Kavli Institute of Astrophysics and Cosmology, 452 Lomita Mall, Stanford, CA
94305, USA.

# Hard X-ray Polarimetry $-$ An overview of the method, science drivers and
recent findings

Tanmoy Chattopadhyay

###### Abstract

The last decade has seen a leapfrog in the interest in X-ray polarimetry with
a number of new polarization measurements in hard X-rays from AstroSat, POLAR,
GAP, and PoGO+. The measurements provide some interesting insights into
various astrophysical phenomena such as coronal geometry and disk-jet
connection in black hole X-ray binaries, hard X-ray emission mechanism in
pulsars and Gamma Ray Bursts (GRB). They also highlight an increase in
polarization with energy which makes hard X-ray polarimetry extremely
appealing. There is a number of confirmed hard X-ray polarimetry experiments
which along with the existing instruments (AstroSat and INTEGRAL) makes this
field further exciting. Polarization experiments may also see a significant
progress in sensitivity with new developments in scintillator readouts, active
pixel sensors, CZT detectors. In particular, the advent of hard X-ray focusing
optics, will enable designing of compact focal plane polarimeters with a
multifold enhancement in sensitivity. In this review, we will focus on the
recent polarimetry findings, science potential of hard X-ray polarimetry along
with possible improvements in the measurement techniques.

###### keywords:

Hard X-ray polarimetry—Scattering polarimetry—Black holes—Neutron stars—Gamma
Ray Bursts—AstroSat—POLAR—PoGO+

<EMAIL_ADDRESS><EMAIL_ADDRESS>
——

12.3456/s78910-011-012-3 #### 000 0000 1– 1

##  1 Introduction

Since the birth of X-ray astronomy, X-ray spectroscopy, timing, and imaging
have met with significant advancement, while the study of the fourth parameter
of radiation or polarization remains majorly unexplored in spite of its
extremely high science throughput. Apart from some coarse polarization
detections, there have not been any dedicated X-ray polarization experiment
primarily due to the low sensitivity of polarimetry compared to spectroscopy,
imaging or timing; which results due to the extremely photon hungry nature of
X-ray polarimetry.

The first successful measurement of polarization in X-ray astronomy dates to
1976 when an X-ray polarimeter on board OSO-8 mission, measured $\sim$19 %
polarization at 2.6 and 5.2 keV for the Crab nebula (Weisskopf $et~{}al$.,
1976, 1978). There were a number of attempts to measure X-ray polarization
with the same polarimeter as well as a few other space-borne and balloon-borne
experiments (Angel $et~{}al$., 1969; Wolff $et~{}al$., 1970; Novick
$et~{}al$., 1972; Griffiths $et~{}al$., 1976; Gowen $et~{}al$., 1977; Silver
$et~{}al$., 1979; Hughes $et~{}al$., 1984) but these could yield only upper
limits at best, due to the low sensitivity of these experiments. After these
initial efforts, no real experiments to measure X-ray polarization were
carried out for more than three decades. Though there were some attempts to
design and build the X-ray polarimeters (e.g. Angel & Weisskopf, 1970; Tsunemi
$et~{}al$., 1992) and few concept proposals for space missions (e.g. XPE,
PLEXAS, Elsner $et~{}al$., 1997; Marshall $et~{}al$., 2003), only one
instrument, Stellar X-Ray Polarimeter (SXRP, Kaaret $et~{}al$., 1994) came
close to a launch on the Russian Spectrum-X-Gamma (SXG) mission in 1998.
However, the mission was eventually cancelled. Later, Gravity and Extreme
Magnetism Small Explorer (GEMS), a dedicated X-ray polarimetry mission
(Jahoda, 2010) was selected for launch in 2014. The mission was also
eventually cancelled due to programmatic issues (see a review on the progress
and development in the X-ray polarimetry field from the initial days by
Weisskopf, 2018). In the absence of any dedicated X-ray polarimetry
experiment, in the last decade there have been a few attempts to measure
polarization for bright X-ray sources by standard spectroscopic instruments
which have moderate polarization measurement capability. To name a few, the
most important results are the detection of high polarization from Cygnus X-1
and Crab nebula by IBIS and SPI on board INTEGRAL (Laurent $et~{}al$., 2011;
Jourdain $et~{}al$., 2012; Forot $et~{}al$., 2008; Dean $et~{}al$., 2008) and
Gamma Ray Bursts by RHESSI and INTEGRAL (Coburn & Boggs, 2003; Götz
$et~{}al$., 2009; McGlynn $et~{}al$., 2007a; McConnell $et~{}al$., 2009). In
most cases, due to the lower polarimetric sensitivity of the instruments,
those detections are far from being conclusive (Rutledge & Fox, 2004; Wigger
$et~{}al$., 2004).

In recent times, there are some interesting polarization measurement reports
in hard X-rays from Cadmium Zinc Telluride Imager (CZTI) on board AstroSat
satellite (Bhalerao $et~{}al$., 2017; Rao $et~{}al$., 2016), balloon borne
instrument, PoGO+ (Chauvin $et~{}al$., 2016), POLAR on board Chinese space
laboratory (Produit $et~{}al$., 2018; Sun $et~{}al$., 2016), GAP on board
IKAROS spacecraft (Yonetoku $et~{}al$., 2006) for bright hard X-ray sources
(Vadawale $et~{}al$., 2018; Chattopadhyay $et~{}al$., 2019; Chauvin
$et~{}al$., 2018a, 2019, b; Zhang $et~{}al$., 2019; Yonetoku $et~{}al$., 2011,
2012). These reports along with those from last two decades (McConnell
$et~{}al$., 2002; Coburn & Boggs, 2003; Laurent $et~{}al$., 2011; Jourdain
$et~{}al$., 2012; Forot $et~{}al$., 2008; Dean $et~{}al$., 2008; Moran
$et~{}al$., 2013; Götz $et~{}al$., 2009, 2013; McGlynn $et~{}al$., 2007b,
2009) have significantly enhanced the interest in the X-ray polarimetry
(Marin, 2018). With IXPE, a dedicated soft X-ray polarimetry mission
(Weisskopf $et~{}al$., 2016; Soffitta, 2017) set to launch in 2021, and a
couple of upcoming dedicated hard X-ray polarimetry missions (e.g. POLIX, Paul
$et~{}al$., 2010, 2016), we expect an exciting time ahead in X-ray
polarimetry.

###  1.1 Hard X-ray Polarimetry: Why?

Scientific importance of X-ray polarimetry has been discussed extensively in
literature (Lei $et~{}al$., 1997; Soffitta, 1997; Krawczynski $et~{}al$.,
2011). In Table 1, the science drivers of X-ray polarimetry at different
energy bands have been summarized for different classes of X-ray sources.

Table 1: Summary of science potential of X-ray polarimetry at different energy
bands.

|  |  |  |  |  |
---|---|---|---|---|---|---
Energy |  Source class |  Science drivers |  Predicted PF % |  Available measurements |  Active missions |  Upcoming/planned missions
|  |  |  |  |  |
0.1$-$1 keV |  BH XRBs, AGNs |  BH spin, GR effects from polarized thermal disk emission (Dovčiak $et~{}al$., 2008; Schnittman & Krolik, 2009) |  $\sim$1-3 % |  |  |
|  Blazars |  First peak of HBL $-$ Jet structure, magnetic field geometry (Tavecchio $et~{}al$., 2018; Zhang $et~{}al$., 2014) |  a few to high % depending on the B field geometry |  |  |
|  Magnetars |  Vacuum birefringence from polarized persistent thermal emission with KT$\sim$0.5 keV (Heyl & Shaviv, 2002) |  $>$80 % |  |  |
|  XDINS1 / XRP2 |  M/R ratio, magnetic field geometry, angle between magnetic axis, rotation axis and viewing direction from polarized thermal emission (Pavlov & Zavlin, 2000) |  $\sim$10-20 % |  |  |
|  Magnetic CVs |  Density profile in accretion column from polarized scattered photons off the polar accretion column (Wu $et~{}al$., 2010) |  a few to 8 % |  |  |
1$-$10 keV |  BH XRBs, AGNs |  BH spin, inclination, study of accretion disk dynamics, GR effects from polarized thermal disk emission (Dovčiak $et~{}al$., 2008; Schnittman & Krolik, 2009) |  $\sim$1-3 % |  A few % of PF for Cygnus X-1 in high soft state (Long $et~{}al$., 1980) |  |  IXPE (2021) (Weisskopf $et~{}al$., 2016; Soffitta, 2017), EXTP (Zhang $et~{}al$., 2016), SOLPEX (Stȩślicki $et~{}al$., 2016)
|  Blazars |  First peak of HBL (faint in this energy range) $-$ Jet structure, magnetic field geometry (Zhang $et~{}al$., 2014; Tavecchio $et~{}al$., 2018) |  a few to high % depending on the B field geometry |  |  |
|  Magnetars |  Vacuum birefringence, signature of RICS (Taverna $et~{}al$., 2014) |  $\sim$20 % |  |  |
|  XRP |  Emission mechanism, geometry - Polar cap/Outer gap/slot gap/striped wind models (Weisskopf $et~{}al$., 2009; Harding, 2019) |  a few tens of % |  $\sim$15 % PF for Crab+nebula by PolarLight (Feng $et~{}al$., 2020) |  |
|  SNR, PWN |  Particle acceleration process in shocks, magnetic field geometry (Bykov $et~{}al$., 2009) |  $\sim$20-50 % from different regions of SNR |  $\sim$19 % PF for Crab nebula by OSO-8 (Weisskopf $et~{}al$., 1978). $\sim$14 % PF by PolarLight (Feng $et~{}al$., 2020) |  |
10$-$100 keV |  BH XRBs |  Corona geometry (Lamp Post/wedge/ spherical/clumpy) from polarized coronal emission (Schnittman & Krolik, 2010) |  $\sim$5 % |  Upper limit of a few % for Cygnus X-1 by PoGO+ (Chauvin $et~{}al$., 2018a) |  |  POLIX (2021) (Paul $et~{}al$., 2010, 2016), PolariS (Hayashida $et~{}al$., 2014), PING-P (2025) (Kotov $et~{}al$., 2016)
|  AGNs |  Corona and torus geometry (Schnittman & Krolik, 2010; Goosmann & Matt, 2011) |  $\sim$10 % |  |  |
|  Blazars |  Second peak of LBL: SSC/ EC/hadronic models (McNamara $et~{}al$., 2009; Zhang & Böttcher, 2013) |  a few % (EC) to 50 % (SSC) |  |  |
|  XRP |  Emission mechanism, geometry - Polar cap/Outer gap/slot gap/striped wind models (Weisskopf $et~{}al$., 2009; Harding, 2019) |  A few tens of % |  $\sim$21 % PF for Crab+nebula by PoGO+ (Chauvin $et~{}al$., 2018b)$,\sim$22 % PF by Hitomi (Aharonian $et~{}al$., 2018) |  |
|  Magnetars |  Signature of RICS from polarized hard X-ray tail (Wadiasingh $et~{}al$., 2019) |  |  |  |
|  APP3 |  Beam shape (pencil/fan beam models) from phase resolved polarimetry near cyclotron energies. Magnetic field, accretion column geometry from accretion shock/disk scattered emission (Meszaros $et~{}al$., 1988) |  up to 30 % |  |  |
|  PWN |  Acceleration mechanism and magnetic field geometry (Weisskopf $et~{}al$., 2009; Harding, 2019) |  $\sim$20-30 % |  $\sim$17.4 % PF for Crab nebula by PoGO+ (Chauvin $et~{}al$., 2018b) |  |
|  Solar flares |  Emission mechanism, electron beaming, magnetic field structure for M and X class flares (Bai & Ramaty, 1978; Leach $et~{}al$., 1985; Zharkova $et~{}al$., 2010) |  $\sim$35-50 % for flares away from Sun’s center |  $\sim$8-40 % PF for 25 flares by CORONAS-F (Zhitnik $et~{}al$., 2006) |  |
100$-$1000 keV |  BH XRBs |  Contribution of jet in hard X-ray flux, jet physics, disk-jet connection (Zdziarski $et~{}al$., 2014) |  $\sim$30-60 % |  $>$50% PF for Cygnus X-1 by INTEGRAL (Laurent $et~{}al$., 2011; Jourdain $et~{}al$., 2012). $>$90 % PF for V404-Cygni by INTEGRAL (Laurent $et~{}al$., 2017) |  AstroSat (Bhalerao $et~{}al$., 2017), INTEGRAL (Winkler $et~{}al$., 2003) |  Daksha4 (2025), POLAR-2 (2024) (Kole, 2019), AMEGO (McEnery $et~{}al$., 2019), e-ASTROGAM (De Angelis $et~{}al$., 2018), SPHiNX (Pearce $et~{}al$., 2019), LEAP (McConnell & LEAP Collaboration, 2016), COSI-2 (Tomsick $et~{}al$., 2019)
|  Blazars |  Second peak of LBL: SSC/EC/hadronic model (McNamara $et~{}al$., 2009; Zhang $et~{}al$., 2014) |  a few (EC) to 50 % (SSC) |  |  |
|  Magnetars |  Signature of QED magneto photon splitting (Wadiasingh $et~{}al$., 2019) |  $\sim$20-60 % |  |  |
|  XRP |  Emission mechanism, geometry - Polar cap/Outer gap/slot gap/strpped wind models (Weisskopf $et~{}al$., 2009; Harding, 2019) |  a few tens of % |  24-32 % PF for Crab+nebula by INTEGRAL, AstroSat (Jourdain & Roques, 2019; Vadawale $et~{}al$., 2018) |  |
|  PWN |  Acceleration mechanism and magnetic field geometry (Weisskopf $et~{}al$., 2009; Harding, 2019) |  $\sim$30-60 % |  39-47 % for Crab nebula by INTEGRAL, AstroSat (Dean $et~{}al$., 2008; Vadawale $et~{}al$., 2018) |  |
|  GRBs |  Prompt emission mechanism (SO/SR/CD models), jet composition, dissipation mechanism (Toma $et~{}al$., 2009; Gill $et~{}al$., 2018) |  a few % to 80 % PF |  a few % ($\sim$12 GRBS) to high PF for $\sim$15 GRBs by GAP, POLAR, AstroSat, INTEGRAL (Kole $et~{}al$., 2020; Zhang $et~{}al$., 2019; Chattopadhyay $et~{}al$., 2019; Yonetoku $et~{}al$., 2011, 2012) |  |
|  Solar flares |  Emission mechanism, electron beaming, magnetic field structure for X class flares (Bai & Ramaty, 1978; Leach $et~{}al$., 1985; Zharkova $et~{}al$., 2010) |  Maximum around 25 % for flares away from Sun’s center |  $\sim$2 $-$ 54 % PF for $\sim$8 flares by RHESSI (Suarez-Garcia $et~{}al$., 2006; Boggs $et~{}al$., 2006) |  |

  * 1

X-ray dim isolated neutron star, 2X-ray pulsar, 3Accretion powered pulsar,
4https://www.star-iitb.in/research/daksha

From Table 1, a number of striking differences between the low energy and high
energy regimes can be highlighted $-$ 1\. there is a large number of new
measurements in hard X-rays, 2. predicted polarization fractions for most of
the X-ray sources are relatively higher in the hard X-ray regime, 3. there is
a large number of confirmed and planned polarimetry missions in near future
along with a couple of active instruments continuing to provide useful
polarization measurements.

