# Prompt Emission Polarimetry of Gamma-Ray Bursts with the AstroSat CZT Imager

Tanmoy Chattopadhyay, Santosh Vadawale, E. Aarthy, N. Mithun, Vikas Chand, Ajay Ratheesh, Rupal Basak, A. Rao, Varun Bhalerao, Sujay Mate, et al.

► To cite this version:

Tanmoy Chattopadhyay, Santosh Vadawale, E. Aarthy, N. Mithun, Vikas Chand, et al. Prompt Emission Polarimetry of Gamma-Ray Bursts with the AstroSat CZT Imager. The Astrophysical Journal, 2019, 884 (2), pp.123. 10.3847/1538-4357/ab40b7. hal-04939604

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# Prompt Emission Polarimetry of Gamma-Ray Bursts with the AstroSat CZT Imager

Tanmoy Chattopadhyay<sup>1,2,3,4</sup>①, Santosh V. Vadawale<sup>2</sup>①, E. Aarthy<sup>2</sup>, N. P. S. Mithun<sup>2</sup>, Vikas Chand<sup>5</sup>, Ajay Ratheesh<sup>5,6,7,8</sup>, Rupal Basak<sup>9,10,11</sup>①, A. R. Rao<sup>5</sup>①, Varun Bhalerao<sup>12</sup>①, Sujay Mate<sup>12,13</sup>, Arvind B.<sup>12,14</sup>, V. Sharma<sup>15</sup>①, and Dipankar Bhattacharya<sup>15</sup>

<sup>1</sup> Pennsylvania State University, University Park, PA 16802, USA; tanmoyc@stanford.edu

<sup>2</sup> Physical Research Laboratory, Ahmedabad, Gujarat, India

<sup>3</sup> Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA

<sup>4</sup> Kavli Institute of Astrophysics and Cosmology, 452 Lomita Mall, Stanford, CA 94305, USA

<sup>5</sup> Tata Institute of Fundamental Research, Mumbai, India

<sup>6</sup> Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy

<sup>7</sup> INAF Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma, Italy

<sup>8</sup> Dipartimento di Fisica, Università La Sapienza, P. le A. Moro 2, I-00185 Roma, Italy

<sup>9</sup> INAF—IASF Bologna, via P. Gobetti, 101, I-40129 Bologna, Italy

<sup>10</sup> Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, I-44122 Ferrara, Italy

<sup>11</sup> Department of Physics, KTH Royal Institute of Technology, and the Oskar Klein Centre for Cosmoparticle Physics, SE-10691 Stockholm, Sweden

<sup>12</sup> Indian Institute of Technology Bombay, Mumbai, India

<sup>13</sup> IRAP, Université de Toulouse, CNES, CNRS, UPS, Toulouse, France

<sup>14</sup> Physics and Astronomy Department, Texas Tech University, Lubbock, TX 79409, USA

<sup>15</sup> The Inter-University Centre for Astronomy and Astrophysics, Pune, India

Received 2017 July 18; revised 2019 August 23; accepted 2019 August 31; published 2019 October 17

## Abstract

X-ray and gamma-ray polarization measurements of the prompt emission of gamma-ray bursts (GRBs) are believed to be extremely important for testing various models of GRBs. So far, the available measurements of hard X-ray polarization of GRB prompt emission have not significantly constrained the GRB models, particularly because of the difficulty of measuring polarization in these bands. The CZT Imager (CZTI) on board AstroSat is primarily an X-ray spectroscopic instrument that also works as a wide-angle GRB monitor due to the transparency of its support structure above 100 keV. It also has experimentally verified polarization measurement capability in the energy range 100–300 keV and thus provides a unique opportunity to attempt spectropolarimetric studies of GRBs. Here we present the polarization data for the brightest 11 GRBs detected by CZTI during its first year of operation. Among these, five GRBs show polarization signatures with $\gtrsim 3\sigma$, and one GRB shows $2\sigma$ detection significance. We place upper limits for the remaining five GRBs. We provide details of the various tests performed to validate our polarization measurements. While it is difficult yet to discriminate between various emission models with the current sample alone, the large number of polarization measurements that CZTI expects to gather in its minimum lifetime of five years should help to significantly improve our understanding of the prompt emission.

**Key words:** gamma-ray burst: general – gamma-ray burst: individual (151006A, 160106A, 160131A, 160325A, 160509A, 160607A, 160623A, 160703A) – instrumentation: detectors – polarization – X-rays: general

## 1. Introduction

Gamma-ray bursts (GRBs) are thought to accompany the birth of stellar-mass black holes in the core collapse of massive stars (Woosley 1993; Iwamoto et al. 1998; MacFadyen & Woosley 1999) or mergers of compact stellar binaries (Eichler et al. 1989; Narayan et al. 1992). Phenomenologically, GRB emission occurs in two distinct phases—the prompt and the afterglow. The initial burst of high-energy emission or the prompt emission is widely believed to originate from a jet close to the black hole, while the long-lasting multi-wavelength afterglow emission is generated far from the compact object by the interaction of the GRB jet with the ambient medium (Piran 2004; Mészáros 2006). Despite the observation of a large number of GRBs in the last decade (Gehrels & Mészáros 2012) with sensitive detectors on board the Swift (Gehrels et al. 2004; Barthelmy et al. 2005) and Fermi (Meegan et al. 2009) missions, the mechanism of the prompt emission has not yet been well understood (Kumar & Zhang 2015) owing to the diversity, extreme variability, and very short duration (seconds) of this phase (Hakkila & Preece 2014; Basak et al. 2017). The prompt emission is believed to be generated either via the synchrotron process

(Rees & Meszaros 1994; Sari et al. 1998) or via inverse Compton scattering (Ghisellini & Celotti 1999; Ghisellini et al. 2000; Lazzati et al. 2004). In addition, a few cases display evidence of a thermal blackbody component, presumably of photospheric origin (Ryde 2004; Pe'er & Ryde 2011; Basak & Rao 2015; Iyyani et al. 2015). One way of distinguishing between these emission processes would be through their unique polarization signatures, so the measurement of X-ray and gamma-ray polarization is considered to be of great importance in the study of GRB prompt emission (Covino & Gotz 2016; McConnell 2017). In particular, a statistical study of GRB polarization could provide critical constraints on the geometry and the radiation process involved (Toma et al. 2009).

