rotation-powered, neutron
such limited observing time and sensitivity that even stars converting rotational energy to the energy of ultra-
10% degree of polarization would not have been detected relativistic particles and radiation through electromag-
. from some of the brightest X-ray sources in the sky, and netic coupling. Strong electric fields and pair production in
statistically-significant X-ray polarization was detected in the very strong (up to a few x 1013 G) magnetic field result
only one of the brightest celestial X-ray sources, the Crab in beamed outflow of relativistic particles and radiation
Nebula. Radio and optical astronomers use polarimetry and consequent “search-light” pulses. Theoretical models
extensively to probe the radiation physics and the ge- predict strong linear polarization varying with pulse phase
ometry of sources. Sensitive X-ray polarimetry promises rotation of the neutron star. However, details
to reveal unique and crucial information about physical sion, as discussed, e.g., in numerous papers pre-
processes and structure of neutron stars (and indeed all sented in this Seminar, and even its location (“polar cap”
classes of X-ray sources). X-ray polarimetry remains the versus “outer gap”) remain unclear. X-ray polarimetry
last undeveloped tool for the X-ray study of astronomical could provide decisive information to test detailed models,
objects and needs to be properly exploited. to determine the emission site, and quite possibly to verify,
observationally, the phenomenon of vacuum birefringence
as predicted by quantum electrodynamics (QED).
2. Background
The origin of the high-energy non-thermal pulsar ra-
Only a few experiments have conducted successful X-ray diation is still a matter of debate. Controversy remains
polarimetric observations of cosmic sources. In rocket ob- over the site of this emission: directly above the polar cap,
servations (Fig. l),t he X-ray polarization from the Crab where the coherent radio pulses originate (e.g., Daugh-
Nebula was measured (Novick et al. 1972). Using the X- erty & Harding 1992; Harding & Muslimov 1998), or in
ray polarimeter on the Orbiting Solar Observatory (OS0)- the outer magnetosphere (e.g., Cheng, Ho, & Ruderman
2 Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars
Fig. 2. Crab pulsar optical light curve, position angle, and de-
gree of polarization as a function of pulse phase from Kanbach
et al. 2005. Data are compared to three different predictions of
theoretical models. Courtesy A. Harding.
X-ray pitch angle would smooth the position-angle sweep
(the variation of the position-angle as a function of pulse
phase). Thus, the X-ray-polarization profile (polarization
amplitude and position angle as a function of pulse phase)
Fig. 1. 1971 Photograph of the NASA Aerobee-350 sounding would be a sensitive probe of the magnetospheric particle
rocket #1709 that first detected polarization from the Crab distribution over pitch-angles.
Nebula. Left to right axe R. Novick, G. Epstein, M. C. Weis- Polarimetry also offers an interesting opportunity to
skopf, R. WoH, & R. Linke. observe an exotic QED effect - vacuum birefringence -
induced by a strong magnetic field. Predicted nearly 70
years ago (Euler & Kockell935, Heisenberg & Euler 1936,
1986a,b; Romani 1996). Polarization measurements would Weisskopf 1936), the effect is yet to be verified observa-
discriminate among beaming geometries (e.g., “polar-cap” t ionally.
versus “outer-gap” models). The effect follows from the result (e.g., Tsai & Erber
The requirements on X-ray polarimetry may be esti- 1975) that the indices of refraction for radiation polarized
mated by examining the optical polarimetry of the Crab parallel (rill) and perpendicular (nl)t o the plane formed
pulsar (e.g., Smith et al. 1988; Romani et al. 2001), which by the direction of propagation and the magnetic field are
shows (Fig. 2) high linear polarization, varying rapidly different and depend on the field strength:
through each pulse component. Because the field line pro-
jection determines the polarization position angle, we ex-
pect a close, but not necessarily identical, correspondence
between the optical and X-ray sweep of the position an-
gle. Previous polarimetry of the Crab, limited to a single
energy (2.6 keV) could place only upper limits of 20% to
30% on the pulsar’s polarization in wide phase bins (Silver
et al. 1978). What is needed are much more sensitive mea-
surements capable of providing, at a minimum, data over for photon energies below the one-photon pair produc-
a large number of pulse phase bins that are small enough tion threshold and magnetic fields much lower than B,, =
to resolve different features of the pulse profile. m2c3/efiM 4.4 x 1013 G (here a! is the fine structure con-
e
The pulsar’s X-ray emission is almost certainly syn- stant and is the angle between the direction of propa-
chrotron radiation. If, however, as has been proposed (e.g., gation of the photons and the magne-tic field). Thus, for a
Sturrock, Petrosian, & Turk 1975), the optical emission field of 3 x 10I2 G, we have n~i- nl 4 x for prop-
were curvature radiation, the X-ray polarization would agation transverse to the field lines. At 1 keV, the path
be orthogonal to the optical polarization (Fig. 2). If, in- length for one wave retardation is only a few mm.
stead, the remarkably flat optical spectrum were a low- Pavlov, MBszdros, and co-workers investigated the in-
pitch-angle extension of the X-ray synchrotron popula- fluence of vacuum birefringence on X radiation from neu-
tion (Crusius-Waetzel, Kunzl, & Lesch 2001), the larger tron stars (see Pavlov & Gnedin 1984 and M6szdros 1992
Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars 3
for reviews). To accurately locate the X-ray-emitting site there would be about 30 short bursts, with burst fluence
and infer its properties, vacuum birefringence effects on ra- 10-7-10-5 erg cmW2( 25-100 keV band) in a time inter-
diation propagating in a nonuniform magnetic field must val of 100 ks. It is not inconceivable to be able to detect
be taken into account. For instance, if the emission site polarization from the total fluence under these conditions.