The field of hard X-ray polarimetry has been quite active in the last 10 $-$
15 years which can be seen through the new developments of dedicated
polarimeters like SPR-N (Bogomolov $et~{}al$., 2003; Zhitnik $et~{}al$.,
2006), POLAR (Sun $et~{}al$., 2016), PoGOLite and PoGO+ (Chauvin $et~{}al$.,
2016), X-Calibur (Guo $et~{}al$., 2011, 2013), GRAPE (Bloser $et~{}al$., 2009;
McConnell $et~{}al$., 2009), GAP (Yonetoku $et~{}al$., 2006), PENGUIN-M
(Dergachev $et~{}al$., 2009), COSI (Yang $et~{}al$., 2018; Lowell $et~{}al$.,
2017) and a large number of new proposals to develop hard X-ray polarimeters,
e.g. COSI-2 (Tomsick $et~{}al$., 2019), POLAR-2 (Kole, 2019), Daksha
111https://www.star-iitb.in/research/daksha, AMEGO (McEnery $et~{}al$., 2019)
etc. There has also been a significant effort in extracting polarization
information from instruments which are not specifically meant for polarimetry
measurements like RHESSI (McConnell $et~{}al$., 2002; Coburn & Boggs, 2003;
Boggs $et~{}al$., 2006; McConnell $et~{}al$., 2007), INTEGRAL (Laurent
$et~{}al$., 2011; Jourdain $et~{}al$., 2012; Dean $et~{}al$., 2008; Forot
$et~{}al$., 2008), AstroSat (Chattopadhyay $et~{}al$., 2014a; Vadawale
$et~{}al$., 2015) and Hitomi (Aharonian $et~{}al$., 2018). Measurements from
these experiments in the last two decades have provided some important
scientific inputs in understanding emission mechanism and geometry in X-ray
pulsars (Vadawale $et~{}al$., 2018; Forot $et~{}al$., 2008; Jourdain & Roques,
2019; Chauvin $et~{}al$., 2018b; Aharonian $et~{}al$., 2018), magnetic field
structure in Pulsar Wind Nebula (PWN) (Vadawale $et~{}al$., 2018; Dean
$et~{}al$., 2008; Chauvin $et~{}al$., 2018b), disk-jet interplay in black hole
X-ray binaries (XRBs) (Laurent $et~{}al$., 2011; Jourdain $et~{}al$., 2012;
Chauvin $et~{}al$., 2018a, 2019), hard X-ray emission mechanism in GRB prompt
emission (Zhang $et~{}al$., 2019; Chattopadhyay $et~{}al$., 2019; Yonetoku
$et~{}al$., 2011, 2012; Götz $et~{}al$., 2009), and emission process behind
solar flares (McConnell $et~{}al$., 2007; Suarez-Garcia $et~{}al$., 2006;
Boggs $et~{}al$., 2006; Zhitnik $et~{}al$., 2006). Though in some cases,
results are marred with large uncertainties and a firm conclusion is not
possible, most of these findings are extremely interesting as they pose new
challenges to the existing theories. One interesting and common feature in all
these measurements is a systematic increase in polarization (see Fig. 7 and 8)
within the hard X-ray band which makes this energy regime extremely promising
for polarimetry experiments.

Polarization measurement in hard X-rays promises to address some of the long-
standing astrophysical problems which might not be otherwise probed by
spectroscopic and timing tools or even polarization measurements in soft
X-rays (see 3rd column of Table 1). Since hard X-rays originate in the close
vicinity of the compact sources, it is likely to carry signatures of high
gravitational and magnetic field close to a black hole or neutron star, e.g.
accretion dynamics close to a black hole, jet launching mechanism from the
black hole both in XRBs and GRBs, emission from the low altitudes of
magnetar’s magnetosphere, structure and dynamics of accretion column in
accretion powered neutron stars. At the same time, hard X-rays originate from
the highest energy particles being cooled off at faster time scales and
therefore polarization in this regime can probe acceleration mechanism of
particles in supernova remnants and PWNs and in the base of jets of blazars,
black hole XRBs or GRBs. Fortunately, because non-thermal emission dominates
over thermal emission in hard X-rays, the polarization fraction is expected to
be higher compared to soft X-rays as also seen in the 4th column of Table 1.
This makes this regime unique as we expect more polarization measurements at
these energies even from moderately sensitive polarimeters.

Because a couple of instruments (on board INTEGRAL and AstroSat) with moderate
polarimetric sensitivity continues to operate and provide useful polarization
information for some of the bright hard X-ray sources and GRBs, we expect the
hard X-ray regime of polarimetry to continue to remain active. There is an
order of magnitude increase in the activity with the new confirmed and planned
experiments in near future (see 7th column of Table 1). POLIX (sensitive in 10
$-$ 30 keV, Paul $et~{}al$., 2016), PolariS (sensitive in 10 $-$ 80 keV,
Hayashida $et~{}al$., 2014), POLAR-2 (sensitive in 50 $-$ 500 keV, Kole,
2019), Daksha (sensitive in 100 $-$ 400 keV) are expected to provide sensitive
polarization measurements for a number of astrophysical sources.

X-ray polarization is an extremely difficult area of research. The near to be
launched IXPE and POLIX, to be launched in 2021, will make measurements in
soft X-rays and the medium energy range respectively. Polarization measurement
in hard X-rays, however, straddles the regime of thermal and non-thermal
emission, particularly in accreting black holes sources and they are thought
to provide inputs to the much sought after details of disk-jet synergy in
powerful jet sources like GRBs, microquasars, blazars etc. A glimpse of such
details are already available by measurements with AstroSat and INTEGRAL,
along with a strong trend of increasing polarisation fraction with energy. In
this review, we mainly focus on this non-thermal regime and summarise the
possible meaningful polarization results for the bright hard X-ray sources
from the upcoming and planned polarimetry experiments. We particularly focus
more on improving the existing and upcoming results by making developments in
the hardware front to increase the sensitivity of the detectors, making more
careful calibration of the instruments, and putting more effort in
understanding the detector systematics. The new developments in the
theoretical modelling front is also discussed.

In the next section, specific science cases of hard X-ray polarimetry (3rd and
4th column of Table 1) have been described followed by a discussion on the new
scientific findings (5th column of Table 1) in section 3

##  2 Science Drivers of Hard X-ray polarimetry

###  2.1 Black Hole XRBs

Polarization measurements in soft X-rays from black hole XRBs can probe
General Relativity (GR) effects on the thermal disk photons and is expected to
constrain some of the key parameters like disk inclination and mass spin ratio
of the black holes (Dovčiak $et~{}al$., 2008; Schnittman & Krolik, 2009). In
the hard spectral state of these systems, the thermal photons being inverse
Compton scattered by the corona introduces a separate polarized spectral
component at energies above 10 keV with polarization characteristics expected
to be dependent on the geometry of corona. Schnittman & Krolik (2010)
investigated the polarimetric signatures for various corona geometries $-$
sandwich, clumpy and spherical corona (see Fig. 1).

Figure 1: Polarization characteristics for various black hole coronal
geometries as a function of observed energy and inclination. The dotted lines
represent disk emission, whereas the dot-dashed and solid lines represent
coronal and total (disk+corona) emission respectively. Figure credit $-$
Schnittman & Krolik (2010) (\raisebox{-.2pt} {c}⃝ AAS. Reproduced with
permission)

Polarization is expected to have a strong dependence on photon energy and
inclination of the system in case of a homogeneous sandwich corona, with
polarization level reaching up to $\sim$10 % at 100 keV for higher
inclinations. On the other hand, for an inhomogeneous clumpy corona and a
standard spherical corona, polarization fractions are predicted to be
relatively low (3 $-$ 4 %) with no strong dependence on energy above 10 keV.
Sensitive energy resolved polarization measurements in the hard state of black
hole XRBs will be a key to probe the geometries of corona.

At energies beyond 100 keV, the radiation from black hole systems in its low
hard state is believed to be of synchrotron origin from high energy electrons
in the jet (Vadawale $et~{}al$., 2001, 2003; Markoff $et~{}al$., 2001). Recent
findings of high polarization measured for high mass black hole binary, Cygnus
X-1, at energies spanning from a few hundreds of keV to a few MeVs (Laurent
$et~{}al$., 2011; Jourdain $et~{}al$., 2012) also suggest the jet origin of
the hard X-ray emission. However, multi-wavelength SED modeling of Cygnus X-1
predicts insignificant contribution of jet in hard X-rays (Zdziarski
$et~{}al$., 2014). On the other hand, there are studies reported in literature
suggesting that radiation in hard X-rays to originate from lepto-hadronic
corona of black holes due to synchrotron radiation, predicting the radiation
to be highly polarized independent of its state (Romero $et~{}al$., 2014).
More recently, Kantzas $et~{}al$. (2020) applied a multi-zone jet model on
first ever simultaneous broadband data ranging from radio wavelengths to MeV
X-rays. They interpreted the high polarization fraction seen in the MeV band
as synchrotron radiation emitted by electrons accelerated inside the jets of
Cygnus X–1 in the presence of a highly ordered magnetic field. However, the
required MeV synchrotron flux for the high polarization is only possible for a
harder power-law index of accelerated electrons of 1.7 compared to that
observed $\sim$2.2 by INTEGRAL-IBIS (Laurent $et~{}al$., 2011). Careful
polarization measurements of black hole systems in both hard and soft spectral
states may lead to a proper understanding of the origin of hard X-rays in
these systems.

###  2.2 Active Galactic Nuclei

The thermal UV photons from the disk of Active Galactic Nuclei (AGNs) are
Comptonized by the corona giving rise to a power-law component in their
spectra. The UV photons from the disk move parallel to the disk and corona
suffering a large number of interactions and upscattered to energies $>$ 10
keV (Schnittman & Krolik, 2010). This causes the coronal emission to be
polarized around 8 %. Spectro-polarimetric studies are expected to be useful
in investigating corona geometry in detail by constraining the number of
clumps and their over-density in case of a clumpy corona geometry. The disk
photons may also be scattered by the molecular torus. Thus, X-ray polarimetry
can also constrain the geometry of the torus (Goosmann & Matt, 2011).
Polarization measurement of the reflected radiation from the disk or the torus
may also complement the reverberation studies for AGNs to study the geometry
of the reflector by estimating the time delay between the direct and reflected
component of radiation (Uttley $et~{}al$., 2014).

###  2.3 Neutron Stars

X-ray polarimetry has a wide range of applications in isolated pulsars,
accreting pulsars, magnetars and help understand the emission mechanism and
geometry in these systems and behaviour of matter in strong magnetic fields
(Weisskopf $et~{}al$., 2009).

####  2.3.1 Rotation powered X-ray pulsars:

The emission mechanism and emission site for high energy radiation from
rotation powered pulsars are still poorly understood. There are models
predicting the high energy pulsar radiation to originate directly above the
polar cap (polar cap model, Daugherty & Harding, 1982), or in the outer
magnetosphere (outer gap model, Cheng $et~{}al$., 2000), or all the way from
the polar cap to the light cylinder along the last open field line (slot gap
model, Dyks & Rudak, 2003). A geometric description of these models is shown
in Fig. 2.

Figure 2: Geometrical illustration of various pulsar models: polar cap/radio
(blue), two-pole caustic (red), outer gap (yellow), and current sheet (green)
models. The light cylinder is shown by the dashed black lines and the dotted
red lines show projections of the null-charge surface. Different models assume
different acceleration region for the electrons with distinct polarization
signatures with rotation phase of the pulsars. Figure credit $-$ Harding
(2019) (reprinted by permission from Springer Nature Customer Service Centre
GmbH)

While these three models imply that the emission originates inside the light
cylinder, current sheet model based on striped pulsar wind (shown in green)
(Kirk $et~{}al$., 2002; Pétri & Kirk, 2005) predicts the radiation to come
from outside of the light cylinder from the particles escaping through open
field lines. Because of the distinct emission geometries, these models predict
distinct phase dependent polarization signatures. Fig. 3 shows variation of
optical linear polarization with pulse phase for Crab pulsar (Smith
$et~{}al$., 1988; Romani $et~{}al$., 2001), along with the predictions of
these models.

Figure 3: Polarization with the rotation phase of pulsars as predicted from
various pulsar models $-$ polar gap, outer gap and slot gap models. As an
example, the measured polarization with phase for Crab pulsar in optical
wavelength is shown in the left most panel (Smith $et~{}al$., 1988; Romani
$et~{}al$., 2001). Figure credit $-$ Weisskopf $et~{}al$. (2009) (reprinted by
permission from Springer Nature Customer Service Centre GmbH).

Phase resolved polarimetry can test these models and help in understanding the
emission sites and emission mechanisms in isolated X-ray pulsars.

####  2.3.2 Magnetars:

Magnetars are neutron stars with large spin periods and highest magnetic field
ever observed in the universe with polar surface values of 1014-15 G. The huge
magnetic energy reservoir powers the magnetars through seismic activity and
heating of the stellar interior (Duncan & Thompson, 1992). Radiation from such
an extreme magnetic and gravity fields makes the magnetars an extremely
interesting object for polarimetry and other astrophysical studies.

Magnetars spend most of the time in quiescence radiating persistent quasi-
thermal emission with KT $\sim$0.5 keV. They show occasional short outbursts
(a few to hundreds in number with duration of $\sim$0.1 s) $-$ famously known
as ‘Magnetar outbursts’ where the radiation extends all the way to sub-MeV
region with a few to thousand times increase in the flux (refer to review
papers on magnetars by Rea & Esposito (2010); Turolla $et~{}al$. (2015);
Mereghetti $et~{}al$. (2015); Kaspi & Beloborodov (2017); Esposito $et~{}al$.
(2018)). INTEGRAL, CGRO, RXTE-HEXTE, NuSTAR have detected hard X-ray tail for
a number of magnetars in quiescence (there are 7 such magnetars) with a
possible cut off energy lying in the sub-MeV region (Enoto $et~{}al$., 2017;
den Hartog $et~{}al$., 2008).

One possible explanation behind the hard X-ray component on top of the thermal
emission assumes Resonant Inverse Compton scattering (RICS, see Wadiasingh
$et~{}al$., 2017; Beloborodov, 2012; Baring & Harding, 2006) of the soft
thermal photons off the relativistic e-/e+ population at the lower altitudes
where the density of the soft X-ray photons and magnetic field are relatively
high. RICS predicts a flat spectrum in hard X-rays with a high linear
polarization making the hard X-ray region extremely promising for polarimetry
studies, particularly for the seven magnetars detected with bright hard X-ray
tails in their quiescence. Detection of high polarization in hard X-rays will
be a clear signature of RICS meachanism in magnetars. A phase resolved
spectro-polarimetry study is supposed to constrain the angle between the
rotation and magnetic axis because at different viewing angles with respect to
the magnetic axis the electron population and beaming geometry are expected to
vary (Wadiasingh $et~{}al$., 2019).

One interesting aspect of magnetar’s hard X-ray polarimetry is the first ever
possible confirmation of QED effects in strong magnetic field. Magnetic photon
splitting of Gamma rays in strong magnetic field
($\gamma+B\longrightarrow\gamma+\gamma$) is one explanation of the sub-MeV
spectral cut off seen in the magnetars. Polarization strongly depends on the
photon splitting modes (splitting of $\perp$(X) mode or both $\perp$(X) and
$\parallel$(O) modes). Therefore, spectro-polarimetry study in hard X-rays
near the sub-MeV cut off region of magnetars offers a unique opportunity to
test the QED effects in strong magnetic field (Wadiasingh $et~{}al$., 2019).

####  2.3.3 Accretion powered pulsars:

In accretion-powered pulsars, theoretical models predict high polarization
owing to the high magnetic field ($10^{12-13}$ G) in those systems,
particularly for emission perpendicular to the magnetic field. Phase resolved
polarization study can therefore be used to determine the beam shape of the
pulsar. For example, for the pencil beam model, the oscillations in
polarization fraction are expected to be out of phase with pulse phase,
whereas for the fan beam model, the opposite signature is predicted (Meszaros
$et~{}al$., 1988). This effect is more prominent at energies near the
cyclotron resonances. Many accretion-powered pulsars have been found to
exhibit cyclotron features in the energy range of 15 $-$ 50 keV. A polarimeter
sensitive in this cyclotron line populated energy regime is expected to
distinguish between the pencil and fan radiation patterns in these systems.

Millisecond X-ray pulsars are accretion-fed systems where the pulsar is spun
up to high rotation speed with period of a few milliseconds. Polarization at
higher energies in these systems derives from Compton scattering of photons in
accretion shock (Viironen & Poutanen, 2004) or possibly from the accretion
disk (Sazonov & Sunyaev, 2001). Polarization measurements from these sources
may test these various models and put tighter constraints on various
geometrical parameters like orbital and dipole axis inclinations.