The past decade has seen 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 (Kalemci et al. 2007; McGlynn et al. 2007, 2009) on board INTEGRAL, as well as BATSE (Willis et al. 2005) on board the Compton Gamma Ray Observatory (see a review by McConnell 2017), have reported several cases of strong polarization. However, these instruments being of primarily spectroscopic nature and not optimized for polarimetry, the
results, limited by statistical and systematic uncertainties, are often thought to be unreliable (Rutledge & Fox 2004; Wigger et al. 2004). Subsequently, GAP (Yonetoku et al. 2006), a dedicated Compton polarimeter with a large field of view flown in 2011, obtained polarization measurements for three bright GRBs (Yonetoku et al. 2011, 2012). More recently, POLAR (Orsi & Polar Collaboration 2011; Sun et al. 2016), a dedicated GRB polarimeter launched in 2016, provided precise polarization measurements for five GRBs in their prompt phase in hard X-rays (Zhang et al. 2019). They showed the polarization of the GRBs to be low, between 4% and 11%, hinting at an unpolarized nature of GRBs in general. However, for firm confirmation, a larger sample with such precise measurements is necessary. POLAR, however, ceased operation on 2017 March 31.

*AstroSat* (Singh et al. 2014), India's first dedicated astronomical satellite, was launched on 2015 September 28, and has been operating successfully. The Cadmium Zinc Telluride Imager (CZTI) instrument on board *AstroSat*, with an array of CZT detectors, is a large-area (~1000 cm²) spectroscopic instrument with a coded mask imaging capability in the energy range 20–150 keV (Bhalerao et al. 2017; Chattopadhyay et al. 2016; Vadawale et al. 2016). The 5 mm thick pixelated CZT detectors used in this instrument present a significant Compton scattering probability in hard X-rays, thereby enabling it to operate as a Compton polarimeter in the energy range 100–300 keV, as demonstrated during ground calibration (Chattopadhyay et al. 2014; Vadawale et al. 2015). At these energies, the supporting structure of CZTI becomes increasingly transparent, making the instrument capable of detecting transient events such as GRBs and performing their polarimetric measurements. On the very first day of its operation, CZTI detected a GRB (GRB 151006A, Bhalerao et al. 2015) at an angle 60° from the pointing direction. A detailed spectropolarimetric study of GRB 151006A has been reported in Rao et al. (2016).

Apart from GAP and POLAR, the previously reported polarization results from *RHESSI* and *INTEGRAL* have the drawback that the instruments were never calibrated before flight with polarized and unpolarized sources, which draws a lot of criticism regarding the reliability of the reported results. CZTI, on the other hand, has been extensively calibrated for polarization measurements before launch, thus boosting confidence in the obtained results. Additionally, because of the large collecting area of the instrument and the favorable Compton scattering geometry presented by the pixels, the polarimetric sensitivity of CZTI is significantly higher than that of other contemporary X-ray polarimeters. Given a minimum lifetime of *AstroSat* of five years, we expect to obtain a large sample of GRB polarizations with CZTI which, along with results from other existing/upcoming GRB polarimetry missions, may lead to a better understanding of these objects.

In its first year of operation (2015 October 6 to 2016 October 5) CZTI detected a total of 47 GRBs, among which we attempted polarization measurements for the 11 brightest events. We select GRBs with fluence higher than $10^{-5}$ erg cm$^{-2}$, so that the number of Compton events is sufficient to attempt polarization measurements. Most of these GRBs appear to show signatures of high polarization. In this paper we report the detailed data analysis and the resulting polarization estimates for these GRBs. These are, however, difficult measurements due to the scarcity of flux in most cases and the extreme photon-hungry nature of X-ray polarimetry. We

have treated the statistical uncertainties and the possible sources of systematics, which may introduce false polarimetric signatures, with utmost care for each of the GRBs. In Section 2, we discuss the polarization capability of CZTI, the analysis procedure, and the details of the individual GRBs in our sample. This is followed by the final results and discussions in Sections 3 and 4 respectively.

## 2. CZTI as a GRB Polarimeter: Analysis Procedure

CZTI consists of an array of 64 CZT modules where each detector is 5 mm thick, providing high quantum efficiency and fine spectral resolution in a broad energy band from a few keV to a few hundred keV. Each detector module is further pixelated into 256 pixels (with a nominal pixel size of 2.5 mm × 2.5 mm). A 0.5 mm thick tantalum coded mask provides imaging capability to the instrument in the energy range 20–150 keV. CZTI also has the advantage of working in a photon tagging mode with a time resolution of 20 µs. All these features make CZTI well suited to study the spectral and timing features of celestial X-ray objects in the region 20–150 keV.

Besides the spectroscopic and timing studies, CZTI also works as a sensitive Compton polarimeter for bright X-ray sources at higher energies. This feature arises out of the significant Compton scattering cross section of 5 mm thick CZT detectors at energies beyond 100 keV and the availability of continuous time-tagged events from CZTI. Compton scattering occurs preferentially in a direction perpendicular to the incident polarization, giving rise to a sinusoidal modulation in the distribution of azimuthal scattering angles (Lei et al. 1997; Kaaret 2014). The flight configuration of CZTI has been shown to possess polarization measurement capability, through detailed experiments and simulation studies during its ground calibration (Chattopadhyay et al. 2014; Vadawale et al. 2015). Because of the increasing transparency of the collimators and the supporting structure in the range 100–300 keV, CZTI works as an open detector and captures high-energy transient events such as GRBs occurring all over the sky. Detection of GRB 151006A on the very first day of its operation (Bhalerao et al. 2015), at a large off-axis angle, demonstrates the capability of CZTI as a wide-angle GRB monitor. This, coupled with the polarimetric capability of CZTI, offers a unique opportunity to attempt polarization measurements of GRBs with CZTI, particularly since GRB prompt emission could be strongly polarized. GRB polarimetry with CZTI is very similar to the on-axis polarimetry of persistent sources, but with the following key advantages.

1. Because CZTI polarimetric observations do not require any change in the hardware configuration, polarimetric analysis can be attempted from data obtained in the standard mode. CZTI detects 4–5 GRBs in a month. Polarimetric analysis can in principle be attempted for any detected GRB.

2. GRB prompt emission is expected to be strongly polarized owing to its non-thermal origin and the involvement of high bulk Lorentz factors, thus making detection easier.

3. Compared to bright persistent sources such as the Crab or Cygnus X-1, GRBs provide higher signal-to-noise ratio in Compton events, resulting in a higher polarimetric sensitivity.
4. Accurate polarimetric background measurements are available just before and after the GRB event.