is near the neutron-star surface (as in polar-cap models),
the vacuum birefringence leads to an energy dependence
3.3. DINSs and CCOs
of the polarization direction at a particular rotation phase
(Hey1 & Shaviv 2000). This results in a 10’ phase shift “Dim” isolated neutron stars (DINSs) are radio-quiet and
N
between the optical and X-ray polarization swings, with non-accreting, exhibiting predominately thermal emission
the X-ray sweep leading. (kT M 50-100 eV) from the neutron-star surface. Periods
The measurement of such a phase shift would not only in the range of 3-12 s have been measured for five of of the
locate the emission site, but it would also represent a di- seven currently known DINSs (Haberl2006 and references
rect observational manifestation of vacuum birefringence. therein), and for two of them period derivatives have been
also measured, which allows one to estimate the dipole
components of magnetic field, B = 2.4 and 3.4 x 1013 G
3.2. Magnetrsrs
(Kaplan & van Kerkwijk 2005a,b), approaching the super-
Soft Gamma-ray Repeaters (SGRs) and Anomalous X- strong magnetic fields of magnetars. Although the spec-
ray Pulsars (A XPs) are presumably isolated, magnetic- trum of the brightest DINS, RX 51856.4-3754 (for which
powered neutron stars, converting magnetic energy ulti- no pulsations have been found even in very long exposures)
mately into high-energy radiation. SGRs and AXPs are is close to a perfect blackbody, most of these objects show
likely to be magnetars, i.e. neutron stars with extremely puzzling absorption lines in their spectra, whose origin has
strong (1 014-15 6) magnetic fields. Magnetically coupled not been understood yet (van Kerkwijk & Kaplan 2006;
seismic activity possibly results in high-energy radiation Haberl 2006). Most likely, these lines are formed in Hy-
and plasma outflows, occasionally in extremely luminous drogen or Helium atmospheres of the neutron stars, but
(up to erg s-l) giant flares of SGRs. Radiation the actual atomic transitions involved, and even the chem-
emitted in such superstrong magnetic fields is inevitably ical composition of the atmospheres, remain to be under-
highly polarized (e.g., Niemiec & Bulik 2006, and refer- stood. Since transitions between different types of atomic
ences therein). X-ray polarimetry can provide important states (so-called tightly-bound and hydrogen-like states)
data for understanding the nature of magnetars and for are sensitive to different (mutually orthogonal) polariza-
studying physical processes in extreme magnetic fields. tions, polarization measurements would be very helpful in
In the widely accepted magnetar model (Duncan & understanding the type of the transitions involved, which,
Thompson 1992), the neutron star’s strong magnetic field in turn, would establish the chemical composition and the
powers persistent emission through low-level seismic ac- strength and geometry of the magnetic field (Pavlov &
tivity and heating of the stellar interior; it powers the Bezchastnov 2005). Moreover, even the continuum spec-
burst emission through large-scale crust fracture (Thomp- trum of neutron stars should be strongly polarized (typi- .
son & Duncan 1995,1996). However, there is no generally eally, a few ~10%b)e cause the atmospheric opacities are
accepted detailed model for the SGR emission, particu- very different in different polarizations (e.g., Pavlov et al.
larly in the active (burst) phase (Lenters et al. 2003, and 1995), and polarization degree and position angle show
references therein), with peak soft-X-ray luminosities b e strong variations with pulsar rotation phase (Pavlov &
tween and lou erg s-l (Hurley 2000). Sources such Zavlin 2000). Therefore, using a soft-X-ray polarimeter,
as 1806-20 may have even brighter soft components dur- one could resolve the puzzle of RX 51856.4-3754 - its
ing giant flares. The persistent radiation of magnetars is period could easier be found in polarized light, and the
relatively faint in soft X-rays (L, 1034-35 erg s-l in the polarization variations could provide useful information
N
Chandra-XMM band). However, recent observations with about its (currently unknown) magnetic field and explain
LNTEGRAL and RXTE have revealed hard-X-ray tails in the lack of spectral features. Finally, since the spectra and
the magnetar spectra (e.g., Kuiper, Hermsen, & Mendez light curves of polarization of thermal radiation of neutron
2004; Gotz et al. 2006), with 20-100 keV luminosities up to stars bear unique signatures of the vacuum polarization in
erg s-l, which makes this range promising for po- a strong magnetic field (van Adelsberg & Lai 2006 and ref-
N
larization observations. If an SGR becomes active, the po- erences therein), polarization observations of DINSs could
larization will be amenable to measurement. Giant flares not only detect this effect but also use it for investigations
are too rare and brief to easily observe and might saturate of surface layers of neutron stars.
many instruments. Still one can expect to observe an SGR We also note that the same arguments are applica-
during an active period when it produces numerous short ble to another class of radio-quiet neutron stars - the
(1-sec) bursts with a flux-dependent event frequency - central compact objects (CCOs) in supernova remnants
dN/dS 0: F5I3 (Gogii~e t al. 2001). For activity such as (see Pavlov et al. 2002, 2004 for a review). These objects
SGR 1900+14 exhibited in 1998 August or in 2001 April, also show thermal spectra, with temperatures in the range
4 Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars
of 100-500 eV (hotter than DINSs but somewhat colder ditions, X-ray emission, absorption, and scattering depend
than magnetars), and they show neither pulsar activity strongly on energy, direction, and polarization.