###  2.4 Gamma Ray Bursts

Despite the detection and study of a large number of Gamma Ray Bursts (GRBs)
in the last decade (Gehrels & Mészáros, 2012) by Swift (Gehrels $et~{}al$.,
2004; Barthelmy $et~{}al$., 2005) and Fermi (Meegan $et~{}al$., 2009), the
prompt emission mechanism has not yet been well understood (Kumar & Zhang,
2015) owing to the unpredictable nature of the GRBs. GRB prompt emission is
widely believed to be of synchrotron origin from high energy electrons in the
jet (Meszaros & Rees, 1993). Apart from synchrotron, other possible mechanisms
are inverse Compton scattering (Ghisellini & Celotti, 1999; Ghisellini
$et~{}al$., 2000; Lazzati $et~{}al$., 2004), thermal blackbody radiation,
presumably of photospheric origin (Ryde, 2004; Pe’er & Ryde, 2011; Basak &
Rao, 2015; Iyyani $et~{}al$., 2015). Measurement of hard X-ray/Gamma ray
polarization has the potential to shed light on the GRB prompt emission
(Covino & Gotz, 2016; McConnell, 2016).

There are various prompt emission polarization models, namely, synchrotron
emission from relativistic electrons energized in internal shocks within the
jet either in globally ordered magnetic field derived from the central engine
(Synchrotron Ordered or ‘SO model’, Lyutikov $et~{}al$., 2003; Nakar
$et~{}al$., 2003; Granot & Königl, 2003) or in random magnetic field generated
in the shock plane within the jet (Synchrotron Random or ‘SR model’, Medvedev
& Loeb, 1999) or emission due to Comptonization of the soft photons (Compton
Drag or ‘CD model’, Shaviv & Dar, 1995) by the relativistic jet. Polarization
is expected to be high in SO model for a wide range of viewing angles ($>$20
%). On the other hand, polarization in the SR and CD model will be dependent
on the geometry of the viewing angle, as for certain viewing angles, net
polarization remains. High polarization ($\sim$40 %) can be achieved from SR
model if the jet is narrow and viewed along the edge (Waxman, 2003; Medvedev,
2007; Sari, 1999; Ghisellini & Lazzati, 1999). Similar to SR model, CD can
also result in high polarization (60 $-$ 100 %) if the jet is narrow and is
observed along the edge (Lazzati $et~{}al$., 2004). Possibility of such a
geometric configuration favorable for high polarization is relatively small
and therefore the GRBs without such favorable viewing geometry are expected to
be unpolarized according to the geometric models (SR and CD). Toma $et~{}al$.
(2009) showed that statistical distribution of prompt emission polarization
for a large sample of GRBs may efficiently distinguish the various theoretical
models (see Fig. 4).

Figure 4: Predicted distribution of polarization fraction with Epeak for a
large sample of GRBs in 50–500 keV energy range for various prompt emission
polarization models $-$ Synchrotron radiation in ordered magnetic field (red),
Synchrotron radiation in random magnetic field (green) and Comptonization of
the soft X-ray photons (blue). Figure credit $-$ Toma $et~{}al$. (2009)
(\raisebox{-.2pt} {c}⃝ AAS. Reproduced with permission)

Study of spectral and temporal evolution of the polarization parameters for
individual GRBs is equally important in the complete understanding of the GRB
jets and emission mechanisms. McConnell $et~{}al$. (2019); Zhang & Yan (2011);
Gill $et~{}al$. (2018) discuss these aspects for matter and magnetic field or
poynting flow dominated jets and the dissipation mechanisms in the jets.

###  2.5 Blazars

Hard X-ray polarimetry for blazars may probe the origin of the second
characteristic emission peak in their spectral energy distribution (Zhang,
2017). For low energy peaked blazars, the low energy peak occurs at the
optical regime whereas the high energy peak occurs in MeVs. The optical
emission is believed to be due to synchrotron radiation from the relativistic
electrons. On the other hand, there exists two different models in explaining
the origin of the high energy peak. According to the Synchrotron Self Compton
model (SSC model, Celotti & Matt (1994)), the optical synchrotron photons are
inverse Compton scattered off the relativistic electrons to high energies. SSC
model predicts around 30 % polarization for uniform magnetic field with
polarization direction identical to that for optical emission. External
Compton model (EC), on the other hand, assumes a different origin for the seed
photons where either the accretion disk photons or photons from broad line
region or dusty molecular torus are upscattered to high energies. Polarization
fraction in this scenario is expected to be significantly lower compared to
the SSC model ($<$5 %) (McNamara $et~{}al$., 2009).

Besides the leptonic models, there exists a completely different approach
based on lepto-hadronic models which can produce equally good fits to the SEDs
of blazars (Zhang & Böttcher, 2013). In the hadronic models, although the
source of the low energy peak is same as that for the leptonic models, the
high energy peak is believed to originate from the high energy proton induced
radiation mechanisms. Because of the dominance of synchrotron radiation in
hadronic models, a relatively higher level of polarization is expected
compared to that for leptonic models (Zhang & Böttcher, 2013).

###  2.6 Solar Flares

Solar flares are the powerful events due to magnetic reconnection in Sun’s
corona, accelerating the electrons towards the chromosphere. Radiation in soft
X-rays is due to thermal heating at the reconnection site and are therefore
expected to be unpolarized. However, because of anisotropies in electron
distribution, the thermal radiation may have a low level of polarization
(Emslie & Brown, 1980).

Figure 5: Variation of flux (top row) and spatially integrated polarization
(bottom row) with observed energy for an extremely beamed electron
distribution in solar flares. $\mu$ (= $\cos\theta$) refers to the direction
of emission where $\theta=0^{\circ}$ is the local solar vertical. Green,
orange and blue denote the total source, primary and albedo components
respectively, whereas the solid and dashed lines refer to electron cut off
energy of 500 keV and 2 MeV respectively. Figure credit $-$ Jeffrey & Kontar
(2011) (reproduced with permission\raisebox{-.2pt} {c}⃝ ESO).

Hard X-rays, on the other hand, is believed to be from non-thermal
Bremsstrahlung emission by the high energy electrons and thus expected to be
highly polarized with degree of polarization depending on multiple factors
like beaming of the electrons, magnetic field structure, back-scattering of
the photons from the photosphere and location of the flare on the disk (Bai &
Ramaty, 1978; Leach $et~{}al$., 1985; Zharkova $et~{}al$., 2010; Jeffrey &
Kontar, 2011). For example, Fig. 5 shows polarization from various components
of the hard X-ray emission of solar flares for different emission sites and
electron energy distributions. Because of sufficient photon flux in X-rays,
solar flares are the potential targets for X-ray polarimetry, particularly in
hard X-rays.

It can be seen that hard X-ray polarimetry has a lot of science potential for
all classes of X-ray sources. However, there have not been any dedicated
attempt to utilize this potential for a long time. Only recently in the last
couple of decades, there are some efforts to measure polarization for some of
the bright hard X-ray sources. In the next section, we will discuss those
measurements and implications on understanding the nature of emission
mechanism in X-ray sources.

##  3 Recent scientific findings of Hard X-ray polarimetry

###  3.1 Cygnus X-1

Cygnus X-1 is a famous bright galactic high mass black hole X-ray binary
system, mostly seen in its hard spectral state. After a few initial attempts
back in 1970s to explore the polarization properties of the source (e.g. Bragg
polarimeter on board OSO-8 measured low polarization around 2.4 % and 5.3 % at
2.6 and 5.2 keV respectively in its high soft state, see Long $et~{}al$.,
1980), lately, there are some valiant attempts to measure polarization of
Cygnus X-1 in hard X-rays, both in the coronal regime (a few 10s of keV to
$\sim$100 keV) and the suspected jet regime (above 100 keV) (Vadawale
$et~{}al$., 2001; Markoff $et~{}al$., 2001; Vadawale $et~{}al$., 2003).

PoGO+ (Chauvin $et~{}al$., 2016; Friis $et~{}al$., 2018), a dedicated balloon
borne hard X-ray polarimeter found the source to be unpolarized in its hard
state (12 $-$ 18 July 2016) in 20-180 keV (Chauvin $et~{}al$., 2018a, 2019).
They placed an upper limit of 5.6 % at position angle of 154$\pm$31∘. They
also found upper limits of 11.6 %, 2.2 %, and 2.9 % assuming position angle
perpendicular to the accretion disk ($\pm$155∘), parallel to the disk
($\pm$330∘), and position angle aligned to that of INTEGRAL results
($\pm$222∘, see below) respectively. These results favour the hard X-ray flux
to be originating from an extended corona which has a small fraction of
reflection component in the hard X-ray band (Chauvin $et~{}al$., 2018a, 2019).
These results also give an upper limit of polarization for the jet component
around 5 $-$ 10 % when the emission from the extended corona was assumed to be
accompanied by a synchrotron jet at energies $<$200 keV.

On the other hand, at higher energies, IBIS (Ubertini $et~{}al$., 2003), on
board INTEGRAL estimated high polarization for this source (67$\pm$30 %) at
220$\pm$15∘ (north-east in anti-clockwise) in 400 $-$ 2000 keV, while emission
in 250 $-$ 400 keV was found to be weakly polarized (Laurent $et~{}al$.,
2011). SPI (Vedrenne $et~{}al$., 2003) on board INTEGRAL, later confirmed the
measurements independently. High polarization (76$\pm$15 % at 222$\pm$3∘) was
estimated in 230 $-$ 850 keV. An upper limit of 20 % was reported in 130 $-$
230 keV (Jourdain $et~{}al$., 2012). The results were interpreted as
synchrotron origin of high energy emission from the relativistic electrons in
the jet. This was further corroborated by simultaneously observed two distinct
spectral components of the source, a thermal comptonization component at
energies below 200 keV and a power-law component beyond 200 keV, mostly due to
synchrotron radiation from the jet (see Fig. 6).

Figure 6: Polarization measurement of Cygnus X-1 using the IBIS instrument on
board the INTEGRAL satellite. Polarization signal is clearly seen in higher
energies (450 $-$ 2000 keV), as can be seen in the modulation curve (left
panel) indicating a separate jet component, as is evident from the energy
spectrum (right panel). Figure credit $-$ from Laurent $et~{}al$. (2011).
Reprinted with permission from AAAS.

In recent years, Cadmium Zinc Telluride Imager (CZTI, Bhalerao $et~{}al$.,
2017) on board AstroSat has attempted a detailed energy resolved polarization
in the hard state of Cygnus X-1. They found the source to be polarized at
38$\pm$7 % with a position angle of 221$\pm$2∘ (North-East, anti-clockwise)
with a hint of increase in polarization fraction (from 17 % to 58 %) in 100
$-$ 500 keV (private communication, Chattopadhyay et al. 2021, under
preparation). This further validates increasing jet contribution at energies
above 100 keV compared to the coronal counterpart. Fig. 7 shows the measured
PF and PA for the source as a function of energy from all these measurements.

Figure 7: Summary of polarization measurements (fraction in top panel and
angle in bottom panel) of Cygnus X-1 by various instruments like IBIS and SPI
on board Integral, OSO-8, and PoGO+. Except for the OSO-8 measurements, all
other measurements correspond to the hard spectral state of the source. When
plotted against observed energy of measurement, we see a clear increase in the
polarization fraction and a swing in polarization angle at higher energies.

Jet origin of the high energy photons can be further validated by exploring
the soft or intermediate state polarization of the source as the jet is
supposed to be quenched in the soft state. Both INTEGRAL and AstroSat have
tried to explore the soft and intermediate state for polarization. However due
lower flux in these states, the measurements are associated with large
uncertainties. More data from these observatories and upcoming missions in the
future will be useful in establishing the hard X-ray emission models of black
hole XRBs.

###  3.2 V404-Cygni

After a 25 years of quiescence, V404 Cygni which is a low mass X-ray binary
with a black hole of $\sim$12 solar mass entered into outburst mode exceeding
its Eddington luminosity. The high flux offered a great opportunity to explore
polarization properties of the source in a broad frequency band. IBIS on board
INTEGRAL observed the source in the month of June, 2015 for 10 times with
exposures greater than 100 ks in each observation. The source was found to be
unpolarized for all the observations except for that on June 20 $-$ 22, 2015.
The emission was found to be highly polarized at 95$\pm$35 % level with
position angle of 160$\pm$15∘ in 450 $-$ 2000 keV (Laurent $et~{}al$., 2017).
It is to be noted that optical and NIR studies of polarization from this
source during the outburst reveals a variable polarization with position angle
around 170∘ and favours the jet origin of the optical and NIR flares (Shahbaz
$et~{}al$., 2016).

###  3.3 Crab pulsar and nebula

Crab is the brightest persistent X-ray source in the sky. From early 1970s,
there have been multiple attempts to measure polarization of Crab using a
several rocket experiments. The first confirmation of Crab polarization was
made by Weisskopf $et~{}al$. (1978) using OSO-8 Bragg polarimeter. For the
off-pulse nebula (non-pulsating) region of the light curve, they reported a
polarization fraction (PF) and polarization angle (PA) of 19.2$\pm$1.0 % and
156.4$\pm$1.4∘ at 2.6 keV and 19.5$\pm$2.8 % and 152.6$\pm$4.0∘ at 5.2 keV
respectively.

Following this historic measurement, polarization measurement of Crab was
attempted a multiple times in other energy bands. However, the detection of
polarization of Crab in hard X-rays came almost after 30 years of the OSO-8
detection. From observations of Crab spanning in 2003 $-$ 2006 by SPI on board
INTEGRAL, Dean $et~{}al$. (2008) reported a PF of 47$\pm$10 % at 123$\pm$11∘
in the energy of 100 $-$ 1000 keV for the off-pulse nebula. For the phase
averaged Crab signal, the PF and PA were found to be 28$\pm$6 % and 117$\pm$9∘
respectively in 130 $-$ 440 keV (Chauvin $et~{}al$., 2013). In the subsequent
years, SPI reported improvements in the detection of PF and PA: 24$\pm$4 % and
120$\pm$6∘ after accumulation of data spanning over 15 years between 2003 and
2018 (Jourdain & Roques, 2019). INTEGRAL-IBIS, sensitive in a similar energy
range as SPI also measured the phase averaged polarization of Crab $-$
$47.0\begin{subarray}{c}+19\\\ -13\end{subarray}$ % at 100.0$\pm$11.0∘ in 200
$-$ 800 keV (Forot $et~{}al$., 2008). They found the off-pulse region to be
highly polarized ($>$72 %) at 120.6$\pm$8.5∘.

In recent years, PoGO+, SGD (Tajima & et al., 2010) on board Hitomi, and CZTI
on board AstroSat reported statistically significant polarization detections
in hard X-rays. CZTI, sensitive at energies $>$100 keV like INTEGRAL, reported
statistically the most significant polarization detection of Crab (Vadawale
$et~{}al$., 2018). They reported a similar level of polarization as INTEGRAL
$-$ 32.7$\pm$5.8 % at 143.5$\pm$2.8∘ for phase averaged Crab in 100 $-$ 380
keV. For the off-pulse region, a PF and PA of 39$\pm$10 % and 140.9$\pm$3.7∘
were reported respectively. PoGO+, sensitive from a few tens of keV, detected
a PF and PA of 20.9$\pm$5.0 % and 124.0$\pm$0.1∘ respectively for phase
averaged Crab and $17.4\begin{subarray}{c}+8.6\\\ -9.3\end{subarray}$ % and
137.0$\pm$15.0∘ for the off-pulse region over the energy range of 20 $-$ 160
keV (Chauvin $et~{}al$., 2018c). SGD, sensitive in the same energy range as
PoGO+, reported a similar PF and PA of 22.1$\pm$10.6 % and
$110.7\begin{subarray}{c}+13.2\\\ -13\end{subarray}^{\circ}$ respectively
(Aharonian $et~{}al$., 2018).

All these observations (summarized in Fig. 8) are in agreement with the
optical measurements of Crab polarization (9.8$\pm$0.1 % and 109.5$\pm$0.1∘
for phase averaged Crab and 9.7$\pm$0.1 % and 139.8$\pm$0.2∘ for the nebula;
for more details, see Słowikowska $et~{}al$., 2009).