## 2.1. Criteria for the Selection of Compton Events

The selection criteria for the Compton events have been discussed in detail in Chattopadhyay et al. (2014). Each event in the CZTI output data has an individual time stamp with a resolution of 20 µs. Any two events occurring within 20 µs will bear the same time stamp. The event file also lists the pixel and detector ID, the energy channel of detection, and veto and alpha coincidence flags. The Compton scattering events are normally expected to be captured within a 20 µs time window. However, since the readout in CZTI is done for one module at a time, if two events are registered in two different pixels in the same module, there is a certain probability that the two events would get different time stamps. Therefore, we select all the double-pixel events happening within a coincidence window of 40 µs, because information on the polarization of the radiation is embedded in these double-pixel events. Events at three, four, or more pixels within a coincidence window are excluded from analysis, primarily because the probability of such events due to Compton scattering is low and it is difficult to identify the first event out of these multiple events. In the case of double-pixel events, the pixel with the lower energy deposition is considered to be the scattering pixel and the higher energy one is the absorbing pixel. It is to be noted that CZTI detectors provide better than 10% and 5% energy resolution at 59.5 and 122 keV respectively. In Compton scattering, the electron recoil energy (lower energy deposition) is normally well below the scattered photon energy and therefore the events are widely separated and easily distinguishable. A time window as long as 40 µs may also result in false chance coincidence events. These events are filtered out by applying the Compton kinematics criteria: (1) spatial proximity of the pixels and (2) the sum and ratio of the deposited energies must be consistent with those expected for true Compton events for the scattering geometry of CZTI. We also exclude all the veto and alpha flagged events ("alpha flag" refers to simultaneous detection of an alpha particle by a CsI scintillator kept inside the $^{241}$Am onboard calibration box and a 59.5 keV X-ray photon in the CZT detector) from further analysis because these events do not carry any polarization information and therefore contribute indirectly to the background.

Figure 1 shows the light curve of GRB 160623A in single events (blue line) and Compton events (black data points). A clear detection of the GRB in Compton events shows the pertinence of the event selection criteria. It is to be noted that CZTI has observed the Crab Nebula for ~790 ks and could obtain a clear pulse profile of the Crab pulsar in the Compton events in the range 100–380 keV (for on-axis sources, Compton events are selected in the energy range 100–380 keV), which also independently validates the Compton event selection algorithm (Vadawale et al. 2018). In order to further make sure that the peak in the Compton events is not a result of chance coincidence of the GRB photons, we generate a light curve for double-pixel events not satisfying the Compton conditions. As we see in Figure 1 (red data points), the GRB does not show up as clearly as in case of Compton events. The small peak in the non-Compton events arises due to a significant probability of chance coincidence, given the high flux of the GRB. This is expected to be more prominent for brighter

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Observed rate of single and double events in CZTI during GRB 160623A. The blue solid line (plotted against the right axis) is obtained from the detected single events. The events satisfying the Compton criteria (plotted against the left axis) are shown in black, and the red data points (plotted against the left axis) are double events not satisfying the Compton criteria. The region between the dashed vertical lines in the light curve marks the prompt emission phase of GRB 160623A. The Compton events within this region are used for further analysis.</figcaption></figure>

GRBs. We discuss the estimation of these events and their effect on the polarization analysis in a later section.

## 2.2. The GRB Sample for Our Study

In its first year of operation CZTI detected a total of 47 GRBs.<fnref n="16" /> Out of these we selected 11 that are bright enough to give a sufficient number of Compton events (the number of double events satisfying the Compton criterion greater than 400) to attempt polarization analysis. Out of these 47 GRBs, 33 were detected by Fermi/GBM and 14 by Swift/BAT, with eight being common between these two instruments. Localization of these GRBs in CZTI coordinates was done using the position information available in the Swift and Fermi GRB databases. Our choice of bright GRBs with sufficient Compton events corresponds to a limiting fluence of $10^{-5}$ erg cm$^{-2}$. The Fermi and Swift catalogs list 18 GRBs above this limit during the corresponding 1 yr period. AstroSat has ~30% of the sky occulted by the Earth at any given time, and during this year had data gaps for ~20.5% of the time due to passage through the South Atlantic Anomaly or telemetry errors. The detection of 11 of the 18 bright GRBs in CZTI (~60%) is consistent with its effective duty cycle and sky coverage.

The observed properties of these 11 GRBs are listed in Table 1. Seven of them have triggered Fermi/GBM detectors (listed chronologically in the table), five have triggered Swift/BAT detectors, while two of them triggered both. The three GRBs triggered only in Swift/BAT are listed next in the table (again chronologically). GRB 160623A, listed last in the table, is a long GRB that triggered Konus/Wind, but was occulted by the Earth for a long time for Fermi/GBM. However, it has localization information from Swift/XRT and prompt spectral information from CZTI detectors. The GRB location error circles quoted in the table are based on those provided by the Swift and Fermi satellites: the localization information is taken, where available, from Swift/XRT, Swift/BAT, and Fermi/GBM catalogs. The durations of the GRBs, $T_{90}$, are measured in the 50–300 keV and 15–150 keV bands for the GBM and