(e.g., pulsar-wind nebulae or 7-ray emission) nor magne- Detailed theoretical studies (Mhkos et al. 1988;
tar behavior (e.g., bursts). Their nature is even less under- M&sz&ros1 992, and references therein) show that the lin-
stood than that of magnetars and DINSs. For instance, the ear polarization depends strongly upon the geometry of
CCO in the Cas A SNR, discovered in the first-light Chan- the emission region’ (accretion column), varies with en-
&a observations (Tananbaum 1999), shows a thermal-like ergy and pulse phase, and reaches values as high as 60%
spectrum emitted from a small fraction of the neutron to 70% for favorable orientations. Calculating the X-
star surface, similar to magnetars (Pavlov et al. 2000), ray spectrum, pulse profile, and polarization from a high-
but no pulsations (Chakrabarty et al. 2001). A particu- temperature, strongly magnetized, rotating neutron star
larly interesting member of this class is 1E 1207.4-5209 is complex. Further, the results depend strongly upon the
in the PKS 1209-51/52 SNR, the only confirmed pulsator assumed distribution of magnetic field, temperature, and
among the CCOs (Zavlin et al. 2000), and the only CCO density in the accretion column (Lamb 1977; M&szkos
whose spectrum shows at least two absorption lines, at 0.7 1982; Kaminker, Pavlov, & Shibanov 1982, 1983; Arons,
and 1.4 keV (Sanwal et al. 2002). The origin of the lines Klein, & Lea 1987; Brainerd & M&z&ros 1991; Isenberg,
remains unknown. Sanwal et al. (2002) have concluded Lamb, & Wang 1998; Araya-G6ches & Harding 2000).
that these lines cannot be associated with transitions in Nevertheless, theoretical modeling has now progressed to
Hydrogen atoms and argued that neither electron nor pro- the point that X-ray polarization measurements can test
ton cyclotron resonance could cause these features. These models and infer parameters of the accreting matter and
-
authors suggest that the lines could due to absorption by of the neutron star.
once-ionized Helium in a magnetic field B 2 x lo1* G For example, phase-resolved polarimetry can distin-
(see also Pavlov & Bezchastnov 2005), while Mori & Hai- guish between pencil and fan radiation patterns, corre-
-
ley (2006) argue that the lines could be formed in an Oxy- sponding to different emission-region geometries. Because
gen atmosphere with B G. Whatever is the ori- the degree of linear polarization is maximum for emis-
gin of the lines and the small, hot emitting areas in CCOs, sion perpendicular to the magnetic field, the flux and de-
only high magnetic fields, possibly with strong multipole gree of polarization are in-phase for fan beams, but out-of-
components, could explain their properties. This means phase for pencil beams. Particularly interesting are those
that the CCO’s radiation is inevitably strongly polarized, cases (e.g., Her X-1,G X1+4, and 4U1626-67) when pulse
and, similar to DINSs, polarization observations would be profiles change dramatically with energy, including pulse-
extremely useful for solving the puzzles of these unusual maxima reversals between 1 and 20 keV (White, Swank,
neutron stars. & Holt 1983). Several authors (Nagel 1981a,b; White,
Swank, & Holt 1983) believe that such behavior requires
both fan and pencil beam components, with each compo-
3.4. Pulsating X-ray binaries
nent dominating at different energies. Hence, polarimetry
can differentiate among the semi-empirical models (e.g.,
Pulsating X-ray binaries are accretion-fed neutron stars,
M6szkos & Nagel 1985; Dermer & Sturner 1991; Bulii
converting kinetic energy into X-ray emission at the stellar
et al. 1992; Isenberg Lamb, & Wang 1998) that qualita-
surface. Rotation and accretion-flow anisotropy, induced
tively reproduce the pulse profiles but predict quite differ-
by very strong magnetic fields to G), modulate
ent phase dependences for the linear polarization.
the X rays. Most theoretical models predict that the linear
Because the linear-polarization direction lies either
polarization of this X radiation is high and varies with
parallel or perpendicular to the magnetic field (depend-
pulse phase (due to rotation of the star) and also varies
ing upon photon energy and absorption depth), the sweep
with energy (due to energy-dependent opacity, cyclotron
of the polarization position angle with pulse phase spec-
resonance, and vacuum birefringence). X-ray polarimetry
ifies the magnetic-field geometry. For instance, abrupt
would provide crucial information to test detailed models,
position-angle changes would indicate a non-dipolar field
to infer parameters and geometries, and to verify vacuum
(Elsner & Lamb 1976). If observed, these position-angle
birefringence observationally.