Figure 8:  Summary of polarization measurements (fraction in top panel and
angle in bottom panel) of total Crab (left) and off-pulse nebula (right) by
various instruments like CZTI on board AstroSat, IBIS and SPI on board
Integral, SGD on board Hitomi, PoGO+ and PolarLight. When plotted against
observed energy of measurement, we see a hint of increase in the polarization
fraction in both phase-averaged Crab and nebula.

The high polarization across the broad energy range indicates synchrotron
emission from radio to MeV region from a magnetically ordered compact emission
site. The measurements support the theory that electrons trapped in a toroidal
magnetic field produce synchrotron radiation with polarization angle parallel
to the spin axis of the pulsar (Nakamura & Shibata, 2007). This is consistent
with the X-ray images taken from NuSTAR showing toroidal ring region
dominating the emission in X-rays (Madsen $et~{}al$., 2015).

The increase in polarization fraction for the off-pulse/nebula (and
nubula+pulsar) could be because of the fact that the higher energy radiation
comes from regions closer to the pulsar whereas the lower energy measurements
encompass the entire nebula and pulsar. Emission from varying morphological
features associated with the Crab pulsar and nebula smears the polarization at
lower energies.

Another interesting aspect is the stability of the source in terms of
polarization given the fact that Crab is extremely stable photometrically and
spectroscopically (see Fig. 9).

Figure 9: Evolution of polarization fraction (top) and angle (bottom) for
phase averaged Crab (or total Crab) with time of measurement by various
instruments.

There are some recent reports claiming detection of change in the polarization
parameters of Crab. Moran $et~{}al$. (2013) detected a change in the
polarization angle of Crab using INTEGRAL-IBIS from 115$\pm$11∘ during
observations between 2003 and 2007 to 80$\pm$12∘ during 2012 $-$ 2014
observation while the polarization fraction remains consistently high. The
change is attributed to the strong GeV flaring activities detected in Crab
during that period which suggests a possible change in magnetic field
orientation during the flares. More recently, Feng $et~{}al$. (2020) using
PolarLight, a gas pixel detector based soft X-ray polarimeter (sensitive in 2
$-$ 8 keV) on board a cubesat platform, reported a drop in polarization
fraction from 24.3$\pm$5.7 % at 144.5$\pm$6.7∘ to
$11.3\begin{subarray}{c}+3.7\\\ -3.8\end{subarray}$ % at 146.9$\pm$9.6∘ of the
pulsed emission of Crab in 3 $-$ 4.5 keV after a glitch in the pulsar detected
on 23 July 2019. The nebular polarization was found to be unaffected. The
change in polarization seen in Crab could be because of possible change in the
co-rotating magnetosphere configuration after the glitch.

As mentioned the previous section, phase resolved polarization study has the
potential to provide useful insights of the acceleration site of the electrons
in pulsars. There is only one hard X-ray phase resolved polarization study
reported by Vadawale $et~{}al$. (2018) using AstroSat-CZTI in 100 $-$ 380 keV
(see Fig. 10).

Figure 10: Dynamic phase resolved polarization of Crab pulsar+nebula from CZTI
on board AstroSat in 100 $-$ 380 keV (a. Polarization fraction, b.
Polarization angle) in total $\sim$800 ks of Crab observation. Polarization
fraction is seen to change across the pulse peaks and in the off-pulse region.
Figure credit $-$ from Vadawale $et~{}al$. (2018). Reprinted by permission
from Springer Nature Customer Service Centre GmbH.

There is a change in polarization angle and fraction reported across the pulse
peaks which is also seen in the optical phase resolved polarization study of
Crab by Słowikowska $et~{}al$. (2009) supporting the Two Pole Caustic (TPC)
and striped wind models of acceleration. However, difference in polarization
properties in two peaks in hard X-rays impose further constraints in the
models. The off-pulse region also shows significant variation in polarization
which is difficult to explain within the existing models. More observational
data as well as further exploration in the theoretical models in future will
be able to constrain the acceleration sites.

###  3.4 GRB polarization from POLAR, AstroSat, GAP, COSI and INTEGRAL

The past decade has seen a several attempts to measure the X-ray/gamma-ray
polarization of GRBs. Instruments such as RHESSI (Coburn & Boggs, 2003), IBIS
(Götz $et~{}al$., 2013, 2014) and SPI (McGlynn $et~{}al$., 2007b; Kalemci
$et~{}al$., 2007; McGlynn $et~{}al$., 2009) on board INTEGRAL, as well as
BATSE (Willis $et~{}al$., 2005) on board CGRO have reported several cases of
strong polarization (see a review by McConnell, 2016). However, because these
instruments are not optimized for polarimetry, the results are limited by
statistical and systematic uncertainties and have been questioned sometimes
(Rutledge & Fox, 2004; Wigger $et~{}al$., 2004).

One notable measurement by IBIS on board INTEGRAL for GRB 041219A shows a
change in polarization from the first peak (no polarization) to high
polarization around 43$\pm$25 % in 200 $-$ 800 keV (Götz $et~{}al$., 2009).
Analysis on finer time scale shows a change in PF and PA within the first peak
resulting in dilution in the polarization signal.

Later, GAP (Yonetoku $et~{}al$., 2006), a dedicated large field of view
(hereafter FOV) Compton polarimeter flown in 2011, provided polarization
measurements for three bright GRBs $-$ GRB 100826A, GRB 110301A, GRB 110721A
in 70 $-$ 300 keV (Yonetoku $et~{}al$., 2011, 2012). They reported high
polarization fraction for GRB 110301A ($\sim$70 %) and GRB 110721A ($\sim$84
%) in the full burst period while for GRB 100826A (time integrated PF of 27
%), a $\sim$90∘ change in polarization angle was reported between the first
and second interval at 99.9 % confidence level.

More recently, POLAR (Sun $et~{}al$., 2016; Orsi & Polar Collaboration, 2011),
a dedicated GRB polarimeter launched in 2016, provided precise polarization
measurements for 14 GRBs (Zhang $et~{}al$., 2019; Kole $et~{}al$., 2020). They
reported lower level of polarization fraction for the GRBs in the full burst
intervals, between 5.9 and 21 %, hinting at unpolarized nature of GRBs in
general. For GRB 170114A, a change in polarization angle was reported by 105∘
between the first and second interval of the burst (Zhang $et~{}al$., 2019).
The time evolution of polarization properties across the bursts is thought to
be a generic feature resulting in the unpolarized nature of the POLAR detected
GRBs.

CZTI on board AstroSat reported polarization measurements for 11 bright GRBs
from the first year of its operation in 100 $-$ 300 keV (Chattopadhyay
$et~{}al$., 2019). For six of the GRBs, high polarization fractions ($>$50 %)
were measured whereas for the remaining GRBs, upper limits were reported. The
selection of energy and GRB intervals were optimized in order to get the best
detection of polarization. Some of the bright GRBs were analyzed in more
details and were found to have time and energy dependent polarization
properties. GRB 160821A showed a $\sim$90∘ flip in polarization angle from the
initial few seconds to the peak region of the burst (Sharma $et~{}al$., 2019).
GRB 171010A was also found to have a change in polarization angle across the
burst (Chand $et~{}al$., 2019). For GRB 171010A (Chand $et~{}al$., 2019) and
GRB 160802A (Chand $et~{}al$., 2018), changes in polarization properties
across the peak energy of the bursts were noticed.

COSI (Yang $et~{}al$., 2018), a balloon borne hard X-ray spectro-polarimeter,
flown in 2017, detected GRB 160530A. An upper limit of $\sim$40 % was reported
for this GRB (Lowell $et~{}al$., 2017) in 200 keV to 2 MeV.

Last few years have been extremely fruitful in the field of GRB polarimetry
science. Measurements from POLAR and AstroSat have almost tripled the GRB
polarization sample in last five years. Roughly, one half of the sample
possesses significant amount polarization either in the full burst interval of
the GRBs or in some cases, only in some selected intervals of the prompt
emission, suggesting synchrotron radiation in an ordered magnetic field
generated close to the center of explosion and carried by ejecta in a poynting
flow dominated jet (Lyutikov $et~{}al$., 2003; Nakar $et~{}al$., 2003; Granot
& Königl, 2003). In the other half of the sample, we see low or no
polarization when integrated over the full burst interval (all the reported
measurements are summarized in Fig. 11).

Figure 11: Measured distribution of polarization fraction with Epeak for GRBs
detected by instruments - CZTI on board AstroSat (black, Chattopadhyay
$et~{}al$., 2019), POLAR (blue, Kole $et~{}al$., 2020), GAP (red, Yonetoku
$et~{}al$., 2011, 2012), IBIS on board INTEGRAL (pink, Götz $et~{}al$., 2009)
and COSI (green, Lowell $et~{}al$., 2017).

There is a strong indication that evolution of polarization parameters across
the bursts has been responsible for the unpolarized nature of the GRBs when
integrated across the burst (Sharma $et~{}al$., 2019; Chand $et~{}al$., 2019;
Yonetoku $et~{}al$., 2011; Götz $et~{}al$., 2009; Zhang $et~{}al$., 2019).
There is also a hint of change in polarization with energy, particularly
across the peak energy (Chand $et~{}al$., 2018, 2019). A firm conclusion on
the prompt emission models from polarization sample study still requires more
precise measurements for a larger sample of GRBs. While POLAR has stopped its
operation on March 31, 2017, AstroSat is still active and is supposed to
provide a large sample of GRB polarization along with those detected by
INTEGRAL.

###  3.5 Polarization of solar flares from RHESSI and CORONAS-F

In the recent past, there are some reports on the measurement of polarization
of solar flares in hard X-rays using RHESSI and SPR-N on board CORONAS-F
(McConnell $et~{}al$., 2007). While RHESSI is primarily a spectroscopic
instrument, Boggs $et~{}al$. (2006) and Suarez-Garcia $et~{}al$. (2006)
attempted to extract polarization information at energies above 100 keV
utilizing the scattering of photons between the Germanium detectors. They
measured a polarization fraction ranging from 2 $-$ 54 % for M and X class
flares that occurred from Sun’s center to limb. SPR-N, a dedicated Thomson
polarimeter sensitive in 20 $-$ 100 keV (Bogomolov $et~{}al$., 2003), on board
CORONAS-F, on the other hand reported polarization measurement for 25 M and X
class flares with an upper limit of 8 $-$ 40 % (Zhitnik $et~{}al$., 2006). For
one of the flares occurred on 29th October 2003, they detected a significant
polarization degree that increases from about 50 % at 20 $-$ 40 keV energy
band to more than 70 % in the 60 $-$ 100 keV band. Due to the large
uncertainties in the measurements, any firm conclusion was not possible.

We can see that though the Sun is very close to us, the hard X-ray polarimetry
measurements are very sparse. This is because the Sun is very faint in hard
X-rays except during large flares and even then the emerging spectra are very
steep giving very few photons in hard X-rays. In fact many GRBs are brighter
than bright solar flares. But, a good measurement of hard X-ray polarization
from the Sun will be very useful to develop the techniques of figuring out the
source emission mechanism based on hard X-ray polarimetry because many of the
source parameters are well constrained (for example, the distance to the Sun
is well measured). CZTI of AstroSat was operational during the current solar
minimum and hopefully it will measure hard X-ray polarisation of a few solar
flares in the next few years when the solar activity is likely to pick up.

Currently we only have a glimpse of the science that could be achieved from
polarization measurements and it appears that focusing on the higher energy
part of the emission is likely to be more rewarding. This energy range,
however, is an extremely difficult area even for spectroscopic measurements.
The hard X-ray focusing techniques, used in Hitomi and NuSTAR, is likely to be
the mainstay of observations in energy ranges up to about 80 keV. To optimally
use the scarce observational platforms that would be available in this energy
range, it is important to develop sensitive polarimetry configurations with
the best possible detection technologies available today. At energies above 80
keV, unlikely to be accessible to focusing techniques in the near future,
conventional open detectors like CZT-Imager are the most effective and we
touch upon possible improvements, like that contemplated in the forthcoming
Indian mission Daksha. We will develop these arguments through section 4 to 5,
starting with the basics of X-ray polarimetry measurement methods in the next
section.

##  4 Hard X-ray Polarimetry: How?

###  4.1 The basics

Since polarization is not a directly measurable quantity, its measurement
requires conversion to some observable quantity. The common feature of any
X-ray interaction with matter, is the dependence of cross-section on
polarization, giving rise to a variable intensity in number of photons or
electrons with respect to the polarization direction. Based on this, there are
three basic techniques to extract polarization information, namely, Compton /
Rayleigh scattering, photo-electron imaging and Bragg reflection (Kaaret,
2014), where the variability in intensity is fitted with a suitable modulation
function, with amplitude of modulation (measure of the degree of polarization)
being obtained from non-linear regression. In all these processes the detected
polarization signal on the detector plane can be described as

$S=\bar{S}[1+a_{0}\cos 2\left(\phi-\phi_{0}\right)],$ (1)

where, $\phi$ is the azimuthal angle with respect to a reference axis on the
detector plane and $\bar{S}$ is the mean number of events / counts in $\phi$
bins. It is evident from Eq. 1, that the distribution of the events, as
discussed earlier, is modulated with $\phi$ having an amplitude $a_{0}$ and
position angle of $\phi_{0}$, where $a_{0}$ is proportional to the degree of
linear polarization.

However, in presence of noise (which we assume to be of Poisson distribution),
there is a certain probability, $P(a,\phi)$, to measure an amplitude of $a$
and phase $\phi$, even though the actual amplitude and position angle in the
source signal are $a_{0}$ and $\phi_{0}$ respectively, given by,

$P(a,\phi)=\dfrac{Na}{4\pi}\exp\left[-\dfrac{N}{4}\left(a^{2}+a_{0}^{2}-2aa_{0}\cos(\phi-\phi_{0})\right)\right],$
(2)

where, $N(=n\bar{S}$, $n$ is the number of $\phi$ bins) is the total number of
detected events. Since, modulation is always positive definite, even if the
source is unpolarized ($a_{0}$ = 0), there is still a finite probability to
measure an amplitude $a$ (i.e. $P(a)\neq 0$).

Sensitivity or the minimum polarization that the instrument will be able to
detect, can be established by estimating the value of modulation amplitude for
unpolarized source signal ($a_{0}$ = 0), which is exceeded by chance with 1
$\%$ probability, i.e.

$\dfrac{N}{2}\int_{a_{1\%}}^{\infty}{a\,\exp\left[-\dfrac{Na^{2}}{4}\right]\,da}=0.01\;.$
(3)

From Eq. 3, we get modulation amplitude for unpolarized source,

$a_{1\%}=\dfrac{4.29}{\sqrt{N}}.$ (4)

Eq. 4 leads to the Minimum Detectable Polarization (MDP) or sensitivity of the
instrument in terms of source and background rates ($R_{src}$ and $R_{bkg}$
respectively) and modulation amplitude for 100 $\%$ polarized signal
($\mu_{100}$),

$\centering
MDP_{99\%}=\frac{4.29}{R_{src}\,\mu_{100}}\,\sqrt{\frac{R_{src}\,+\,R_{bkg}}{T}},\@add@centering$
(5)

where, $T$ is the time exposure for polarization measurement.

Once the modulation curve is obtained for any unknown polarized radiation, the
conventional way to measure polarization fraction, $P$, is to first obtain the
modulation amplitude from the modulation curve (with $C_{max}$ and $C_{min}$
being the maximum and minimum number of counts in the modulation curve as
shown in Fig. 12),

$\mu=\dfrac{C_{max}-C_{min}}{C_{max}+C_{min}},$ (6)

and then normalize it with respect to the modulation factor for 100 $\%$
polarized beam, $\mu_{100}$, such that,

$P=\dfrac{\mu}{\mu_{100}}.$ (7)

Figure 12: An example of how modulation signature looks for highly polarized,
medium polarized and low polarized radiation (black, blue, green
respectively).

$\mu_{100}$ is typically estimated from simulations or experiments. For any
polarization measurement technique, $\mu_{100}$ and efficiency should be as
high as possible to have sensitivity well above the expected degree of
polarization from the astrophysical sources (see Eq. 5). Number of detected
photons required to estimate various MDP levels in absence of any background
are shown in Fig. 13.