<footnote n="16">¹⁶ http://astrosat.iucaa.in/czti/?q=grb</footnote>
<table><caption>**Table 1**
The Sample of GRBs Selected for Polarization Study with CZTI</caption><thead><tr><th>GRB<br>(Detectors)</th><th>Localization<sup>a</sup></th><th>T<sub>90</sub><br>(s)</th><th>(t<sub>1</sub>, t<sub>2</sub>)<sup>b</sup><br>(s)</th><th>α/-p</th><th>Spectral<br>Parameters<br>β</th><th>E<sub>p</sub>/E<sub>c</sub><br>(keV)</th><th>Afterglows<sup>c</sup></th><th>Fluence<sup>d</sup></th><th>Incident Direction<br>(θ, φ)<br>(deg)</th><th>Parts Passed Through</th></tr></thead><tbody><tr><td>151006A (GBM)</td><td>2′′3</td><td>84.0</td><td>(0, 37.0)</td><td>-1.17<sup>+0.08</sup><sub>-0.07</sub></td><td>-2.16<sup>+0.05</sup><sub>-0.18</sub></td><td>447<sup>+207</sup><sub>-121</sub></td><td>X</td><td>0.5 (1.6)</td><td>60.82, 67.57</td><td>UVIT, SXT, CZTI collimator</td></tr><tr><td>160106A (GBM)</td><td>1°1</td><td>39.4</td><td>(-1.5, 14.7)</td><td>-0.53<sup>+0.07</sup><sub>-0.06</sub></td><td>-2.31<sup>+0.14</sup><sub>-0.21</sub></td><td>400<sup>+45</sup><sub>-40</sub></td><td>...</td><td>3.5 (5.6)</td><td>106.12, 255.69</td><td>CZTI collimator</td></tr><tr><td>160325A<br>(GBM, BAT)</td><td>1′′7</td><td>43.0</td><td>(-0.8, 15.2)<br>(39.2, 47.2)</td><td>-0.71<sup>+0.07</sup><sub>-0.06</sub></td><td>-2.26<sup>+0.20</sup><sub>-0.30</sub></td><td>238<sup>+25</sup><sub>-22</sub></td><td>X, U, O, NIR</td><td>0.76 (4.78)</td><td>0.66, 159.44</td><td>Coded mask</td></tr><tr><td>160509A (GBM)</td><td>2′′3</td><td>371.0</td><td>(3.7, 20.6)</td><td>-0.75<sup>+0.02</sup><sub>-0.02</sub></td><td>-2.13<sup>+0.03</sup><sub>-0.03</sub></td><td>334<sup>+12</sup><sub>-10</sub></td><td>X, O, R</td><td>4.5 (48.7)</td><td>105.74, 85.45</td><td>CZTI collimator, LAXPC</td></tr><tr><td>160802A (GBM)</td><td>1°0</td><td>16.4</td><td>(-1.0, 4.0)<br>(12.0, 19.0)</td><td>-0.61<sup>+0.04</sup><sub>-0.04</sub></td><td>-2.40<sup>+0.10</sup><sub>-0.13</sub></td><td>280<sup>+17</sup><sub>-14</sub></td><td>...</td><td>2.2 (8.8)</td><td>52.96, 273.12</td><td>CZTI collimator</td></tr><tr><td>160821A<br>(GBM, BAT)</td><td>1°0</td><td>43.0</td><td>(130, 158)</td><td>-0.97<sup>+0.01</sup><sub>-0.01</sub></td><td>-2.25<sup>+0.03</sup><sub>-0.03</sub></td><td>866<sup>+25</sup><sub>-24</sub></td><td>O</td><td>20.0 (47.0)</td><td>156.18, 59.31</td><td>Satellite body (below)</td></tr><tr><td>160910A (GBM)</td><td>4′′3</td><td>24.3</td><td>(5.9, 10.4)</td><td>-0.36<sup>+0.03</sup><sub>-0.03</sub></td><td>-2.38<sup>+0.05</sup><sub>-0.06</sub></td><td>330<sup>+13</sup><sub>-13</sub></td><td>X, O, R</td><td>0.42 (12.3)</td><td>65.54, 333.45</td><td>LAXPC, CZTI collimator</td></tr><tr><td>160131A (BAT)</td><td>2′′2</td><td>325.0</td><td>(26.2, 42.4)</td><td>-1.00<sup>+0.14</sup><sub>-0.14</sub></td><td>...</td><td>388<sup>+2735</sup><sub>-185</sub></td><td>X, U, O, R</td><td>0.9 (6.8)</td><td>116.86, 184.64</td><td>Radiator plate, CZTI<br>collimator</td></tr><tr><td>160607A (BAT)</td><td>1′′5</td><td>33.4</td><td>(3.3, 16)</td><td>-1.16<sup>+0.04</sup><sub>-0.04</sub></td><td>-1.56<sup>+0.07</sup><sub>-0.10</sub></td><td>586<sup>+518</sup><sub>-259</sub></td><td>X, O</td><td>0.8 (3.9)</td><td>138.85, 315.78</td><td>Solar panel, satellite body</td></tr><tr><td>160703A (BAT)</td><td>3′′9</td><td>44.4</td><td>(-4.2, 2.9) (3.8, 24.2)</td><td>-1.11<sup>+0.04</sup><sub>-0.04</sub></td><td>-2.50<sup>+0.26</sup><sub>-0.35</sub></td><td>176<sup>+25</sup><sub>-42</sub></td><td>X, U, O, R</td><td>0.6 (1.6)</td><td>10.14, 95.05</td><td>Coded mask, CZTI<br>collimator</td></tr><tr><td>160623A (CZTI)</td><td>3′′5</td><td>90.4</td><td>(0, 7)</td><td>-0.88<sup>+0.05</sup><sub>-0.05</sub></td><td>-2.95<sup>+0.11</sup><sub>-0.14</sub></td><td>327<sup>+46</sup><sub>-36</sub></td><td>X, O, NIR, R</td><td>5.3 (18.0)</td><td>140.46, 118.06</td><td>Satellite body (below)</td></tr></tbody></table>

**Notes.**

<footnote>a Localization given with 90% error radius, taken from Swift/XRT, Swift/BAT, and Fermi/GBM catalogs. For GRB 160910A, the error is only statistical.</footnote>

<footnote>b $t_1$ and $t_2$ are with respect to GBM/BAT trigger time; for GRB 160623A with respect to CZTI trigger time: UT 204353981.02834 (seconds since 2010 January 1, 00:00:00 UTC). Konus/Wind observations of GRB 160131A, GRB 160607A, GRB 160703A, and GRB 160623A: Tsvetkova et al. (2016a) (GCN 18974), Tsvetkova et al. (2016b) (GCN 19511), Frederiks et al. (2016a) (GCN 19649), and Frederiks et al. (2016b) (GCN 19554).</footnote>

<footnote>c Afterglows—O: optical, X: X-rays, R: radio, NIR: near-infrared, U: UVOT.</footnote>

<footnote>d Fluence in units of $10^{-5}$ erg cm$^{-2}$ in the range $t_1$ to $t_2$; 100–300 keV; values in brackets are fluence in the 10–1000 keV band for the time-integrated GRB.</footnote>
BAT detections respectively, and are collected from various circulars from the Gamma-ray Coordinates Network (GCN) as well as the respective websites. For GRB 160623A, however, $T_{90}$ is obtained from CZTI-Veto. The time durations selected for polarization analysis ($t_1$ and $t_2$) are given with respect to the trigger time of Fermi/GBM (for the first seven GRBs), Swift/BAT (for the next three GRBs), and CZTI (for GRB 160623A). There are multiple values of the duration for three GRBs, determined based on the availability of the Compton events in the CZTI data. If afterglow measurements exist, they are indicated in the table with symbols X (Swift/XRT X-rays), O (optical), U (Swift/UVOT), R (radio), and NIR (near-infrared): this information is gathered from available GCN circulars on these GRBs.

In order to compare the observed polarization fractions with theoretical predictions, estimates of the peak energy of the GRBs are required (Toma et al. 2009). To obtain the peak energies of the selected GRBs, we carried out a spectroscopic analysis using the data obtained from GBM, BAT, and CZTI. The GBM and the LAT data on low-energy events were retrieved from the Fermi Science Support Center archives.<fnref n="17" /> The spectral analysis was done for the same time intervals that have been used for polarization measurements. The photon spectra were fitted with a Band model (Band et al. 1993) for the seven GRBs detected by GBM, and with a power law with an exponential cut-off ($\propto E^{-p}\exp(-E/E_c)$) for the three GRBs detected by BAT. From the spectral parameters, we calculated the fluence in the selected time intervals in the energy range 100–300 keV as well as the time-integrated fluence in the 10–1000 keV band (given in parentheses in the ninth column of Table 1). For the three BAT-detected GRBs, we use the Konus/Wind spectral parameters (given in the second line of the table) to determine the 10–1000 keV time-integrated fluence. For GRB 160623A, we use Konus/Wind data to determine the spectral parameters using the Band model, which are then combined with the CZTI-Veto spectrum to determine the fluence. The relevant model parameters are provided in Table 1. The peak energies are in near agreement with the time-integrated peak energies given in the respective catalogs or GCN circulars. The errors in the parameters quoted here represent 90% confidence intervals. Except for GRB 160325A, all the GRBs were detected outside CZTI’s primary field of view. In such off-axis detections, the radiation passes through different parts of the satellite structure and other instruments before reaching the CZTI detectors. The last two columns of Table 1 show the polar ($\theta$) and the azimuthal ($\phi$) angles of detection of the bursts in the CZTI coordinates and the spacecraft components that the GRB photons pass through. GRB photons can scatter off the material in various parts of the satellite structure, affecting the detected polarization properties. It is important to account for these effects by means of detailed Geant4 simulations of the full satellite. This will be discussed in later sections.