changes would support other evidence for such fields
More than 50 binary X-ray sources in our Galaxy and in some accreting pulsars (Bulik et al. 1992), due per-
the Magellanic Clouds exhibit pulses with periods from 69 haps to thermo-magnetic effects (Blandford, Applegate, *
ms to 23 min (e.g., Nagase 1989; Bildsten et al. 1997). In- & Hernquist 1983) or crustal breaking and migration
terpreting absorption features between 10 and 100 keV of field-carrying platelets (Ruderman 1991). Such mea-
(Coburn et al. 2002, and references therein), observed surements require a polarimeter sensitive in the en-
in about a dozen pulsating X-ray binaries, as cyclotron ergy bands near the electron-cyclotron energy E,, =
absorption lines (Gnedin & Sunyaev 1974) implies very (11.6 keV)(B/1012G). Because the polarization depen-
strong magnetic fields, 1012-13 G, strengths that we dence on energy is strongest near E,,, one could establish
N
commonly associate with these objects. Under such con- which model is most reliable and obtain magnetic-field
Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars 5
measurements for sources in which the cyclotron line is massive for the others. X-ray polarimetry can provide im-
yet undetected. portant information on the X-ray emission mechanism and
As with radio pulsars (53.1), X-ray polarimetry of the site (disk, corona, or jet) of its origin.
pulsating X-ray binaries may detect effects of vacuum
birefringence. Recent studies of neutron-star atmospheres
4. Instrumental apP;roaches
(e.g., Lai & Ho 2003) and magnetospheres (e.g., Hey1 &
Shaviv 2000) treat this phenomenon. The most vivid po-
There are a limited number of ways to measure linear
larization signature is a 90” position-angle jump at an
polarization in the range 0.1-50 keV, sufficiently sensitive
energy-dependent phase, occurring where normal-mode
for astronomical sources. Before reviewing some of these,
propagation through the so-called “vacuum resonance”
we emphasize that meaningful X-ray polarimetry of such
(Pavlov & Shibanov 1979) changes from adiabatic to nona-
sources is dificult:
diabatic (Pavlov & Gnedin 1984; Lai & Ho 2003). Detec-
tion of such a jump would provide a direct observation of 1. In general, we do not expect sources to be strongly
this QED effect. Moreover, the jump’s phase at a given en- (~10%p)o larized. For example, the maximum polar-
ergy depends on accretion-column inclination and density ization from scattering in an optically think, geomet-
scale length in the radiating region, affording estimates of rically thin, accretion disc is only about 10% at the
these quantities. most favorable (edge-on) viewing angle. Hence, most
In the only X-ray polarimetry on pulsating X-ray bi- of the X rays from such a source carry no polarization
naries to date, Silver et al. (1979) found 99%-confidence information and thus merely increase the background
upper limits of 13.5% polarization for Cen X-3 and 60% (noise) in the polarization measurement.
polarization for Her X-1, at 2.6 keV. In order to make 2. With one notable exception - namly, the Bragg-
significant progress one needs dramatic improvements in crystal polarimeter (54.3) - the modulation of the
sensitivity whereby the polarization may be studied both polarization signal, which is the signature of polariza-
as a function of energy and as a function of pulse phase. tion in the detector, is much less than 100% (typi-
cally, 20%-40%) even for completely polarized source.
Unfortunately, a Bragg-crystal polarimeter has but a
3.5. Other applications
narrow spectral response, thus limiting the number of
We have concentrated on the role that X-ray polariza- photons detected and providing little information on
tion measurements can play in understanding the X-ray the spectral dependence of the polarization.
emission from neutron stars. It is worth emphasizing that 3. The degree of linear polarization is positive definite, so
X-ray polarimetry has far broader applications and would that any polarimeter will always measure (not neces-
allow one to explore such systems as Galactic accretion- sarily statistically significantly) a polarization signal,
disks, Galactic superluminal sources, active galactic nu- even from an unpolarized source. Consequently, the
clei, etc. statistical analysis (54.2) becomes somewhat compli-
Galactic accretion-disk systems involve accretion- cated.
powered neutron stars or black holes, converting kinetic
energy into X-ray emission in the hot inner regions of the It is partly for these reasons that X-ray polarimetry
disk. While the X-ray polarization of radio pulsars, magne- has not progressed as rapidly as X-ray imaging, timing,
tars, and pulsating X-ray binaries is due to strong neutron- and spectroscopy, since the pioneering experiments per-
star magnetic fields, the polarization of accreting binaries formed in the early 1970’s. There are also sociological and
with a low-field-neutron-star or black-hole primary will psychological reasons, especially those involving the com-
likely be dominated by scattering. Due to their complexity, petition for observing time and the projected rate of re-
accretion-disk systems as a group exhibit rich diversity: turn for instruments at the focus of telescope facilities (see
magnetodisks, coronae, winds, quasi-periodic oscillations, also $5) which have played a role in stifling the develop
millisecond pulsations in spun-up pulsars, bursting, etc. ment of X-ray polarimetry.
X-ray polarimetry can probe the properties of the com- Two different types of X-ray polarimeters have flown
plex structure of accretion-disk systems, and explore the to date - Bragg-crystal polarimeters (54.3) and scatter-
space-time structure close to a black hole. This latter is ing polarimeters (54.4). Note that we here differentiate
an especially interesting application of X-ray polarimetry. between instruments that have been expressly designed
G superluminal sources (microquasars) and and constructed to measure polarization and those that
extra c sources such as AGNs (quasars, blazars, possess a degree of sensitivity to polarization, but were
Seyfert galaxies, etc) are all disk-jet sources, converting not designed for this purpose. We shall comment on these
kinetic energy of accreted material into X radiation and latter in 55. In this paper, we also discuss (54.5) the advan-
directed beams of relativistic plasma. Such sources are tages and disadvantages of a more “modern” approach to
comprised of an interacting binary containing a black hole, studying X-ray polarization, which uses the polarization
stellar-mass size in the case of microquasars and super- dependence of K-shell photoelectron emission.