Figure 13: An example of Minimum Detectable Polarization (MDP) and required
number of photons to be detected in absence of background. The MDP values are
estimated assuming a polarimeter with an effective area of 80 $cm^{2}$ and
$\mu_{100}$ of 0.4 averaged over 20 $-$ 1000 keV. The blue lines in the right
axis correspond to the required time exposures for various source intensities.

With polarimetric efficiency, $\epsilon_{pol}=0.4$ and $\mu_{100}=0.4$
averaged over 20 $-$ 1000 keV, an MDP of 10 % requires detection of $\sim$104
photons or an exposure of 2.5 million seconds for a 200 cm2 collecting area
polarimeter for a 10 mCrab source. The numbers shown in Fig. 13 are an order
of magnitude higher than that required for imaging and spectroscopy studies
which makes X-ray polarimetry extremely difficult.

###  4.2 The available techniques

There are mainly three conventional techniques available to convert the
polarization of radiation into some measurable quantity $-$ scattering, photo-
electric, and Bragg reflection. Here we will briefly discuss the basics of the
measurement techniques followed by a comparison in hard X-rays. For more
details on the techniques, readers are suggested to see Kaaret (2014).

####  4.2.1 Scattering polarimetry

Scattering polarimetry is based on Compton or Rayleigh scattering, where the
photon is scattered off an electron and imparts either a small energy to the
electron (Compton scattering) or travels with the same energy (Rayleigh
scattering). The differential cross-section for Compton scattering is given by
Klein-Nishina formula (Heitler, 1954),

${\dfrac{d\sigma}{d\Omega}}={\dfrac{r_{e}^{2}}{2}}\left({\dfrac{E^{{}^{\prime}}}{E}}\right)^{2}\left({\dfrac{E^{{}^{\prime}}}{E}}+\dfrac{E}{E^{{}^{\prime}}}-2\sin^{2}\theta\cos^{2}\phi\right),$
(8)

where $E$ and $E^{\prime}$ are the incident and scattered photon energies
respectively given by,

${\dfrac{E^{{}^{\prime}}}{E}}={\dfrac{1}{1+\dfrac{E}{mc^{2}}\left(1-\cos\theta\right)}}.$
(9)

$r_{e}$ is the classical electron radius, $m$ is the mass of electron,
$\theta$ is the polar scattering angle, and $\phi$ is the azimuthal angle
between the polarization direction and scattering plane as shown in Fig. 14.
Cross-section for Rayleigh scattering is obtained from Eq. 8 with
$E^{{}^{\prime}}$ made equal to $E$. In both Compton and Rayleigh scattering,
the distribution of the scattered photons with azimuthal angle, $\phi$, is
modulated by $\cos^{2}\phi$ function.

Figure 14: Schematic of Compton scattering geometry. $\theta$ and $\phi$
represent polar and azimuthal angle of scattering respectively. The primary
photon is preferentially scattered perpendicular to the polarization vector
giving rise to an asymmetry in the distribution of azimuthal angle with
$x-2\sin^{2}{\theta}\cos^{2}{\phi}$ probability. Value of ‘x’ depends on the
incident and scattered photon energies, given by E and $E^{\prime}$
respectively (x $=$ 2 for $E=E^{\prime}$).

It is evident that the amplitude of modulation is maximum for
$\theta=90^{\circ}$, however, the probability of scattering is found to be
minimum at 90∘ compared to that for forward and back-scattering (see Fig. 15).
This makes scattering polarimeters to have moderate or low modulation factors
as compared to Bragg and photoelectric polarimeters (discussed later).

Figure 15: Probability of Compton scattering and modulation amplitude as a
function of scattering angle and incident photon energies (shown in different
colors) are shown in the top and bottom panel respectively. We see the
probability of scattering is minimum for $\theta=90^{\circ}$ where we expect
highest modulation amplitude which results in an overall low/moderate level of
modulation factor in Compton polarimeters.

Scattering polarimeters, being based on recording of the photons scattered at
various azimuthal angles, they consist of scatterers surrounded by an array of
absorbers in order to absorb the scattered photons. An important feature of
Compton polarimetry is the extremely low background in comparison to the
Rayleigh mode, which is achieved due to the requirement of simultaneous
detection of both the primary Compton scattering event in the scatterer as
well as the detection of the scattered photon by the surrounding absorber.
Since, the energy transferred to the electron in a scattering event is
typically a small fraction of the incident photon energy, scattering
polarimeters working in Compton mode are unable to work at lower energies.
This is demonstrated in Fig. 16 where the deposited energy in a Compton
scattering event is shown as a function of scattering angle and incident
photon energies.

Figure 16: Electron recoil energy deposited in the scatterer in Compton
scattering as a function of scattering angle and different photon energies. A
lower energy threshold of 2 keV in the scatterer only allows active
coincidence between scatterer and absorbers for energies greater than $\sim$25
keV. The lower energy threshold in the plastic determines the threshold energy
of the Compton polarimeter and its polarimetric sensitivity.

A lower energy threshold of 2 keV in the scatterer (shown by blue horizontal
line in Fig. 16) only allows photons of energies 25 keV or above to deposit
sufficient energy in the scatterer to achieve temporal coincidence between the
scatterer and absorber. On the other hand, since Rayleigh polarimeters do not
require temporal coincidence, they are sensitive to lower energies as well,
where the lower energy cut off depends on the turn over between the
photoelectric and Rayleigh scattering probabilities.

####  4.2.2 Photoelectric polarimetry

In photo-absorption of the X-ray photons, the k-shell photo-electrons are
preferentially ejected in the direction of polarization, constituting the
basic asymmetry in the azimuthal angle distribution. Cross-section of
photoelectric absorption is given by,

${\dfrac{d\sigma}{d\Omega}}=\dfrac{r_{e}^{2}Z^{5}}{137^{4}}{\left(\dfrac{mc^{2}}{E}\right)}^{7/2}\dfrac{4\sqrt{2}\sin^{2}\theta\cos^{2}\phi}{{(1-\beta\cos\theta)}^{4}},$
(10)

where $\theta$ is the polar angle between the direction of incoming photon and
ejected k-shell electron and $\phi$ is the azimuthal angle of the ejected
electron with respect to the polarization vector (see Fig. 17). Modulation in
the ejected angle distribution is maximum for $\theta=90^{\circ}$ (see Eq.
10).

Figure 17: Schematic of Photo-electric absorption geometry. $\theta$ is the
polar angle of the ejected k-shell electron and $\phi$ is the angle between
polarization vector and electron ejection plane. The photo-electron is
preferentially ejected along the polarization direction of the photon giving
rise to an asymmetry in the ejected electron distribution which is proportion
to $\sin^{2}{\theta}\cos^{2}{\phi}$. Each photo-absorption event is associated
with an Auger electron emission shown by the green sphere here.

Since at energies of a few keV, the photo-electrons are preferentially emitted
at 90∘ polar angle, modulation amplitude is expected to be higher for
photoelectric polarimeters compared to the scattering polarimeters.
Furthermore, since at lower energies, most of the photons interact via
photoelectric absorption, polarimetric efficiency for the photoelectric
polarimeters is high in soft X-rays making it intrinsically more sensitive
instrument compared to scattering or Bragg polarimeters at lower energies.
However, at higher energies, Compton polarimeters are more sensitive due to
the increase in scattering probability of photons. Therefore, these two
techniques are sensitive in different energy ranges and are complimentary to
each other.

Tsunemi $et~{}al$. (1992) and Michel & Durst (2008) discuss the method to
image photo-electron track in pixelated semiconductor detectors. In
semiconductor materials, the photo-electron tracks are very small ($\sim$1
$\mu$m for 10 keV electron). Imaging these short photo-electron tracks
requires pixel sizes much less than the track length. With current solid state
detectors having pixel sizes of a few tens of $\mu$m, it is extremely
difficult to image the photo-electron tracks, making these detectors
insensitive to polarization measurements. Fig. 18 compares the photo-electron
track lengths in solids and gases with typical pixel sizes available in
today’s state-of-the-art solid state detectors like Charge Coupled Devices
(CCDs, Lumb $et~{}al$., 1991; Gruner $et~{}al$., 2002; Lesser, 2015) where the
typical pixel size is around 20 $\mu$m with substrate thickness of $\sim$100
$\mu$m or Timepix sensors (Llopart $et~{}al$., 2007) with typical pixel size
of $\sim$55 $\mu$m and relatively thicker substrate of 300 $\mu$m. Photo-
electron imaging in CCDs or Timepix sensors is therefore possible only at very
high energies.

Figure 18: Range of electron computed as a function of energy in solid
(Silicon) and gases (argon at STP). Horizontal lines represent typical pixel
size of 15 $\mu$m in CCD and 55 $\mu$m in Timepix detectors to illustrate that
photo-electron track imaging in CCDs and Timepix detectors is possible at very
high energies where track length is significantly larger than the pixel sizes.

Since in gases, photo-electron tracks are typically of the order of a few
millimeter, Gas Electron Multiplier (GEM) based gas detectors (Sauli, 1997)
are expected to be more sensitive to imaging photo-electron tracks, where the
image is either formed by two dimensional readout anode pixels in Gas Pixel
Detectors (GPD, Costa $et~{}al$. (2001); Bellazzini $et~{}al$. (2006, 2007),
see Fig. 19) or with one dimensional readout strips in Time Projection
Chambers (TPC, Black $et~{}al$. (2007), see Fig. 20), where the other
dimension is obtained from the drift time of the electrons.

Figure 19: Schematic of a GEM based Gas Pixel Detector (GPD). Figure credit
$-$ Costa $et~{}al$. (2001) (Reprinted by permission from Springer Nature
Customer Service Centre GmbH). Figure 20: Schematic of a GEM based Time
Projection Chamber (TPC) polarimeter. Figure credit $-$ reprinted from Black
$et~{}al$. (2007) with permission from Elsevier.

####  4.2.3 Bragg reflection polarimetry

Bragg crystal polarimeter (Toraskar, 1975; Novick, 1975; Silver $et~{}al$.,
1990) utilizes the polarization dependence of Bragg reflection, where the
photons are preferentially reflected perpendicular to the polarization
direction. The integrated reflectivity, $\Delta\theta(E)$, of a crystal is
given by

$\Delta\theta(E)=\frac{N^{2}F^{2}{r_{0}}^{2}\lambda^{3}}{2\mu(E)}\bigg{[}\frac{1}{\sin(2\theta_{B})}-\frac{\sin(2\theta_{B})}{2}\bigg{(}1+\cos(2\phi)\bigg{)}\bigg{]},$
(11)

where, N is the number of scattering cells per unit volume, F is the structure
factor, $r_{0}$ is the classical electron radius, $\mu$ is the absorption
coefficient, $\theta_{B}$ is the Bragg reflection angle, $\lambda$ is the
wavelength of radiation, and $\phi$ is the azimuthal angle between the
electric vector and the reflection plane of radiation (see Fig. 21).

Figure 21: Schematic of Bragg reflection geometry. A crystal preferentially
reflects the incident photons perpendicular to the polarization direction
giving rise to an asymmetry in the azimuthal angle ($\phi$) distribution which
is proportional to 1-$\cos^{2}\phi$ for a Bragg reflection angle of 45∘.

Since modulation in the azimuthal reflection is found to be maximum at
reflection angle of 45∘, a crystal kept at angle 45∘ to the incident X-ray
radiation surrounded by a proportional counter in order to absorb the
reflected X-rays, constitute a good polarization analyzer. Both the crystal
and the detector are rotated around the incident flux direction to obtain
count rates as a function of azimuthal angle. Such a system provides
modulation factor close to unity irrespective of the incident beam energy (see
Fig. 22).

Figure 22: Modulation factor in Bragg reflection as a function of angle of
reflection. Modulation factor is close to unity for Bragg reflection angle of
45∘.

However perfect atomic crystals reflect X-rays in a narrow energy band
extending over a small fraction of an eV, resulting in a poor polarimetric
efficiency, making it insensitive to X-ray polarimetry measurements. Ideally
imperfect crystals that are mosaic of small crystal domains with random
orientations provide higher effective widths (few eVs) and therefore more
suitable for Bragg polarimetry.

Bent crystals can also be used to focus the X-rays onto a small detector in
order to minimize the background (Schnopper & Kalata, 1969). The Bragg
polarimeter on board OSO-8 used a parabolic mosaic graphite reflector (Novick,
1975) which obtained the most precise polarization measurement of Crab so far
in soft X-rays (Weisskopf $et~{}al$., 1976, 1978). A multi-layer optic using
the same Bragg principle can also be used as a polarimeter. Using a
combination of a number of gratings and multi-layer planes, it is possible to
develop broadband sensitive soft X-ray polarimeters in the sub-keV region
($<$1 keV, see Marshall $et~{}al$., 2010, 2018).

###  4.3 Comparison of the techniques in hard X-rays

The polarimetry techniques discussed above have their relative advantages and
disadvantages. Bragg reflection, despite of achieving high modulation factor,
work only at discrete energies or in a narrow sub-keV band which results in a
low polarimetric sensitivity. Compton scattering polarimeters have a moderate
modulation factor and polarimetric efficiency but are unable to work at lower
energies where X-ray flux from the sources is expected to be relatively
higher. However, advantage of Compton polarimeters is that it can work in a
broad energy range in hard X-rays. On the other hand, gas-based photoelectric
polarimeters (GPD, TPC) possess high modulation factor and efficiency in soft
X-rays but the efficiency drops fast at higher energies. With changes in the
design and gas density or pressure, these gas detectors, TPC in particular,
are expected to work at higher energies. With the development in the detector
technology, it might also be possible to image photo-electron tracks in hard
X-rays in Silicon or CdTe based semiconductor detectors with very small
spatial segmentation.

Top panel of Fig. 23 depicts a quantitative picture where a comparison between
photo-electric and scattering efficiency has been made for materials suitable
for these techniques.

Figure 23: top: A comparison of efficiencies in Photo-electric (black) and
scattering method (blue) of polarimetry as a function of energy is made for
various materials and thicknesses suitable for these techniques, bottom: A
comparison in polarimetric sensitivity or MDP is made for various photo-
electric and scattering polarimetry configurations as a function of energy.
The MDP values are in arbitrary unit. See text for more details.

For photoelectric efficiency (shown in black), we have considered two
configurations $-$

  1. 1.

GEM based gas detectors in GPD and TPC configurations with standard and
slightly optimistic gas depth, pressure and composition labelled as,

     * •

A $-$ GPD with 1 cm of He-DME at 1 bar

     * •

B $-$ TPC with 7.8 cm of DME at 180 Torr

     * •

D $-$ GPD with 3 cm of Ar-DME at 3 bar

     * •

F $-$ TPC with 10 cm of Ar-DME at 3 bar.

  2. 2.

State-of-the-art semiconductor detectors with available substrate material and
thicknesses,

     * •

E $-$ 100 $\mu$m Silicon CCD

     * •

C $-$ 5 $\mu$m Silicon monolithic CMOS

     * •

G $-$ 300 $\mu$m Silicon Timepix detector

     * •

H $-$ 1 mm CdTe Timepix detector.

For scattering efficiency (shown in blue), two types of materials have been
considered $-$

  1. 1.

low atomic number (Z) materials as scatterer of suitable depth and shape,

     * •

I $-$ 10 cm thick BC404 bar

     * •

J $-$ 10 cm thick lithium bar.

  2. 2.

State-of-the-art high Z semiconductor detectors,

     * •

K $-$ 5 mm thick CZT detectors

     * •

L $-$ 1 mm thick CdTe Timepix detectors.

From the efficiency plots, it is evident that for energies above a few tens of
keV, scattering technique is more suitable for polarimetry. The slightly
optimistic configurations of GPD and TPC (see ‘D’ and ‘F’, Fabiani, 2018) have
sensitivity ranging up to a few tens of keV. Photo-electron track imaging in
pixelated semiconductors (‘E’, ‘G’, ‘H’) can also extend the measurements to a
few tens of keV, in particular, 1 mm thick CdTe Timepix (see ‘H’) possesses
high detection efficiency in a broad energy range from a few keV to a few
hundreds of keV.