The light curves of these 11 GRBs are displayed in Figure 2. The GBM light curves in the 15–100 and 100–300 keV bands are shown in magenta and black for seven GRBs, while 15–100 keV BAT light curves are shown in magenta for the three GRBs detected only by SWIFT. For GRB 160623A, the CZTI-Veto light curve in the 100–300 keV band is shown in

black. The time durations selected for polarization analysis are shown between vertical lines.

## 2.3. AstroSat Mass Model

Polarization analysis of off-axis sources is challenging because the polarization properties of photons are affected by interactions with satellite elements and CZTI housing elements. These interactions are highly dependent on direction and energy. To account for this we modeled the entire AstroSat with accurate chemical and geometrical properties inside a Geant4 simulation (Agostinelli et al. 2003) including all the payloads of AstroSat: SSM, UVIT, SXT, LAXPC, CZTI, and the satellite bus. The mass model is essential to model the effect of the surrounding material on unpolarized and polarized radiation (see Sections 2.4 and 2.5).

We modeled the payload and satellite bus geometries as accurately as possible. Some elements of the geometry are coded using the Geant4 geometry classes, while for the complex structure we used the Cadmesh interface (Poole et al. 2012) to import the CAD models into the Geant4 detector construction. Figure 3 shows the mass model of AstroSat simulated in Geant4. The mass model of CZTI and the Physics codes had been extensively validated during ground calibration of the CZTI pixels and polarization experiments with on-axis calibration sources (Vadawale et al. 2015). The Geant4 geometries of other instruments (LAXPC, SXT, UVIT, SSM) and spacecraft were included at a later date after the launch of AstroSat. However, these geometries are based on the actual CAD models and hence are expected to be highly accurate.

Nevertheless, it is important to validate the complete AstroSat mass model by means of observed data. We validated the mass model in three different ways using a large number of GRBs, including the 11 GRBs reported in the present work, which more or less uniformly span all possible incident angles in the spacecraft reference frame.

1. **Count distribution.** We simulated the count distribution in all 64 CZT modules using Geant4 simulations to generate the simulated detector plane histograms (DPH) and compared them with the observed DPH. We found that the observed DPH agree well with the simulated ones. Figure 4 shows such a distribution for GRB 160521B. The mass model distribution accounting for all onboard instruments shows a marked improvement over the ray-tracing results for CZTI alone.

2. **Localization.** The DPH comparison is sufficiently good to be used for estimating the location of a GRB for which an independent position measurement is not available. We utilized the mass model for localizing the known GRBs by DPH comparison, thereby confirming its robustness. Results for GRB 160802A are given in Figure 5. The DPH comparison roughly peaks at the GRB location (shown as a plus sign in the figure) and it is well within the 90% contour.

3. **Broadband spectroscopy.** Using Geant4 simulations of the mass model, we generated the response for X-rays impinging in the direction of the GRB. Responses were generated for both single-pixel events and the two-pixel Compton events. We simulated monoenergetic incident photons from 50 keV to 1 MeV every 20 keV and from 1 MeV to 2 MeV every 200 keV and recorded the energy distribution for each of the monoenergetic inputs. The

<footnote n="17">¹⁷ https://fermi.gsfc.nasa.gov/ssc/data/access/</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** The GRB light curves are shown here for the energy ranges 15–100 keV (magenta) and 100–300 keV (black) (see text for details). The vertical green lines represent the time intervals that have been used to extract double events for polarization measurements.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Mass model of *AstroSat* simulated in Geant4 with a zoomed-in view of the CZT Imager.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Comparison of count distributions for GRB 160521B from mass model simulation (top left), data (top right), and ray-tracing (bottom). The mass model-simulated DPH agrees well with the observed DPH. We also see a clear improvement in the count distribution from the full satellite mass model compared to the ray-tracing distribution for CZTI alone.</figcaption></figure>

distribution was then convolved with a Gaussian of
appropriate width. For Compton response, the total
absorbed energy for a given incident photon was obtained
by adding the energies in scattering and absorbing pixels.
Usually, the Compton response is sensitive in the
100–350 keV band. However, if we utilize the low-gain
pixels in CZTI (around 20% of the detector plane), the
energy response extends up to 600 keV. Although we do
not use the low-gain pixels for polarization analysis, we
do utilized them for better Compton spectroscopy. We
extract GRB spectra from CZTI data and *Fermi* data for
the same start and end times used in polarization analysis.
The GRB spectrum for single-pixel events is generated
using the standard method whereas the Compton
spectrum is obtained by selecting the Compton events
in the same GRB region and adding the energies of two-
pixel events. For background we select the pre- and post-
GRB regions and add them.

Figure 6 shows the broadband fitting of GRB 160821A
using *Fermi* and CZTI data, where the single-pixel and

double-pixel Compton spectra from CZTI are shown in light
blue and magenta respectively. The same spectral model
measured using *Fermi* data was used here for fitting (see
Table 1). Only the relative constant for CZTI data was kept
free and found to be around 0.12 ± 0.02, within the error of
the *Fermi* normalization of 0.14 ± 0.02. The spectral
shapes for both the single and Compton spectra agree quite
well, which demonstrates the robustness of the *AstroSat*
mass model. It is to be noted that the Compton spectrum
was obtained from the same Compton events used for
polarimetry. Further, we stress here that we have not refitted
the spectrum; we used the same *Fermi* parameter values
(except for CZTI normalization) for the combined *Fermi*
and CZTI data to reproduce the observed spectra.

It is to be noted that, for our region of interest above
100 keV, the interaction of photons with elements of low
atomic number (Z) is not important. Discrepancy in the low-
Z element geometry might be reflected in the DPH and
localization, which are reproduced at lower energies. At
higher energies, it is the high-Z element geometries that
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Localization of GRB 160802A (with known localization) using DPH comparison from mass model simulation and observed data. The plus sign is the actual GRB location and the filled circle represents the peak of DPH comparison.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Broadband spectroscopy of GRB 160821A with the same *Fermi* model as given in Table 1. The light blue and magenta are for CZTI single-pixel (100–200 keV) and double-pixel Compton events (100–600 keV). The black, red, green, and blue are for sodium iodide scintillators (NaI 06, NaI 07, and NaI 09) and bismuth germanate scintillator (BGO 01), respectively.</figcaption></figure>

dominate the spectroscopy and polarization output. The spectroscopy results shown here clearly demonstrate that the geometries of the high-Z elements have been defined accurately. This directly signifies the robustness of the polarization results to be discussed in the later sections.