6 Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars
We emphasize the importance of the comparison we with a, = (2/N)lj2.S imilarly, when the upper limit of
make here, as there appears to be some confusion con- the integral in Eq. 6 gets very large compared to 1 and for
cerning the relative merits of the different approaches. The q5 close to 40, P(q5) becomes a normal distribution with
recent literature has asserted such statements as “conven- ut$ = ua/ao.
tional polarimeters based on Bragg diffraction or Thomp- To establish an instrument’s sensitivity to polarized
son scattering methods are characterized by a poor sen- flux, the most relevant statistical question is, if the data
sitivity.. .” (Bellazzini et al. 2006). Such broad statements are unmodulated (no real measure of polarization: a0 =
are misleading, if not incorrect, in that they ignore the 0), what is the probability of measuring, by chance, an
various contexts in which an X-ray polarimeter might fly, amplitude of modulation that is greater than or equal to
as well as issues of proven performance, cost, and simplic- the measured value? The amplitude of modulation is, after
ity. all, positive definite and a value will be measured. In this
case, Eq. 4 may be integrated analytically and, if the data
are Poisson distributed, one finds
4.1. Polarimeter basics
NSa2
All the polarimeters we discuss here have the following P(a‘) da’ = exp (--). (7)
4
characteristic in common. The detected polarization signal
behaves as Note that NS is simply the total number of counts. It has
+ + become customary to single out the amplitude that has
S = S[l a0 cos(27,b q50)], (3) only a 1%p robability of chance occurence. Solving Eq 7,
where 7,b is an angle with respect to the instrument’s axis, this amplitude (al%)i s
in the plane transverse to the incident photon’s direction. 4.29
Here a0 and q50 are related to the degree of linear polar- al% = (N5)1/2* (8)
ization and its position angle, respectively.
The total number of counts, 8, is simply related to the
source (Rs)a nd background (RB)c ounting rates and the
4.2. Statistics total observing time (T) through NS = (Rs+ RB)T.F ur-
thermore, we are interested in the modulation expressed
We assume that the detected signal is drawn from a broad-
as a fraction of the mean source counts, not the mean total
band noise source characterized by a mean and variance
counts, i.e. as = al%/S so that
c2.T hen the probability of measuring a particular ampli-
tude of modulation a and phase q3 is given by 4.29 Rs + RB] ’I2
1 as=-R[S . (9)
NS2a NS2 +
P(Ulq5) = (a2 a; - 2aao cos(Aq5) ,(4)
Finally, one needs to account for the possibility that
the polarimeter does not fully respond to 100%-polarized
where Aq5 z q5-40 and N is the number of different values
radiation. It is convenient to introduce the “modulation
of for which measurements were made -i.e. the number
$J factor”, M, which is the degree of modulation expected
of data points.
in the absence of background and for a 100%-polarized
It follows that the probability of measuring a particular
beam. Thus, independent of the position angle, the min-
amplitude a independent of q5 is
imal detectable polarization at the 99% confidence level,
MDPgg, is
+
-as 4.29 Rs RB1 1/2 .
MDPg9 = =
M T
where IO is the modified Bessel function of order zero.
The probability of measuring a particular angle q5 in- It is sometimes mistakenly assumed that Eq. 10 for the
dependent of the amplitude a is: minimal detectable polarization describes the uncertainty
of a measurement of the polarization: That is not the case.
Eq. 10 indicates when one may be confident that the sig-
nature of polarization has been detected - Le., that the
source is not unpolarized - but not the uncertainty of
its value (Eq. 4). We emphasize this point because the
minimal detectable polarization (MDP) often serves as
In the following we assume Poisson distributed data the figure of merit for polarimetry. While it is a figure of
and set 0’ = 3. There are two interesting limiting cases merit that is useful and meaningful, a polarimeter useful
which can be calculated analytically. In the first we con- for attacking astrophysical problems must have an MDP
sider large arguments of the Bessel function in Eq. 5 and significantly smaller than the degree of polarization to be
for a close to ao; P(a) then becomes a normal distribution measured.
Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars 7
4.3. Crystal polarimeters II!
dl I I I I
The first successful X-ray polarimeter for astronomi-
cal application utilized the polarization dependence of
Bragg reflection. Weisskopf et al. (1972) describe the -
first sounding-rocket experiment (Fig. 1) using crystal po-
0 -
larimeters, which Schnopper & Kalata (1969) had first
suggested for an astronomical application.