In the bottom panel of Fig. 23, we compare the polarimetric sensitivity of
some of the photoelectric and scattering polarimetric configurations which
show significant detection efficiency in hard X-rays $-$ D, F, H, I, J, K.
Polarimetric sensitivity for instruments based on these materials will depend
on the collecting area, background rates and multiple other factors.
Therefore, the following assumptions were made on the collecting area and
backgrounds while estimating and comparing the sensitivities among the various
polarimetry configurations.

  * •

Because of the availability of hard X-ray focusing optics in 3 $-$ 80 keV
range (shown by a green line in the bottom panel of Fig. 23), for materials
sensitive up to a few tens of keV, we considered small area focal plane
configurations.

For example, for ‘D’ and ‘F’, a compact 16 cm2 geometric area of GPD and TPC
is considered at the focal plane of a NuSTAR or Hitomi type of hard X-ray
telescope.

  * •

For ‘H’, ‘I’, ‘J’, because of the high photon detection efficiency in a broad
energy range from a few tens to hundreds of keV, we considered both hard X-ray
focal plane and a large area wide FOV configuration.

For example, for ‘H’, a 16 cm2 geometric area and 1 mm thick CdTe Timepix
detector was assumed with state-of-the-art pixel size of 55 $\mu$m (Llopart
$et~{}al$., 2007) at the focal plane of a hard X-ray telescope. For the non-
focal configuration (labelled as ‘H*’), we assumed a large array of CdTe
Timepix detectors with total collecting area of 900 cm2 and FOV of
60${}^{\circ}\times$ 60∘.

For ‘I’ (or ‘J’), let us consider a 10 cm long active BC404 plastic
scintillator (or a 10 cm long passive Lithium) surrounded by an array of CsI
scintillators at the focal plane of a hard X-ray telescope. Clearly, while ‘I’
because of the active scattering element, works as a Compton polarimeter, ‘J’
with passive Lithium scatterer, works as a Rayleigh polarimeter. For the non-
focal configuration (labelled as ‘I*’), a 900 cm2 of geometric area is
considered from an array of 10 cm long and 10 mm cross BC404 scintillators (in
6 $\times$ 6 array surrounded by a single array of CsI scintillators in 25
identical modules) with a FOV of 60${}^{\circ}\times$60∘.

  * •

For materials sensitive beyond 100 keV which is inaccessible by focusing
optics, only possible polarimetric configuration is a large area wide FOV
detector array.

For example, for ‘K’ or 5 mm thick CZT or any other high Z materials like
Germanium, we consider a 900 cm2 CZT detector array with pixel pitch of 2.5 mm
(same as CZTI instrument on board AstroSat, Bhalerao $et~{}al$., 2017) with
60∘ $\times$ 60∘ FOV. A lower substrate thickness of CZT or CdTe like 1 mm
CdTe in Timepix configuration would result in a relatively lower sensitivity
due to lower scattering efficiency (Hahn $et~{}al$., 2016) and therefore has
not been considered for sensitivity calculations.

For sensitivity calculations (MDP, see Eq. 5), values of modulation factor are
either taken from literature or calculated analytically in some cases (for
details of the analytical model, see Chattopadhyay $et~{}al$., 2013). In case
of analytical modeling, we ignored effects of Kα fluorescence photons, charge
sharing in semiconductor detectors, charge diffusion in gas detectors and
other complicated phenomena affecting the azimuthal modulation. However, the
values quoted here should not be widely apart from the true values and
suitable for the purpose of comparison among different techniques. We
considered a Crab like spectrum for source flux calculations. For calculation
of background, two different contributions were considered $-$ 1\. Cosmic
X-ray background (CXB) within the FOV (CXB multiplied by either photoelectric
efficiency of the photoelectric polarimeters or by scattering efficiency in
case of scattering based polarimeters). The spectrum for hard X-ray cosmic
background used in the calculations was taken from Türler $et~{}al$. (2010)
computed based on INTEGRAL observations, 2. A conservative number of 10
counts/cm2 particle induced X-ray background was considered to estimate the
random chance events between the scatterer and absorbers for Compton
polarimeters assuming a coincidence time window of 10 $\mu$s. The values of
MDP shown in the figure are in arbitrary units, meant to compare the different
techniques as a function of energy.

From the bottom panel of Fig. 23, we see that CdTe Timepix in both focal and
non-focal configurations yields lower sensitivity because of the large pixel
size compared to the electron track length resulting in low modulation
factors. In this regard, there have been a several attempts to make small
pixel size CCDs (Tsunemi $et~{}al$., 1992; Michel & Durst, 2008; Kotthaus
$et~{}al$., 1998; Hill $et~{}al$., 1997) and CMOS (2.5 $\mu$m pixel, see
Asakura $et~{}al$., 2019) detectors. But the polarization analyzing power of
these detectors is still on the lower side particularly at the lower energies.
A thicker silicon or 5 micron CdTe instead of a 5 micron silicon on CMOS
readout integrated chip (ROIC) can see a significantly higher polarization
sensitivity in a broad energy range due to the enhanced photoelectric
efficiency. Similarly, a much smaller pixel size in 1 mm CdTe-Timepix
detectors will see a significant improvement in the overall sensitivity. This
is particularly interesting because such a detector can provide sensitive
timing, imaging, spectroscopic and polarization information simultaneously as
a focal plane detector, while in the large area wide FOV mode, the instrument
will provide spectroscopic, timing and polarimetry sensitivity in a broad
energy range from a few keV to a few hundreds of keV. However, there is no
report on small pixel size CdTe Timepix detectors in literature. Also, one
should keep in mind the effects of charge sharing on polarization for such
smaller pixel size and thick CdTe detectors.

Though at energies beyond 10 keV, scattering polarimetry outweighs
photoelectric polarimeters, the optimistic configurations of GPD and TPC (see
‘D’ and ‘F’, Fabiani, 2018) can result in higher sensitivity up to $\sim$25
keV. However, in absence of any experimental demonstration of such thicker gas
detectors, Lithium scatterer based Rayleigh polarimeters at the focal plane of
a hard X-ray telescope, have the best sensitivity in 10 $-$ 25 keV range. Due
to the enhanced background level in Rayleigh polarimeters, the sensitivity
goes down significantly at higher energies. At those energies (25 $-$ 80 keV),
a compact Compton polarimeter can provide the best polarimetric sensitivity
because of the concentration of flux and lower background.

Beyond 100 keV, an array of CZT detectors or a 2D array of low Z plastics and
high Z CsI absorbers are expected to provide similar level of sensitivity.
Though plastics have significantly higher scattering efficiency at these
energies compared to CZTs and similar modulation factor values, the relatively
higher detection volume in case of plastic-CsI array (10 cm depth compared to
5 mm depth in CZTs) introduces large chance background events. Plastic
scatterer array has the advantage of lower energy threshold compared to the
CZTs which make them sensitive below 100 keV as well. One should also keep in
mind the relative complexities in realization of a large area detector plane
in case of scintillators and CZTs, requirement of power in these
configurations, readout electronics, availability of active coincidence and
other critical factors to develop the payload.

Consistent with this discussion, we have seen a lot of efforts in the last few
years to develop Rayleigh polarimeters in 10 $-$ 30 keV range (Paul
$et~{}al$., 2016) and Compton polarimeters at higher energies both as focal
plane detector (Chattopadhyay $et~{}al$., 2013, 2014a, 2015; Krawczynski
$et~{}al$., 2011) and large area of scintillators or CZTs or Germanium
detectors (McConnell $et~{}al$., 2009; Chattopadhyay $et~{}al$., 2014b;
Vadawale $et~{}al$., 2015; Orsi & Polar Collaboration, 2011; Caroli
$et~{}al$., 2012, 2018; Yang $et~{}al$., 2018). In the next section, we will
review instrumentation of different scattering polarimetry configurations
suitable in the three energy bands: 10 $-$ 25 keV, 25 $-$ 80 keV and beyond 80
keV.

##  5 Scattering polarimetry configurations: Instrumentation in hard X-ray
polarimetry

As we discuss the best possible scattering polarimetry configurations in
detail in three hard X-ray energy bands, we will touch upon the actual
instrument designs of the past, present and upcoming hard X-ray polarimetry
experiments. For details of the overall payload designs, readers are requested
to refer to the references given here and Table 2 where all the past, present
and planned scattering polarimetry experiments have been summarized.

Table 2: Details of various hard X-ray polarimetry instruments (scattering
polarimeters). See a review by Fabiani (2018)

|  |  |  |  |  |
---|---|---|---|---|---|---
Instrument name |  Configuration |  Mission type | year |  Material and geometry |  Energy |  Science
Past |  |  |  |  |  |
SPR-N (Bogomolov $et~{}al$., 2003) |  50 cm2 |  Satellite |  2001 $-$ 2005 |  Hexahedral prism of 5 cm thick Be with 3 pairs of surrounding scintillators (2 cm$\times$4 cm$\times$.3 cm) |  20 $-$ 100 keV |  Solar flares
PHENEX (Kishimoto $et~{}al$., 2007; Gunji $et~{}al$., 2008) |  $\sim$44 cm2 (88 cm2 in 2009 flight), collimated, FOV $\sim$4.8∘ FWHM |  Balloon-borne | 2006, 09 |  4 units (8 units in 2009 flight) of array of 36 plastic scintillators (5.5, 5.5, 40 mm) surrounded by 28 CsI(Tl) scintillators (5.5, 5.5, 40 mm) |  40 $-$ 200 keV |  Crab
PENGUIN-M (Dergachev $et~{}al$., 2009) |  $\sim$78 cm2 |  Satellite |  2009 $-$ 10 |  4 P-terphenyl scintillators (5 cm dia, 3 cm thick) surrounded by 6 NaI(Tl) scintillators (7 cm dia, 5 mm thick) |  20 $-$ 150 keV |  Solar flares
GAP (Yonetoku $et~{}al$., 2006) |  176 cm2 area, wide FOV |  IKAROS spececraft |  2010 $-$ 11 |  dodecagon plastic scintillator (140 mm gap between two opposite faces) surrounded by 12 CsI scintillators (6 cm long, 5 mm width) |  50 $-$ 300 keV |  GRBs
GRAPE (Bloser $et~{}al$., 2009; McConnell $et~{}al$., 2009) |  $\sim$144 cm2 (216 cm2 in 2014 flight), wide FOV |  Balloon-borne | 2011, 14 |  16 units (24 units in 2014 flight) of 6$\times$6 plastics (5, 5, 50 mm) surrounded by 28 CsI(Tl) scintillators (5, 5, 50 mm) |  50 $-$ 500 keV |  GRBs
PoGO+ (Chauvin $et~{}al$., 2016; Friis $et~{}al$., 2018) |  Large area ($\sim$400 cm2), collimated, narrow FOV ($\sim$2∘) |  Balloon-borne | 2016 |  Array of 12 cm long and 3 cm cross 61 hexagonal plastic scintillators (EJ-204) |  20 $-$ 180 keV |  Crab, Cygnus X-1
SGD (Aharonian $et~{}al$., 2018) |  large area (210 cm2, narrow FOV Compton camera) |  Satellite | 2016 |  32 layers of Si ($\sim$25, 25, 0.6 mm, 3.2 mm pixel) and 8 layers of CdTe sensors ($\sim$25, 25, 0.75 mm, 3.2 mm pixel) surrounded by 2 layers of CdTe from all sides |  50 $-$ 200 keV |  Pulsars, BH XRBs, AGNs, supernova remnanats
COSI (Yang $et~{}al$., 2018) |  Large area (256 cm2), wide FOV Compton camera |  Balloon-borne | 2016 |  12 cross-strip Ge detectors (8, 8, 1.5 cm) in 2$\times$2$\times$3 array, 2 mm of strip pitch |  0.2 $-$ 2 MeV |  GRBs, galactic sources
POLAR (Sun $et~{}al$., 2016; Produit $et~{}al$., 2018) |  large area ($\sim$500 cm2), wide FOV |  Space lab in LE orbit |  2016 $-$ 17 |  25 identical units of 64 plastic scintillator array (EJ-248M, 176 mm long, 5.8$\times$5.8 mm2 cross-section) |  50 $-$ 500 keV |  GRBs
X-Calibur (Guo $et~{}al$., 2011, 2013; Beilicke $et~{}al$., 2014; Kislat $et~{}al$., 2019) |  Focal plane |  Balloon-borne | 2016, 19 |  Plastic scintillator (13 mm dia, 14 cm long) with array of CZTs (2,2,0.2 cm) |  20 $-$ 80 keV |  BH XRBs, NS, AGNs
Active |  |  |  |  |  |
INTEGRAL-IBIS (Forot $et~{}al$., 2008) |  large area (2600 cm2 (CdTe array) & 3100 cm2 (CsI array)), 9${}^{\circ}\times 9^{\circ}$ FOV Compton camera |  Satellite | 2002- |  Compton camera $-$ 1st layer of 128$\times$128 CdTe array (4, 4, 2 mm, 9.2 mm pixel pitch) and 2nd layer of 64$\times$64 CsI scintillator array (8.4, 8.4, 300 mm); gap of 94 mm between the two layers |  250 $-$ 2000 keV |  Crab, Cygnus X-1, transients
INTEGRAL-SPI (Chauvin $et~{}al$., 2013) |  large area (500 cm2), 16∘ FOV |  Satellite | 2002- |  Array of 19 Germanium detectors (7 cm long, hexagonal shape) |  130 $-$ 1000 keV |  Crab, Cygnus X-1, transients
AstroSat-CZTI (Chattopadhyay $et~{}al$., 2014a; Vadawale $et~{}al$., 2015) |  Large area ($\sim$924 cm2), wide FOV (above 100 keV) |  Satellite | 2015- |  Array of 64 CZTs (4, 4, 0.5 cm, 256 pixels) |  100 $-$ 350 keV |  Crab, Cygnus X-1, transients
Planned |  |  |  |  |  |
POLIX (Paul $et~{}al$., 2010, 2016) |  large area (640 cm2), collimated (3${}^{\circ}\times$3∘ FOV) |  Satellite | 2021 |  Li/Be scatterer with 4 position sensitive proportional counters (4$\times$1080 cm2) |  5 $-$ 30 keV |  Pulsars, BH XRBs, AGNs, supernova remnanats
Daksha1 |  Large area, wide FOV |  Satellite | 2023 |  Three separate detector planes of SDD, CZT and NaI detectors, polarimetry from CZT array |  $\sim$100 $-$ 400 keV |  galactic sources, transients
POLAR-2 (Kole, 2019) |  large area ($\sim$2000 cm2), wide FOV |  Space lab in LE orbit | 2024 |  100 units of 64 plastic scintillator array (EJ-248M, 178 mm long, 6$\times$6 mm2 cross-section) |  0.03 $-$ 1 MeV |  GRBs
PING-P (Kotov $et~{}al$., 2016) |  $\sim$30 cm2 area |  Satellite | 2025 |  3 P-terphenyl detectors (3.6 mm dia, 3 cm thick) surrounded by 6 CsI scintillators (4.5 cm dia, 5 cm thick) |  20 $-$ 150 keV |  Solar flares
PolariS (Hayashida $et~{}al$., 2014) |  Focal plane |  Satellite |  |  8$\times$8 array of plastic scintillators (2.1, 2.1, 40 mm) surrounded by 4$\times$4 array of GSO scintillators (4.3, 4.3, 6 cm) |  10 $-$ 80 keV |  BH XRBs, NS, SNRs
SpHiNX (Pearce $et~{}al$., 2019) |  large area (800 cm2), wide FOV |  Satellite |  |  6 hexagonically packed plastic (EJ-204) surrounded by 6 cm long, 24 GAGG scintillators (7 units, total 120 GAGGs and 42 plastics) |  50 $-$ 600 keV |  GRBs
COSI-2 (Tomsick $et~{}al$., 2019) |  Large area (256 cm2), wide FOV Compton camera |  Satellite |  |  Same as COSI with an additional layer of Ge detector array |  0.2 $-$ 2 MeV |  GRBs, galactic sources
LEAP (McConnell & LEAP Collaboration, 2016) |  large area (5000 cm2), wide FOV |  ISS |  |  Similar to GRAPE but with segmented scintillators with individual SiPM readout |  50 $-$ 500 keV |  GRBs
AMEGO (McEnery $et~{}al$., 2019) |  Large area, wide FOV |  Satellite |  |  60 layers of 4 $\times$ 4 array DSSDs (95, 95, 0.5 mm, 500 $\mu$m strip pitch), an array 3D CZTs (8, 8, 40 mm) and 6 layers of CsI(Tl) crystal bars (15, 15, 380 mm) |  200 keV $-$ 1 GeV |  Pulsars, XRBs, AGNs, PWNs, GRBs
e-ASTROGAM (De Angelis $et~{}al$., 2018) |  Large area, wide FOV |  Satellite |  |  layers of 5 $\times$ 5 array DSSDs (95, 95, 0.5 mm, 240 $\mu$m pitch) and an array of small scintillation crystals (33856 CsI(Tl) bars of 5, 5, 80 mm) readout by SDDs |  300 keV $-$ 3 GeV |  Pulsars, XRBs, AGNs, PWNs, GRBs