## 2.4. Background Event Analysis

In Chattopadhyay et al. (2014) and Vadawale et al. (2015) the various sources of background events have been discussed in detail. The most significant contribution to background comes from radiation reflected by the Earth and from diffuse cosmic X-ray background across the side collimators and supporting structure, which undergo Compton scattering in the

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Integrated effective area of the CZTI Imager (module-wise) in the 100–300 keV band for GRB 160509A. We simulate the *AstroSat* mass model in Geant4 to estimate the effective area of the modules and pixels for the same photon energy distribution and off-axis viewing angle as for the observed GRB. The effective area has been normalized with respect to its maximum value. The contours shown in white, red, and blue enclose pixels with normalized effective areas of 15%, 18%, and 20% respectively.</figcaption></figure>

CZTI pixels. However, we see that the background rate obtained from the onboard data is 2–3 times higher than the values estimated from numerical simulations (Vadawale et al. 2016). In the uncleaned event data from CZTI, we observe cosmic-ray showers in the CZTI detectors. Though we filter out the cosmic-ray events, there is a certain probability that a fraction of these events still passes through the filtering conditions, giving rise to a higher than expected background rate. The various levels of transparency of the collimators and the supporting structures result in an unequal distribution of effective area across the detector pixels. This results in a shadow pattern in the detector plane for the observed GRBs. It is possible to suppress the background events by selecting events only from pixels with higher effective area. In order to estimate the pixel-wise effective area for a GRB, simulation is done for a large number ($10^9$) of incident photons in the energy range 100–400 keV. In the simulation, we employ the processes for low-energy X-ray photons—G4LowEnPolarized-PhotoElectric, G4LowEnPolarizedRayleigh, G4LowEnPolarizedCompton, G4LowEnBremss, G4LowEnIonization. The current simulations are done using version 4.10.03 of Geant4. Interaction positions, energy depositions, and all other relevant information are stored in the output event file. Further analysis of the selection of valid Compton events and estimations of effective area are done using an IDL code. Figure 7 shows the estimated effective area of the CZTI detector modules for GRB 160509A ($\theta = 105^\circ.7, \phi = 85^\circ.5$, power-law index = 0.75) in the 100–300 keV band. The three contours shown in the figure enclose pixels with effective areas of 15% (white), 18% (red), and 20% (blue) of the maximum effective area. In our analysis
we select events only from pixels with effective area >10% and thus filter out a fraction of background events, resulting in a higher signal-to-background contrast.

An important step in the background analysis is to estimate the chance coincidence events during the GRB that mimic true Compton events. In Figure 1, the red points are obtained for events involving two non-neighboring pixels with the other Compton criteria kept the same. The small peak in the light curve during the GRB is because of (1) chance coincidence events of the GRB photons within the 40 µs time window in non-neighboring pixels, and (2) the Compton scattering events between non-neighboring pixels. The number of Compton events between non-neighboring pixels can be estimated from Geant4 simulation. We subtract this number from the total number of events under the peak to estimate the chance events in non-neighboring pixels during the GRB. The estimated chance events are found to be small in number compared to the valid Compton events (<1%–2%) for the brightest of the GRBs. These numbers agree well with the theoretically computed values based on Poisson’s chance coincidence rate in a temporal window of 40 µs. We are particularly interested in the chance event rate in neighboring pixels during the GRB because these events would mimic the Compton events, leading to a false estimation of polarization. There are expected to be fewer chance events in neighboring pixels than in non-neighboring pixels since the number of neighboring two-pixel combinations is ~35 times lower than the number of non-neighboring two-pixel combinations (for 256 pixels in a module). Consequently, we expect the chance events to be reduced by a factor of ~35 compared to the number in non-neighboring pixels of 1%–2%, which makes them negligible.

## 2.5. Estimation of Modulation Amplitude (μ) and Polarization Angle (φ₀) and their Uncertainties

In order to obtain the distribution of azimuthal scattering angles for the GRB photons, through which the polarization signature is derived, we first generate an eight-bin azimuthal angle distributions for combined background and GRB events (e.g., the Compton events contained within the vertical dashed lines in Figure 1). The azimuthal angle distribution for background events alone is then subtracted from the total distribution to obtain the source distribution. The background distribution is obtained by averaging the pre-GRB and post-GRB azimuthal count distributions. The azimuthal angle for a given valid event is defined with respect to the “X” axis on the CZTI plane (perpendicular to the radiator plate) in an anticlockwise direction when viewed from the top. The background count rate has been found to vary from orbit to orbit due to progressively different ground traces. However, one of the advantages of GRB polarimetry is the availability of the events just before and after the GRB prompt emission, which makes it easier to estimate the background azimuthal distribution than that for a persistent source. The background-subtracted azimuthal angle histogram for GRB 160821A, as an example, is shown in Figure 8 (left) in black. We see a significant difference in the count rates detected by the edge pixels (angular bins 0°, 90°, 180°, and 270°) and the corner pixels (angular bins 45°, 135°, 225°, and 315°). This is due to the unequal solid angles subtended by the edge and corner pixels to the central pixel (Chattopadhyay et al. 2014). It is to be noted that the azimuthal angle distribution for any off-axis source is supposed to differ significantly from that for an

on-axis source. This is because of the break in symmetry in the pixel geometry with respect to the incident photon direction. This complicates the overall shape of the azimuthal angle distribution. However, both these effects can be taken care of by normalizing the azimuthal distribution of the GRB by that for 100% unpolarized radiation, of the same spectrum and incident at the same off-axis angle as the source. If $P_i$ stands for the count of polarized photons in the ith angular bin, $U_i$ that for unpolarized photons in the same angular bin, and $\bar{U}$ the average number of photons for the unpolarized distribution, then the corrected distribution for the polarized photon count may be obtained as

$$C_i = \frac{P_i}{U_i} \bar{U}. \qquad (1)$$

We obtain $U_i$ or the unpolarized distribution by simulating 100% unpolarized incident radiation with the AstroSat mass model at the same angle of incidence and with the same spectrum as the observed GRB. The red line in Figure 8 (left) shows the raw azimuthal unpolarized distribution, whereas the black histogram, in the right panel, shows the modulation curve for the GRB following the correction given in (1). The error bars on the modulation curve represent the $1\sigma$ uncertainties in each bin, which are mostly dominated by the statistics of low photon counts during the GRB prompt emission and the uncertainty in estimating the background azimuthal distribution. We propagate these individual contributions to finally estimate the error in the azimuthal bins:

$$\sigma_C^2(\phi) = \left(\frac{\bar{U}}{U_i}\right)^2 \left(\frac{R_G}{T_G} + \frac{R_B}{T_G} + \frac{R_B}{T_B}\right) + \left(\frac{(C_i \bar{U})^2}{U_i^3}\right). \qquad (2)$$

The first term represents the statistical error associated with the GRB and background counts. $R_G$ and $R_B$ are the GRB and background count rates respectively. $T_G$ and $T_B$ are the durations of the GRB and of the selected background exposure. The statistical uncertainty in the background distribution can be made negligible with a sufficiently large background exposure. The second term in Equation (2) stands for the geometric correction (Equation (1)). Since the geometric correction is based on Geant4 simulations of a very large number of photons (10⁹), this term results in a negligible contribution to the final error.