To understand the operating principle of such devices,
consider a single flat crystal. The number of reflected X-
rays (N) during an observation of length T, given incident
radiation with a spectral distribution I(E) (keV/keV/cm2-
sec), is
‘(E’)R (E ’, e)A (e )dE’,
Energy (keV)
where A(8) is the projected area of the crystal in the di-
rection of the incident flux and R(E,e ) is the probability Fig. 3. Theoretical reflectivity versus energy for a 40 bilayer,
that a photon of energy E incident on the crystal at angle Ni/C synthetic multilayer, each layer being 34 Athick. F’rac-
tional thickness Ni (0.4) and C (0.6). For 0 A(upper) and 5
13 will be reflected. For a continuum it can be shown (see,
A(1ower) interlayer roughness.
e.g., Angel & Weisskopf 1970) that this expression reduces
to
N length in depth along the direction of the incident photon,
-T = I(E)A(BBA) e(E)f&(6~), (12) then an X-ray entering the crystal may encounter many
such domains, each at a slightly different Bragg angle, en-
where E is related to OB through the Bragg condition:
hancing the probability of a Bragg reflection taking place
nhc before the photon might be absorbed. One can contrast
E=
2dsin(O~) this behavior with that which takes place in a perfect crys-
‘
tal where there is (essentially) only one very large domain
Here d is the interplanar spacing of the crystal lattice, n
with a single orientation; only X-rays with a very narrow
is the order of the reflection, and A6(E)i s the integrated
bandwidth (<< 1e V) can satisfy the Bragg condition, and
reflectivity at incident energy E
all other X-rays are absorbed (or continue to pass through
I the crystal). As a consequence, perfect crystals have very
ae(E)
= R(E,e)de. (14) low integrated reflectivity, which makes them poor can-
didates for polarization analyzers of the continuum fluxes
For partially polarized radiation (P 5 1.0) prevalent from astrophysical sources. An ideally imperfect
crystal can have an integrated reflectivity 10 to 100 times
greater than that of an ideally perfect crystal of the same
material. Angel & Weisskopf (1970) performed a theoreti-
1 sin 20B +
X(--- (1 Pcos24)), cal study of the integrated reflectivity of a number of natu-
sin 28B 2
rally occurring crystals and discussed their potential for X-
where 4 is the angle between the electric vector and the ray astronomy applications. The highest integrated reflec-
plane of reflection, and N, is the number of scattering tivity they found was for graphite (AB(E)= 1.5 x low3).
cells per unit volume, F is the crystal structure factor, Actual realizations using pyrolitic graphite have achieved
ro is the classical electron radius, and p is the absorption values closer to 1 x Synthetic multilayer crystals,
coefficient. The variation of the counting rate as a function wherein alternating layers of high-Z, low-Z materials (e.g.,
of q5 is maximal for 9~ at 45 degrees and the azimuthal Ni/C) are constructed, may achieve comparable and even
variation goes as cos 24. larger integrated reflectivities at low energies. The per-
The integrated reflectivity is not the same for all crys- formance of these crystals depends critically on the inter-
tals, even of a given material, but depends on the relative layer surface roughness which is not easy to control. Figure
orientation of the crystal domains. These latter may be 3 e.g., illustrates such effects. Multilayer crystals operat-
viewed as small “crystalets”. The integrated reflectivity is ing at low energies are especially attractive for observing
highest in the case of the “ideally imperfect” or “mosaic” effects from the so-call “dim” (they are anything but dim)
crystal where perfect alignment of the the crystal planes is isolated neutron stars.
maintained only over microscopic domains in three dimen- Only three crystal polarimeters have ever been con-
sions. If these domains are much less than an absorption structed for extra-solar X-ray applications and only two
8 Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars
- both using graphite crystals without X-ray telescopes the x-axis. Tables of the form factor F may be found in
- were ever flown (sounding rocket, Weisskopf et al. the literature (e.g., Hansen et al. 1964)
1972; OSO-8 satellite, Weisskopf et al. 1976; Spectrum- Incoherent scattering dominates at larger scattering
X (not flown), Kaaret et al. 1994 and numerous references angles and approaches the Thommn limit at sufficiently
therein.) large angles. In the nonqelativistic limit, the cross-section
One of the strongest virtues of the crystal polarimeter for incoherent scattering of X-rays polarized along the x-
is, for Bragg angles near 45 degrees, that the modulation axis is:
of the reflected flux approaches 100%. One can see from
Eq 10 that this is very powerful all other things being equal.
Thus a factor of two increase in the modulation factor im-
proves the minimum detectable polarization (MDP) by a Tables for the incoherent scattering function, I, are also
factor of 2. To achieve the same improvement in sensi- available in the literature (e.g., by Cromer & Mann 1967).
tivity by other means would require either an increase in Various factors dominate the consideration of the de-
effective area or observing time by a factor of 4. sign of a scattering polarimeter. The most important of
The most severe disadvantage of the crystal polarime- these are: (1) to scatter as large a fraction of the inci-
ter is the narrow bandwith of the response - about 23 eV dent flux as possible while avoiding multiple scatterings
for graphite with a mosaic spread (rocking curve width) of (which clearly blurs the polarization dependence); (2) to
0.5 deg. The integrated reflectivity from the second order achieve as large a modulation factor as possible; (3) to
Bragg reflection is smaller than that from the first order collect as many of the scattered X-rays as possible; and
and, of course, the typical flux from astronomical sources (4) to minimize the detector background. The scattering
are usually comparatively weaker so that the overall loss competes with photoelectric absorption in the material,
in sensitivity renders the second (and higher) order(s) of both on the way in and, of course, on the way out. The
marginal utility. Filling in gaps in energy coverage there collection efficiency competes with the desire to minimize
fore requires using different crystals, which, in general, the background. Most practical designs have the detec-
implies a very poor “filling factor”. Here the filling factor tor integrating the two scattering angles over some range
refers to one’s ability to make use of the real estate in which impacts the modulation factor.