  * 1

https://www.star-iitb.in/research/daksha

###  5.1 10 $-$ 25 keV: Narrow FOV Rayleigh scattering polarimeter

As discussed in Fig. 23, a Rayleigh scattering based polarimeter is best
suitable for polarization measurements in 10 $-$ 25 keV. Since Rayleigh
polarimeters do not work in active coincidence between the scatterer and
surrounding absorbers, total background is dominated by the cosmic X-rays on
the surrounding absorbers. A small contribution comes from the scattered
cosmic X-rays within the FOV of the instrument onto the surrounding detectors.
It is important to use proper active or passive shielding around the absorbers
to keep the background level at its minimum. The overall sensitivity depends
on the modulation factor and scattering efficiency of the scatterer.
Particularly, the modulation factor critically depends on the shape of the
scatterer. Vadawale $et~{}al$. (2010) has explored various scatterer geometry
(disk, hollow cone, hollow pyramid, slab) and scatterer material (Li, LiH, Be)
and compared their sensitivities. There are multiple options for detectors and
their configuration for absorbers surrounding the scatterer $-$ an array of
CZT detectors in rectangular configuration on four sides of the scatterer,
four rectangular shaped position sensitive multi-wire proportional counters,
cylindrical array of high Z scintillators (e.g. CsI(Tl), NaI etc.). High Z
scintillators and the CZT detectors have high detection efficiency to high
energies making the polarimeters sensitive up to $\sim$100 keV, whereas the
proportional counters are sensitive up to a few tens of keV. Proportional
counters are however more preferred in the 10 $-$ 25 keV range because of
their lower energy threshold compared to scintillators and CZTs.

POLIX (Paul $et~{}al$., 2010, 2016) is an example of Rayleigh scattering
polarimeter sensitive in 5 $-$ 30 keV (see Fig. 24).

Figure 24: POLIX: a Rayleigh scattering based polarimeter sensitive in 5 $-$
30 keV, scheduled for launch in 2021. Figure credit $-$ Paul $et~{}al$.
(2010).

The instrument has been selected for a small satellite mission for Indian
Space Research Organization (ISRO), scheduled for launch in 2021 in a low
Earth and low inclination equatorial orbit. The polarimeter consists of a
Be/Li disk shaped scatterer of 640 cm2 collecting area surrounded by
proportional counters (4$\times$1080 cm2), placed on four sides of the
scatterer. A collimator is used to restrict the FOV of the instrument to
$3^{\circ}\times 3^{\circ}$ with a flat top response to overcome the satellite
pointing inaccuracies. To reduce systematic, the payload spins around the roll
axis by 0.5 $-$ 5 rpm. The instrument is expected to provide an MDP level of 2
$-$ 3 % for a 50 mCrab source in 106 s of exposure.

SPR-N (Bogomolov $et~{}al$., 2003) on board solar mission CORONAS-F exploits
Rayleigh scattering on a 5 cm thick and 50 cm2 collecting area Beryllium
packed inside a hexahedral prism with 3 pairs of scintillation detectors
surrounding the scatterer. Because of the use of scintillators, SPR-N
polarimeter is sensitive in 20 $-$ 100 keV range. As discussed in the previous
sections, the instrument has been successful in providing polarization
measurements for 25 solar flares (Zhitnik $et~{}al$., 2006).

###  5.2 25 $-$ 80 keV: Focal plane Compton polarimeter

Above $\sim$25 keV, Compton polarimeters at the focal plane of hard X-ray
optics can be the most sensitive polarimetry instruments. Focal plane
configuration ensures ideal scattering geometry (high modulation factor) which
along with concentration of flux in hard X-rays and low background due to the
small detector area and active co-incidence between the scatterer and
absorbers makes a multi-fold enhancement in the sensitivity. In recent years,
multiple groups across the globe have started investigating possible
implementation of Compton scattering based X-ray polarimeter coupled with
NuSTAR type of hard X-ray optics, e.g. X-Calibur (Guo $et~{}al$., 2013;
Beilicke $et~{}al$., 2014), CXPOL (Chattopadhyay $et~{}al$., 2013, 2014b,
2015), PolariS (Hayashida $et~{}al$., 2014). X-Calibur had two balloon flights
in 2016 and 2019 with InFOC$\mu$S (International Focusing Optics Collaboration
for $\mu-$Crab Sensitivity) focusing optics. PolariS uses a modified Hitomi
focusing telescope. Intial launch date of PolariS under JAXA was set in 2020.
CXPOL is a focal plane Compton polarimetry instrument development program in
India which uses a NuSTAR type of optic (under development) and is under
active consideration for future X-ray astronomy mission under ISRO (private
communication). All these experiments use a narrow long scatterer
(X-Calibur$-$13 mm diameter and 14 cm long plastic, CXPOL$-$ 5 mm diameter and
10 cm long long plastic, PolariS$-$ 2.1$\times$2.1$\times$40 mm3 plastic in
8$\times$8 array) surrounded by either a cylindrical or rectangular array of
detectors (see Fig. 25 as an example of focal plane Compton polarimeter).

Figure 25: An example of focal plane Compton polarimeter used in CXPOL
experiment (Chattopadhyay $et~{}al$., 2013, 2015). It uses a a long narrow
plastic scatterer surrounded by a cylindrical array of long CsI scintillators.

The long and narrow cylindrical scatterer geometry yields high scattering
efficiency and low probability of multiple interactions in the scattering
volume.

This type of instruments can achieve $\sim$1 $\%$ MDP level in 1 Ms exposure
for 100 mCrab sources assuming NuSTAR type of focusing area. Polarimetric
sensitivity is supposed to be critically dependent on the lower energy
threshold of the plastic scatterer which will depend on many factors $-$ light
output of the plastic, light collection efficiency, position of interaction,
readout method and the readout noise. There are variety of different plastic
scintillator manufacturer like ELJEN technology
222https://eljentechnology.com/products/plastic-scintillators, SAINT-GOBAIN
333https://www.crystals.saint-gobain.com/products/bc-408-bc-412-bc-416, CRYOS-
BETA 444http://www.cryos-beta.kharkov.ua/organic.php which provide sensitive
plastic scintillators. Scintillation properties of most of these scintillators
(ELJEN and BICRON) are similar with around 1.36$\times$104 photons/MeV light
output, 0.7 $-$ 1 ns rise time and 1.8 $-$ 3 ns of decay time and spectral
emission peaking in 410 $-$ 430 nm range. CRYOS-BETA manufactured p-terphenyl
provides higher light output 2.74$\times$104 and slightly higher density,
however longer decay time constant of 3.7 ns. Proper reflection wrapping
material to contain the scintillation photons inside the detector volume is
another critical parameter to improve the lower energy threshold. All these
properties should be carefully inspected along with the photo-multiplier tube
characteristics (e.g. quantum efficiency spectrum) to design a sensitive
Compton polarimeter. Because of all these statistical processes involved in
the detection of X-rays in scintillators, plastics are expected to have a
decreasing detection probability at lower energies, proper understanding of
which is extremely important. Fabiani $et~{}al$. (2013) and Chattopadhyay
$et~{}al$. (2014b) described a method based on Compton scattering to estimate
the behavior of plastics at lower energies where Compton scattered X-rays from
the plastic rod is collected by an independent detector at different known
polar scattering angles and known incident energies. Since the plastic and the
surrounding detector are in active coincidence, at lower scattering angles the
deposited energy being low, below the detection threshold, there will be no
signal from the other detector. Chattopadhyay $et~{}al$. (2014b), for a 5 mm
diameter and 10 cm long BC404 plastic coupled to a photo-multiplier tube (PMT
$-$ Hamamatsu R6095), found $\sim$6 $\%$ detection probability at energies
down to $\sim$0.5 keV, with a linear increase in the probability up to 3 keV.
Detection probability reaches maximum (100 $\%$) at around 7 keV. These
parameters set the energy threshold of the polarimeter at around 20 keV.
Better sensitivity requires better detection probability in the plastic which
can be obtained by further optimization in the use of wrapping material (e.g.
TETRATEX, teflon, VM2000, BC-620 paint) or better scatterers (Fabiani
$et~{}al$., 2013).

There are several options in the choice of detectors for the surrounding
absorber array. X-Calibur uses an array of 2$\times$2$\times$0.2 cm3 CZT
detectors (64 pixels) on four sides of the plastic scatterer. CXPOL
(Chattopadhyay $et~{}al$., 2015) and PolariS (Hayashida $et~{}al$., 2014), on
the other hand, use long CsI(Tl) and GSO scintillator bars respectively to
detect the scattered X-rays. Use of CZT detector array provides 2D positional
information of the scattered photons which can be used to extract the polar
scattering angle (if plastic is vertically position sensitive) and therefore
can be used to further filter out the chance background events. CZT detectors
also provide better energy resolution which enable sensitive spectroscopic
measurements from the Compton events ($E=E_{plastic}+E_{CZT}$). Advantage of
scintillators is simpler electronics and better uniformity. They can be used
in cylindrical array which does not suffer any intrinsic azimuthal asymmetry
as in case of rectangular configuration and therefore can be operated without
the need of payload spin. Particularly, with the development of MAPMTs
555https://www.hamamatsu.com/us/en/product/optical-sensors/pmt/index.html and
Si photomultipliers (SiPM) 666https://www.hamamatsu.com/us/en/product/optical-
sensors/mppc/index.html, because of their small and compact size, low weight,
scintillators can have the compactness needed to develop focal plane
instruments. PolariS uses MAPMT to readout the GSO scintillator array from the
flat bottom side. MAPMTs still employs high HV bias ($\sim$1000 V) between the
anode and cathode and crosstalk between the anode pixels reduces the
sensitivity of the detectors. SiPM units (Buzhan $et~{}al$., 2002, 2003; Otte,
2006), on the other hand, operates with low voltage ($\sim$31 V, above
breakdown voltage) and do not suffer from crosstalk. The extremely small size
($\sim$3 mm$\times$3 mm), light weight, robust nature provides required
compactness. The wide spectral range matches with the emission spectra of most
scintillators. It is also possible to read a scintillator bar from both sides
which will provide vertical position sensitivity as in case of CZTs.

Though SiPMs have been mostly used at higher energies (Bloser $et~{}al$.,
2013; Sanaei $et~{}al$., 2015), lower energy (20 $-$ 80 keV) application of
SiPMs was demonstrated only recently during CXPOL experiment (Chattopadhyay
$et~{}al$., 2015) to readout CsI(Tl) scintillators with SiPM PM3350 from KETEK
777https://www.ketek.net/sipm/. One major issue of SiPMs is the high
background level ($\sim$500 kHz/mm2), therefore use of SiPMs at lower energies
requires very good light collection at the SiPM which will depend on the
scintillator light output and decay time constant. A smaller decay time
constant ensures simultaneous arrival of the optical photons to the SiPM which
will yield higher signal to noise ratio. Therefore, NaI(Tl), LaBr3(Ce), CeBr3
with small decay constants make them good candidates for SiPM readout (Goyal
$et~{}al$., 2018) (see Table 3). However, some of these detectors suffer from
intrinsic background in the MeV region (Iyudin $et~{}al$., 2009; Cebrián
$et~{}al$., 2012) which can be a disadvantage for the polarimeter.

Table 3: Possible inorganic scintillators as absorber array and their
properties

|  |  |  |  |  |
---|---|---|---|---|---|---
Scintillator name |  Light Yield (/keV) |  Decay time constant (ns) | Density (gm/cc) |  Hygroscopic |  Maximum emission (nm) |  Hardness (Mho)
|  |  |  |  |  |
GSO(Ce)1 |  8 $-$ 10 |  30 $-$ 60 | 6.7 |  No |  430 |  5.7
CeBr${}_{3}^{2}$ |  60 |  19 | 5.1 |  Yes |  380 |
NaI(Tl)3 |  38 |  250 | 3.67 |  Yes |  415 |  2
CsI(Tl)4 |  54 |  1000 | 4.51 |  Slight |  550 |  2
CsI(Na)4 |  41 |  630 | 4.51 |  Yes |  420 |  2
GAGG(Ce)5 |  40 $-$ 60 |  50 $-$ 150 | 6.63 |  No |  520 |  8

  * 1

https://www.advatech-uk.co.uk/gso_ce.html

  * 2

https://www.advatech-uk.co.uk/cebr3.html

  * 3

https://www.crystals.saint-gobain.com/products/nai-sodium-iodide

  * 4

https://www.crystals.saint-gobain.com/products/csitl-cesium-iodide-thallium

  * 5

https://www.advatech-uk.co.uk/gagg_ce.html

New generation SiPMs with lower background level and faster post-avalanche
recovery of the micro-pixels are the key to achieve lower energy threshold of
20 keV of the scintillators and Compton polarimeters. Cooling down the SiPMs
to lower temperature should also improve the overall background and
sensitivity of the instruments.

PENGUIN-M (Dergachev $et~{}al$., 2009) on board the CORONAS-PHOTON solar
mission, launched in 2009 and PING-P (Kotov $et~{}al$., 2016) in the 2025
upcoming solar mission use similar Compton polarimetry geometry but with non-
focal configuration to measure polarization of solar flares in 20 $-$ 150 keV.
Both the instruments use p-terphenyl active scatterer with NaI(Tl) and CsI
scintillators as absorbers respectively read by individual PMTs (see Table 2).

###  5.3 $>$80 keV: large detector array configuration

As discussed in section 4 and shown in Fig. 23, at energies above 80 keV with
no focusing optics in hard X-rays, large array of high Z detectors like
pixelated CZTs or Germanium detectors or an array of plastic and inorganic
scintillators make sensitive Compton polarimeters. They can be utilized both
in narrow FOV (when collimated) for pointed observations or in wide FOV
configuration to detect transients like GRBs or solar flares. Use of
collimators restricts the energy range to a few hundreds of keV, but possesses
higher sensitivity due to lower background. However, one should consider the
fact that a large FOV instrument can observe multiple hard X-ray objects
simultaneously and therefore the effective exposure in this case is T/N rather
than T, where T is the exposure and N is the number of sources in the FOV.
Most of the Compton polarimetry experiments seen in the last decade e.g.
AstroSat-CZTI, INTEGRAL-SPI, POLAR, GRAPE, GAP, PHENEX, PoGO+ utilize one of
these configurations.

####  5.3.1 Array of high Z detectors

Any spatially segmented spectrometer should intrinsically provide Compton
polarimetry capability if the readout preserves the 2-pixel or multi-pixel
events. CZT detector based spectrometers can be used in this configuration
because of the significant Compton scattering cross-section of thick CZTs (as
shown in Fig. 23). CZT detectors have already been used extensively in
developing sensitive spectrometers over the years in SWIFT (Barthelmy
$et~{}al$., 2005), INTEGRAL (Ubertini $et~{}al$., 2003), NuSTAR (Harrison
$et~{}al$., 2013), AstroSat (Singh $et~{}al$., 2014), Hitomi (Kunieda
$et~{}al$., 2010), EXIST (Hong $et~{}al$., 2009), RT-2 experiment on board
CORONAS-PHOTON (Nandi $et~{}al$., 2011) exploiting its high detection
efficiency in a broad energy band from a few keV to a few hundreds of keV,
fine spectral energy resolution at near room temperature and sufficient
radiation hardness. CZT spectrometers can also provide simultaneous
polarimetry measurements at energies beyond 100 keV utilizing the spatial
segmentation (see bottom panel of Fig. 23).