In order to estimate the polarization angle and modulation amplitude (and thereby the polarization fraction), we use two different approaches: (1) standard fitting of the geometry-corrected modulation curve by a sinusoidal function, and (2) using Markov chain Monte Carlo (MCMC) simulations.

### 2.5.1. Estimation by Fitting of Modulation Curves

We use the standard $\chi^2$ fitting algorithms available in IDL to fit the modulation curve with a cosine function to estimate the modulation amplitude and the polarization angle, given by

$$C(\phi) = A \cos(2(\phi - \phi_0 + \pi/2)) + B, \qquad (3)$$

where A, B, and $\phi_0$ are the fitting parameters. The modulation factor, which is directly proportional to the polarization of the photons, is given by the ratio of A to B, and the polarization angle in the detector plane is given by $\phi_0$. The fitted cosine curve
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 8.** Left: the background-subtracted raw eight-bin azimuthal angle distribution for GRB 160821A obtained from the Compton events (~100–300 keV) is shown in black. The error bars are the Poisson error on each azimuthal bin for the 68% confidence level. The azimuthal distribution shown in red is that obtained by simulating unpolarized incident radiation from the same GRB. Right: the geometrically corrected modulation curve for GRB 160821A. The solid blue line is a sinusoidal fit to the modulation curve while the red dashed line is obtained from an MCMC method for a modulation amplitude ~0.23 with a detection significance >3σ (one parameter of interest at 68% confidence level) and a polarization angle ~−39° in the CZTI plane.</figcaption></figure>

<table><caption>**Table 2**
Measured Polarization Fractions (PF) and Position Angles (PA) for the GRBs</caption><thead><tr><th>GRB Name</th><th>N<sub>Compt</sub>(100–400 keV)</th><th>PF (%)<sup>a</sup></th><th>CZTI PA (deg)</th><th>Sky PA (deg)</th><th>P<sub>chance</sub> (%)</th><th>μ<sub>100</sub><sup>b</sup></th></tr></thead><tbody><tr><td>GRB 151006A</td><td>459</td><td>&lt;84 (α = 0.05, β = 0.5)</td><td>...</td><td>...</td><td>4</td><td>0.32 (0.27)</td></tr><tr><td>GRB 160106A</td><td>950</td><td>69 ± 24</td><td>−23° ± 12°</td><td>108° ± 12°</td><td>4</td><td>0.23</td></tr><tr><td>GRB 160131A</td><td>724</td><td>94 ± 33</td><td>41° ± 5°</td><td>87° ± 5°</td><td>&lt;0.1</td><td>0.36</td></tr><tr><td>GRB 160325A</td><td>835</td><td>59 ± 28</td><td>11° ± 17°</td><td>158° ± 17°</td><td>5</td><td>0.24</td></tr><tr><td>GRB 160509A</td><td>460</td><td>&lt;92 (α = 0.05, β = 0.5)</td><td>...</td><td>...</td><td>3</td><td>0.29 (0.24)</td></tr><tr><td>GRB 160607A</td><td>447</td><td>&lt;77 (α = 0.05, β = 0.5)</td><td>...</td><td>...</td><td>11</td><td>0.32 (0.29)</td></tr><tr><td>GRB 160623A</td><td>1400</td><td>&lt;46 (α = 0.05, β = 0.5)<br/>&lt;57 (α = 0.01, β = 0.5)</td><td>...</td><td>...</td><td>49</td><td>0.25 (0.29)</td></tr><tr><td>GRB 160703A</td><td>448</td><td>&lt;55 (α = 0.05, β = 0.5)<br/>&lt;68 (α = 0.01, β = 0.5)</td><td>...</td><td>...</td><td>0.7</td><td>0.45 (0.41)</td></tr><tr><td>GRB 160802A</td><td>901</td><td>85 ± 30</td><td>−36° ± 5°</td><td>147° ± 5°</td><td>&lt;0.1</td><td>0.39</td></tr><tr><td>GRB 160821A</td><td>2549</td><td>54 ± 16</td><td>−39° ± 4°</td><td>25° ± 4°</td><td>&lt;0.1</td><td>0.42</td></tr><tr><td>GRB 160910A</td><td>832</td><td>94 ± 32</td><td>44° ± 4°</td><td>46° ± 4°</td><td>&lt;0.1</td><td>0.35</td></tr></tbody></table>

**Notes.**

for GRB 160821A is shown by the solid blue line in Figure 8 (right). The number of Compton events used to obtain the azimuthal distribution is ~2500. A clear modulation in the azimuthal distribution signifies that the GRB is highly polarized with a modulation amplitude (μ) around 0.229 ± 0.062 at an angle −39°08 ± 3°86 in the detector plane. The green dashed line is the simulated azimuthal distribution for 100% polarized radiation from GRB 160821A for the same observed polarization angle. The value of the modulation amplitude (μ<sub>100</sub>) is given in Table 2.

### 2.5.2. Estimation by MCMC Simulations

In this case the modulation amplitude, the polarization angle, and their uncertainties are estimated using an MCMC (Geyer 2011) method based on the Metropolis–Hastings algorithm (Hastings 1970; Chib & Greenberg 1995). The reason for following the approach of Bayesian statistics is the clarity in the fitting procedure and the robustness in the estimation of the parameter uncertainties compared to a χ² analysis, particularly for GRBs registering relatively fewer

Compton events. It is not correct to assume a Gaussian distribution to estimate errors on the polarization fraction and the polarization angle. Vaillancourt (2006), with the use of a Rice distribution to compute the polarization probability density, has shown that there is a significant departure from the Gaussian distribution for the low-significance measurements of polarization degree. This can be taken care of in the MCMC simulations to estimate the error on polarization fraction and angle properly. MCMC analysis also allows a comparison of the models, which is important in achieving a confirmation of the detection of polarization. Therefore, we follow the MCMC approach for estimating the modulation amplitude and the polarization angle and in particular their uncertainties. It is to be noted that Lowell et al. (2017) recently used an advanced method of likelihood analysis for the GRB detected by the COSI balloon flight (Chiu et al. 2015). They found better results with the new method than with the standard χ² fitting.