a satellite payload that lies perpendicular to the incident Only two polarimeters of this type have ever been con-
flux. Unless stacked (and, because of photoelectric absorp- structed for extra-solar X-ray applications and only one -
tion, stacking cannot be extended arbitrarily) two crystal utilizing blocks of lithium with proportional counters cov-
polarimeters, which effectively cover two energies, divide ering the 4 sides of the blocks orthogonal to the incident
the available area in half, three - one-third, etc. This flux - was ever flown (rockets - three times: in 1968, see
may be contrasted to the scattering and electron tracking Angel et al. 1969; in 1969 see Wolff et al. 1970, and in
polarimeters discussed below which cover a much larger 1971 see, e.g,, Novick et al. 1972; satellite - Spectrum-X
bandwidth with a filling factor of unity, typically, how- (never flown) see Kaaret et al. 1994 and numerous refer-
ever, at the price of a smaller modulation factor. ences therein.)
The virtue of the scattering polarimeter is that it has
4.4. Scattering polarimeters reasonable relative efficiency over a moderately large en-
ergy bandwidth, typically several keV in width. The band-
There are two scattering processes from bound electrons width is large compared to the energy resolution of poten-
that must be considered: coherent and incoherent scatter- tial detectors, e.g., proportional counters, CCDs, etc., so
ing. A comprehensive discussion of both of these processes that polarization measurements as a function of energy
may be found in many atomic physics textbooks (see, e.g., are feasible. The principal disadvantage is a modulation
James 1965). Coherent scattering dominates at small scat- factor less than unity, since only for scattering into 90 deg
tering angles. In the limit of zero scattering angle, the X- will the modulation approach unity in the absence of back-
ray behaves as if it were scattered from a charge Ze, where ground and for a 100%-polarized beam. In order to obtain
e is the charge of an electron. Coherent scattering, there- any reasonable efficiency requires integrating over a range
fore, leads to an enhancement of forward scattering over of scattering angles and realistic modulation factors are
pure Thomson scattering from free electrons. In the non- under 50%, unless the device is placed at the focus of
relativistic limit, the cross-section for coherent scattering a telescope (the modulation factor for the scattering po-
for X-rays traveling along the z-axis and polarized along larimeter on Spectrum-X reached -75%) where it is feasi-
the y-axis is ble to make the scattering volume small which then limits
the range of possible scattering angles.
-bcoh = r~[~os~ecos~~+sin~(b11~1~. The two most popular materials that have been consid-
dw
ered for scattering polarimeters are lithium and beryllium.
Here ro is the classical electron radius, 6’ is the polar scat- The lower the Z, the lower the peak response energy, and,
tering angle, and q5 is the azimuthal angle measured from for cosmic X-ray sources, the higher the sensitivity. The
Weisskopf et al.: The prospects for X-ray polarimetry and its potential use for understanding neutron stars 9
K-absorption edges for these two materials are at .0554 flR5T AUPUFlCATlON
STAGE
keV (Li) and 0.188 keV (Be). The peak energy response
GATE
of typical practical designs are typically 31 7 keV (Li) and I I
15 keV (Be) but it should be noted that the exact peak
N
.
energies are somewhat designldetector-dependent
4.5. Photoelectron tracking polarimeters CCD CAMERA
The angular distribution (see, e.g., Heitler 1954) of the
\PEmURE
-\
K-shell photoelectron emitted as a result of the photo- STOP
DYNASIL
electric absorption process depends on the polarization of WINDOW
the incident photon. In the non-relativistic limit
FIELD SHAPING
RINGS
SECOND AMPLIFICATION
STAGE
Here a0 is the fine structure constant, ro is the classical Fig. 4. Experimental setup for the optical imaging chamber.
electron radius, Z is the charge of the nucleus of the ab-
%
sorbing material, and P = v/c. The variable 5 = and
f(C) is unity away from the absorption edge. to record the avalanche of secondary electrons that result
The considerations for the design of a polarimeter that from gas-multiplication in a high field after the the pri-
exploits this effect are analogoust o those for the scattering mary photoelectron track (and that of the original Auger
polarimeter. In this case the competing effects are the de- electrons) drift into a region where this multiplication may
sire for a high efficiency for converting the incident X-ray take place. The concept is shown in Figure 5. The resulting
flux into photoelectrons and the desire for those photo- charge may then be read out by finely pixellated collection
electrons to travel large distances before interacting with electrodes.
elements of the absorbing material. Detecting the direction of the emitted photoelectron
Here we will concentrate on polarimeters that use gas (relative to the direction of the incident flux) is itself not
mixtures to convert the incident X-rays to photoelec- simple. The reason for this is that electrons, when they
trons. We do this for the following reasons: (1) there are interact with matter, give up most of their energy at the
two promising approaches to electron tracking polarime- end of their track, not the beginning. Of course, in the
try that use this approach and we are quite familiar with process of giving up its energy to the local medium in
both of them; and (2), especially at the X-ray energies of which the initial photo-ionization took place, the electron
interest here (and where the X-ray fluxes are the great- changes its trajectory, thus losing the information as to
est), the range of the primary photoelectrons in solids are the initial polarization. Therefore, devices that wish to
very tiny (e.g 1.5pm in silicon at 10 keV). Tracking such exploit the polarization dependence of the photoelectric
N
events in solids then requires pixels much smaller than the effect have the additional challenge that they must track
current state of the art, making this type of polarimetry the ejected photoelectron’s path, and the most important
essentially impossible at the energies of interest. element of that path is the direction to the first interaction
To our knowledge, the first electron tracking polarime- which gives up the least amount of energy.