Multiple groups across the globe are actively involved in developing CZT
detectors optimized for polarimetry and experimentally demonstrating their
polarization measurement capability (see an overview on the ongoing efforts by
Caroli $et~{}al$., 2018). CZT Imager (CZTI, Bhalerao $et~{}al$., 2017; Rao
$et~{}al$., 2016) on board AstroSat (Agrawal, 2006; Singh $et~{}al$., 2014) is
a large area coded mask hard X-ray spectrometer. It has been successfully
utilized as a hard X-ray Compton polarimeter in 100 $-$ 350 keV (Chattopadhyay
$et~{}al$., 2014a; Vadawale $et~{}al$., 2015). AstroSat-CZTI employs a total
of 64 CZT detector modules (each module is 40$\times$40$\times$5 mm3 in size
with 16$\times$16 pixel array of 2.5 mm pitch) with integrated readout ASIC
providing a collecting area of 1024 cm2 for hard X-ray imaging and
spectroscopy in 10 keV to 150 keV range (see Fig. 26).

Figure 26: Schematic of CZT Imager on board AstroSat. The 64 CZT detector
array is shown in blue along with CZTI bottom housing (grey), collimator and
supporting structures (grey towers) and radiator plate (red). Picture credit
$-$ Bhalerao $et~{}al$. (2017) (reprinted by permission from Springer Nature
Customer Service Centre GmbH).

The readout provides a time resolution of 20 $\mu$s which makes it possible to
use the instrument as a sensitive polarimeter in 100 $-$ 300 keV (Vadawale
$et~{}al$., 2018). The collimators, coded mask and the supporting structure of
the payload become increasingly transparent at higher energies enabling the
instrument to detect GRBs and measure their polarization (Chattopadhyay
$et~{}al$., 2019).

Unlike other polarimetry configurations where the low Z scatterer(s) and high
Z absorbers are physically isolated, in CZT detectors, a similar distinction
of scatterer and absorbers is not possible which can make the identification
of the 1st or the scattering event and 2nd or the photo-absorption event
slightly complicated. At lower energies (below 260 keV), this identification
can be done from the respective energy depositions as the electron recoil
energy is always lower than the scattered photon energy (see Fig. 27).

Figure 27: Compton polarimetry in pixelated CZT detectors. The pixel with low
energy deposition shown in grey or the 1st event and one of the adjacent 8
pixels with high energy deposition shown in red or the 2nd event provide the
azimuthal Compton scattering angle for polarization analysis.

However, at energies beyond 260 keV, energy deposited in the electron recoil
can be larger than the scattered photon energy for some range of scattering
angles which makes the extraction of azimuthal angle complicated. Unlike the
low Z plastic scatterers, CZT detectors (Z $\sim$50) have escape lines around
30 keV than can produce fake 2-pixel events (around 1 % probability for the
CZT detectors used in CZTI) that can reduce the sensitivity of the instrument.
On the other hand at higher energies (above 200 keV), bremsstrahlung photons
emitted from the high energy photo-electrons can register as 2-pixel events
diluting the modulation patterns (see Fig. 28).

Figure 28: Different processes generating 2-pixel events in 2.5 mm pixel and 5
mm thick CZT detectors as a function of energies: photo-electric $-$ photo-
electric (blue, asterisks), 1-compton $-$ photo-electric (pink, diamond),
1-compton $-$ 1-photo $-$ electric (red, triangle), photo-electric $-$ multi-
Compton (green, square), photo-electric $-$ bremsstrahlung (yellow, diamond),
photo-electric $-$ bremsstrahlung-Compton (light blue, triangle). Figure
credit $-$ Chattopadhyay $et~{}al$. (2014a) (reprinted by permission from
Springer Nature Customer Service Centre GmbH).

Therefore, it is important to accurately extract the true Compton events based
on the energy depositions and other Compton kinematics criteria. It is
possible to filter out most of the 2-pixel hits arising from the photo-
electric escape events by setting the energy threshold of the CZT pixels above
30 keV (in the analysis software), however at the expense of higher low energy
cut ($\sim$150 keV) for polarization analysis resulting in slightly lower
sensitivity.

Because of the asymmetry in the scattering geometry due to the square pixels,
these detectors can possess inherent modulation in the azimuthal angle
distribution. Modulation factors in CZT detectors also depend on the
polarization angle. For polarization along the corner pixels, modulation
factors are significantly higher than that for the edge pixels. This is
because the electric field vector when aligned along the corner pixels favors
polar scattering angle close to 90∘ for the Compton scattering events which
yields high modulation factors as shown in Fig. 15 (for more details, see
Chattopadhyay $et~{}al$., 2014a). All these effects should be carefully
evaluated using detailed laboratory experiments and simulations for correct
interpretation of the data from this type of polarimetry instruments.

A thick CZT detector ($\sim$5 mm) provides sufficient scattering probability,
however limits the pixel size to a couple of millimeter in order to minimize
charge sharing between the pixels (Kalemci & Matteson, 2002; Kim $et~{}al$.,
2011; Veale $et~{}al$., 2014; Chattopadhyay $et~{}al$., 2016). This in turn
limits the number of bins to only eight as most of the two pixel events are
contained within a 9-pixel island. Accurate measurement of polarization angle
requires a larger number of azimuthal bins. Reduction in the substrate
thickness will allow for smaller pixel sizes which in turn might provide
larger number of azimuthal bins. Optimization in pixel size and thickness of
the detectors and pixel geometry (e.g. square vs. hexagonal) can play an
important role in developing sensitive CZT based Compton polarimeter.

With the increasing success of inferring photon interaction site along the
depth of the detector (Zhang $et~{}al$., 2012; Kuvvetli $et~{}al$., 2014),
CZTs can now be utilized as Compton camera and therefore can constrain the
source direction for each 2-pixel event which will reduce the chance
background events significantly. Working principle of a Compton camera has
been demonstrated in Fig. 29.

Figure 29: Working principle of a Compton camera. From the two known energy
depositions, polar scattering angle, $\theta$, can be inferred which along
with the known x, y, z-locations of the events can be used to obtain the
source direction within the circumference of the Compton cone.

From the two known energy depositions and x, y, z-locations of the events, the
source direction can be constrained within the circumference of a Compton
cone. The interaction depth (z) is calculated from the ratio of charges in the
segmented cathode to the charge in strip anode in CZT drift detectors
(Kuvvetli $et~{}al$., 2014) or by calculating the electron cloud drift time
based on the time difference between the signals from the cathode and the
anode (Kim $et~{}al$., 2019). Compton polarimetry based on 3D CZT detectors
has already been evaluated and proposed (Caroli $et~{}al$., 2012). See Caroli
$et~{}al$. (2018) for an overview of 3D CZT detector development for
polarimetry experiments. The uncertainty in determining the Compton scattering
angle depends on the energy resolution of the detector for E1 (1st
interaction) and E2 (2nd interaction) and E, total energy (see Eq. 12) and
position resolution in x, y, z direction,

$\cos\theta=1-\dfrac{mc^{2}E_{1}}{E_{2}(E_{1}+E_{2})}.$ (12)

CZT detectors are expected to provide better than $\sim$5 % energy resolution
around 100 keV at room temperatures. The 2D spatial resolution in the x,
y-direction is limited by the pixel size (2.5 mm pixel size assuming CZTI type
of detectors). A $<$1 mm resolution in the z direction for a 5 mm thick CZT
has been reported (Kim $et~{}al$., 2019; McEnery $et~{}al$., 2019). Based on
these parameters, comparison in polarization sensitivity between a 900 cm2
planar array of 2D CZT and 3D CZT detectors is made in Fig. 30.

Figure 30: Same as bottom panel of Fig. 23 with sensitivity of a 3D CZT
detector array (KC) and 3D sensitive scintillator detector array (I*C) as a
function of photon energy. We see a significant improvement in sensitivity
compared to the respective 2D configurations (K and I*) with the availability
of 3D position of each event enabling reconstruction of source photon
direction.

The sensitivity improves significantly for 3D CZTs due to the restricted FOV
along the circumference of the Compton scattering cone. However, one should
keep in mind the complexity due to large volume of data flow (full temporal
profile with a few tens of $\mu$s timing resolution for both anode and cathode
for each event) and realization of a large detection plane using this type of
detector.

Germanium detector based hard X-ray spectrometers (e.g SPI, Vedrenne
$et~{}al$., 2003) on board INTEGRAL, can also be utilized for Compton
polarimetry where Compton scattered events are identified from two events in
two individual detector bars. Advantage of Germanium detectors is that they
can be made thicker $\sim$ a few cm, which makes them sensitive in a broad
energy range with high Compton scattering efficiency. Unlike CZT detectors,
Germanium detectors require cooling to very low temperatures to minimize the
leakage current. SPI is a coded mask instrument utilizing 19 hexagonal high
purity Germanium detector bars (each with thickness of 7 cm) closely packed in
a hexagonal shape. Events depositing energies in two detectors within a
coincidence window of 350 ns are used to extract polarization information in
200 $-$ 1000 keV (Chauvin $et~{}al$., 2018c). SPI was not optimized for
polarimetry and never tested for polarization before the launch of INTEGRAL.
The instrument in 18 years of operation lost 4 detectors with a $\sim$53 %
reduction in the multi-detector effective area and significant degrade in the
polarimetric sensitivity. Germanium detector array with proper optimization
for Compton polarimetry can serve as a sensitive spectro-polarimeter in a wide
energy band.

####  5.3.2 Array of low Z and high Z scintillators

An obvious extension of the focal plane configuration with plastic scatterer
based Compton polarimeter in $>$80 keV is a square array of plastic
scintillators for the requirement of large collecting area surrounded by an
array of high Z inorganic scintillators on four sides. Availability of MAPMTs
makes this type of configuration possible where a single MAPMT (e.g.
8$\times$8 pixels) can read the full array of plastic and inorganic
scintillators (total 8$\times$8 array of scintillators). One advantage of this
configuration compared to the high Z detector array is that the instruments
are also sensitive at lower energies $\sim$50 keV because of higher Compton
scattering efficiency of the low Z plastics at lower energies. The lower
energy limit can be further improved with the improvement in the lower energy
threshold in the plastic scintillators (discussed in the previous section).
This type of configuration, however, suffers from light leak between the
adjacent plastic scintillators and between the anode pixels in the MAPMTs
which reduce the modulation factors of the instruments and enhance the
intrinsic chance background events. The upcoming polarimetry designs under
this configuration take care most of these shortcomings by employing new
detection technologies (see below).

GRAPE (Bloser $et~{}al$., 2009; McConnell $et~{}al$., 2009), a balloon-borne
wide FOV hard X-ray GRB polarimeter and PHENEX (Kishimoto $et~{}al$., 2007;
Gunji $et~{}al$., 2008), another balloon-borne but narrow FOV hard X-ray
polarimeter employ this type of geometry. Both PHENEX and GRAPE use long (40
and 50 mm respectively), square shaped (5.5$\times$5.5 mm2 and 5$\times$5 mm2
respectively) plastic scintillators in 6$\times$6 array at the center
surrounded by 28 CsI (Tl) scintillators of same dimensions to detect the
plastic scattered X-rays (see Fig. 31). All the scintillators are read by a
single MAPMT.

Figure 31: An example of scintillator array configuration for Compton
polarimetry as used in GRAPE experiment. See text for more details. Picture
courtesy $-$ McConnell $et~{}al$. (2009) (reprinted by permission from authors
and SPIE).

Molybdenum collimators in PHENEX modules restrict the FOV to 4.8∘ (FWHM) in an
energy range of 20 $-$ 200 to perform pointed observations. The balloon
flights of GRAPE and PHENEX did not yield any significant measurements either
due to small effective exposure because of problems in attitude control system
or higher than expected background level resulting in low sensitivity. One
major issue with the MAPMT readout is the cross-talk between the pixels
reducing the polarimetric sensitivity of the instruments. SiPM readout can
solve the cross-talk problem. An array of SiPMs along the length of the
scintillators can provide significant improvement in the sensitivity by
lowering down the energy threshold in the plastic scintillators, also enabling
Compton imaging from 3D readout of the events which in turn reduces the
background events. Fig. 30 compares sensitivity between 2D (same as in Fig.
23) and 3D scintillator array. Even though the lower energy threshold is kept
same in both 2D and 3D plastics, we see a significant improvement in the
sensitivity for the 3D scintillator array due to reduced background. Updated
design of GRAPE employs a large number of small, scintillator cubes, each of
which is readout by its own SiPM (McConnell $et~{}al$., 2018). LEAP (McConnell
& LEAP Collaboration, 2016), recently selected for phase A study for NASA’s
future astronomy mission is based on the same design. In a tightly packed
scintillator array, light leak between the adjacent scintillators is another
concern, minimization of which requires an efficient wrapping material making
them optically isolated. This also promotes better light collecting efficiency
and thereby improving the sensitivity. SPHiNX (Pearce $et~{}al$., 2019), a
newly proposed Swedish GRB polarimetry mission (sensitive in 50 $-$ 500 keV)
uses SiPM readout for the surrounding GAGG scintillators along its width and
length. It uses normal PMT readout for the plastic scatterers. The design uses
7 units of 6 hexagonically packed triangle-shaped EJ-204 plastic scintillators
each read by its own PMT surrounded by 24 GAGG scitillator bars read by SiPM
array. The shared walls of the 7 hexagons are read by the common SiPMs in
order to reduce the number of readout channels.

Design of GRB polarimeter, GAP (Yonetoku $et~{}al$., 2006), on board 2010
IKAROS solar power sail mission, is based on a simple Compton scattering
geometry. GAP uses a single but large 12 sided plastic scintillator (gap
between two opposite sides $\sim$ 140 mm and height of 60 mm) read by a single
large 51 mm diameter PMT surrounded by 12 CsI scintillators (6 cm long and 5
mm width) read by individual small subminiature PMTs. The large plastic
provides a collecting area of $\sim$176 cm2 with a large FOV.

####  5.3.3 Array of low Z scintillators

This type of configuration uses only an array of low Z plastic scintillators
and therefore play a dual role of both scatterer and absorber. The advantage
of this configuration is that the instrument can be scaled up easily in
collecting area by increasing the number plastic scintillators. The recent
polarimetry experiments, POLAR and PoGO+, utilized this configuration in
developing the instruments.

POLAR (Sun $et~{}al$., 2016; Produit $et~{}al$., 2018) on board Chinese space
laboratory TG-2, is a wide field GRB polarimeter, sensitive in 50 $-$ 500 keV.
One unit of POLAR (total of 25 units) comprises 64 plastic scintillator bars
(EJ-248M, 17.6 cm long and 5.8 mm sides) readout by one MAPMT. As mentioned
earlier, MAPMT suffers from optical cross-talk between the adjacent pixels
which limits the sensitivity of the instrument. It also requires high voltage
for operation, failure of which caused an untimely end of the POLAR mission.
These shortcoming will be taken care of in the successor mission, POLAR-2
(Kole, 2019), planned for launch in 2024, by employing SiPMs to readout the
plastic bars from the back side instead of MAPMTs. POLAR-2 uses similar
configuration of array of 64 plastics of similar depth and cross-section,
however with a total of 100 units, thereby enhancing the effective area by an
order of magnitude. To overcome the high background of SiPMs, POLAR-2 will
passively cool the SiPMs to -10∘C which ensures a lower background level and
therefore better energy threshold of the plastics ($\sim$2 keV). This improves
the effective area performance of POLAR-2 at lower energies. POLAR-2 with its
planned sensitivity and energy range of 30 $-$ 1000 keV is expected to provide
accurate polarization measurements for $\sim$50 GRBs/year with polarization
level of $\sim$10 %.