ter specifically designed to address polarization mea- It is instructive to examine the image of a track and we
surements for X-ray astronomy and using a gas as the show one obtained under relatively favorable conditions
photoelectron-emitting material was that designed by with an optical imaging chamber in Figure 6. The initial
Austin & Ramsey (1992 - see also Austin & Ramsey 1993; photoionization has taken place at the small concentration
Austin, Minamitami, & Ramsey 1993) These scientists of light to the north (top) of the figure. The bright spot to
used the light emitted by the electron avalanches which the north indicates the short track of an Auger electron.
takes place after the release of the initial photoelectron As the photoelectron travels through the gas mixture it
in a parallel plate proportional counter. The light was fo- either changes direction through elastic scattering and/or
cused and detected by a CCD camera. A schematic dia- both changes direction and loses energy through ioniza-
gram of the experimental setup is shown in Figure 4. The tion. As these take place, the path strays from the di-
use of two multiplication stages (Le. two parallel-plate pro- rection determined by the incident photon’s polarization.
portional chambers) permits triggering of the camera and Of course, the ionization process is energy dependent and
allows for efficient light yields. Of course the detection most of the electron’s energy is lost at the end, not the
scheme produces a two dimensional projection of the pho- beginning, of its track. It should be clear from this pic-
toelectron’s track and this reduces the modulation factor. ture that, even under favorable conditions - by which we
Another gas-detector approach, first discussed by mean those where the range of the photoelectron is quite
Costa et al. (2001), uses “pixillated” proportional counters large compared to its interaction length - the ability to
10 Weisskopf et al.: The prospects for X-ray polarimetry and its potentia3 use for understanding neutron stars
Fig. 5. Cartoon showing the principle of the gas-multiplication
electron-trxking polarimeter. Courtesy J. Swank.
t '
.
.*.
determine a precise angular distribution depends on the
capability and sophistication of the track-recognition soft- Fig. 6. The two dimensional projection of a track produced
ware, not only the spatial resolution of the detection sys- when a 54 keV X-ray was absorbed in 2 atm of a mixture of
tem. The burden falls even more heavily on the software argon(90%), CH4(5%), and trimethylamine (5%). The partic-
at lower energies where the photoelectron track becomes ular track is 12i1 4-mm in Iength.
very short and diffusion in the drifting photoelectron cloud
conspires to mask the necessary track information.
There are pros and cons in each approach. The op-
Although polarimeters exploiting this effect have been
tical imaging chamber has the advantage of flexibility in
discussed in the literature, no device of this type has ever
its readout scale, which can be configured by the appro-
been flown and those built have undergone limited testing
priate choice of optics so that its detection pixel is small
in the laboratory. The claims for the potential performance
compared to the electron track length, especially at the
of these devices at the energies of peak performance de-
low-energy end of the polarimeter response. In contrast,
pend on Monte-Carlo simulations to extend experimental
the keds ize of the pixels (N 50-100-pm) theinselves de-
results. Experimental verification of performance exists at
termine the low-energy response when gas-multiplication
5.4 and 6.4 keV (Bellazzini et al. 2006). We eagerly await
detection is used. This is probably more of a limitation
experimental verification of performance at lower energies,
than might appear at first sight since the arrangement of
around 3 keV, where peak performance is claimed.
detection cells is, in and of itself, asymmetric in position
Both approaches for imaging the projection of the elec- angle, with a built in response at 24, the signature of po-
tron track are quite interesting, especially for use at the larization. This built-in asymmetry not only impacts the
focus of an X-ray telescope (34.6). Electron tracking po- modulation factor (it vanishes if the length of the track is
larimeters must also deal with a energy dependent modu- smaller than the size of a cell), but also introduces spurious
lation factor. This is completely in contrast to the crystal polarization signatures when the track length is compara-
polarimeter, and is more severe than for a typical scat- ble to, or even somewhat larger than the characteristic size
tering polarimeter. This energy dependence will not only of a detection cell. We feel that it is naive to believe that
complicate the calibration of such an instrument, but also such effects can be accurately accounted for by means of
the data analysis. To our knowledge, no published reports Monte-Carlo simulations alone.
of the projected sensitivity of such devices have ever con- The optical imaging chamber, however, is more lim-
sidered the impact of the finite energy resolution and the ited in its selection of fill-gas mixtures in that they
energy-dependent modulation on the data analysis. To do must produce large amounts of light via the addition of
so here is beyond the scope of this paper, but we note that photo-sensitive vapors without any competing (non-light-
the impact of this complication on the sensitivity should producing) collisions with other additives. This potentially
not be ignored. limits control over diffusion which in turn may limit the
The considerations for the choice of the detector gases lowest-energy response of such a device. More detailed
are somewhat different for the two approaches to electron study is required to explore the fill-gas parameter space.
-
tracking discussed here high light yield versus reason- We encourage all experimenters working with gas-
able electron amplification - but both must trade a high multiplication detectors for use as X-ray polarimeters to
absorption efficiency for a long electron track in order to publish a calibration using polarized and, equally impor-
work efficiently as a polarimeter. tant, unpolarized sources in the regime for which the range