We perform MCMC simulations for a large number (1 million) of iterations. For each iteration, the likelihood is estimated based on randomly sampled parameter values in the

<footnote><sup>a</sup> α is the maximum allowed probability of false detection; β is the minimum probability of detection of polarization.</footnote>

<footnote><sup>b</sup> The bracketed values are the μ<sub>100</sub> values averaged over polarization angles 0°–45° in the CZTI plane.</footnote>
<figure><img src="image_12.png" /><figcaption>**Figure 9.** Left: evolution of the MCMC chain with iterations for GRB 160821A. The MCMC simulations are done with total of 1 million iterations. In the plot, we show the evolution for 1000 intermediate interpolated iterations. Right: posterior probability distribution of the fitting parameters *A*, *B*, and $\phi_0$ as obtained from MCMC iterations. We compute the uncertainties in the parameters by integrating the probability distribution for a desired confidence level.</figcaption></figure>

model of Equation (3). A set of parameter values for a given iteration is accepted or rejected by comparing the posterior probability for that iteration with that from the previous iteration (ratio of posterior probabilities should be greater than unity for accepting the parameter values). The posterior probabilities for those iterations with ratio less than unity are further compared to a random number before finally accepting or rejecting the parameter values. In this way, starting from a uniform distribution of the parameter values (*A*, *B*, $\phi_0$), we evaluate the posterior probability for these iterations. Figure 9 (left) shows the evolution of the chain with iterations. While the modulation factor and polarization angle are estimated from the best fitted values of the parameters (*A*, *B*, and $\phi_0$), uncertainties on them are computed from the distribution of the posterior probabilities of the parameters. Figure 9 (right) shows the posterior probability density for *A*, *B*, and $\phi_0$ for GRB 160821A.

Uncertainties on *A*, *B*, and $\phi_0$ are estimated by integrating the probability distribution function for the 68% (1σ) confidence level. The final uncertainty on $\mu$ is estimated by propagating the error on *A* and *B*. The MCMC method yields a modulation amplitude of 0.230 ± 0.066 and a polarization angle -39.16 ± 4.00, values that are similar to what we obtained from standard fitting. We compared the two methods for a couple of other bright (GRB 160131A and GRB 160910A) and faint (GRB 160607A and GRB 160703A) GRBs. For GRB 160131A, we find the best fit results for polarization fraction and angle to be 0.348 ± 0.104 and -42.7 ± 4.89 respectively from the curve fitting method, while the MCMC estimates of the same are 0.347 ± 0.116 and 41.20 ± 5.00. For GRB 160910A, curve fitting gives a modulation amplitude of 0.33 ± 0.10 and a polarization angle of -46.47 ± 4.24.

Similar values are also returned by the MCMC method: 0.328 ± 0.109 and 43.54 ± 4.00 respectively. We see that for bright GRBs, the two methods give similar results, in fitted parameters as well as in their associated errors. For fainter GRBs, we find that the MCMC method yields slightly higher uncertainty values than the curve fitting method. For example, for GRB 160607A, the results from the curve fitting method for modulation amplitude and polarization angle are 0.209 ± 0.203 and -42.17 ± 11.73 respectively, whereas from the MCMC method the corresponding estimates are 0.206 ± 0.2 and -42.14 ± 25.0. For the other faint burst, GRB 160703A, these values are found to be 0.376 ± 0.244 and 42.94 ± 7.38 from the curve fitting method, and 0.372 ± 0.256 and 42.19 ± 15.00 respectively from the MCMC method. The slightly larger errors estimated in the MCMC method result from the fact that MCMC explores a larger parameter space. Consequently, for fainter bursts, where the modulation amplitude and polarization angles are not strongly constrained, MCMC returns larger uncertainties.

For all the GRBs, we repeat the same procedure outlined above: namely to first filter the Compton events and then generate the raw azimuthal distribution, followed by the correction for pixel geometry and off-axis viewing angles of the GRBs. The corrected modulation curves are then fitted using the MCMC method to estimate the modulation amplitude, the polarization angle, and the associated uncertainties. The next step is to obtain the polarization fractions of the GRBs. Estimation of the polarization fraction requires measurement of modulation factor for 100% polarized radiation ($\mu_{100}$). In order to estimate $\mu_{100}$, we simulate the AstroSat mass model in Geant4 with a large number of polarized photons (10⁹) for the same off-axis viewing angles and photon energy
distribution of the GRBs. Chattopadhyay et al. (2014) show that $\mu_{100}$ strongly depends on the polarization angle and therefore it is important to estimate $\mu_{100}$ at the fitted polarization angles for the GRBs. This is done by interpolating in a table of $\mu_{100}$ values computed using Geant4 for a discrete grid of polarization angles. The uncertainty in the measured polarization angle introduces an error in $\mu_{100}$, which is propagated into the polarization fraction as

$$ \sigma_P = \frac{\mu}{\mu_{100}} \sqrt{\frac{\sigma_{\mu}^2}{\mu^2} + \frac{\sigma_{\mu_{100}}^2}{\mu_{100}^2}} \quad (4) $$

It is to be noted that the mass model simulations suggest that for off-axis photons the dependence of $\mu_{100}$ on the polarization angle is not as strong as in the case of on-axis photons. Apart from a few GRBs, the polarization angles in most cases have been constrained within 5°–10°, which makes this error negligible compared to the statistical error involved in the measurement of $\mu$. Details of the polarization fractions of the GRBs and the final uncertainties will be discussed in the next section.

As discussed earlier, the results from curve fitting and MCMC methods agree well for the bright GRBs, while for fainter GRBs the uncertainties estimated using the MCMC method are slightly higher. In order to investigate the error estimation further, we carried out Geant4 simulations for each of these bursts for a large number of cases ($10^4$) with the same number of observed Compton events and used this sample to estimate the true errors in $\mu$ and polarization angle. We then compared these error estimates with those obtained from MCMC. We found them to be in good agreement, with the uncertainties obtained from the MCMC method being slightly less than the true errors. This is because the Geant4 estimates include the variations caused by different realizations of photon propagation paths through the spacecraft structures. We incorporate these additional contributions in the final estimate of uncertainties for each burst, as described below.

Polarization measurements are often susceptible to systematic uncertainties and therefore it is important to take into account all possible sources of systematics for the final error estimations. Here we discuss the possible systematics involved in the polarization measurements with CZTI.

1. There can be additional uncertainty in $\mu$ due to the multiple possibilities of interaction of the incident GRB photons with the surrounding satellite structure. As mentioned above, we estimated this through multiple ($10^4$) Geant4 simulations for each burst. The resulting systematic error in $\mu$ is found to be around 8% for brighter GRBs (e.g., GRB 160821A) and around 11% for the moderately bright GRBs (e.g., GRB 160131A, GRB 160802A), while it can be as high as 20% for faint GRBs (e.g., GRB 160703A, GRB 160607A). Additional uncertainty in the polarization angle, on the other hand, is found to be negligible.

2. There can be systematics involved in the selection of background. To investigate this effect, we estimate the modulation amplitude taking both pre- and post-GRB background events independently as well as in combination. The estimated modulation factors and polarization angles are found to be within ~1% of each other.

3. Polarization analysis involves normalization of the observed azimuthal angle distribution with respect to

that for unpolarized radiation. The latter is obtained from Geant4 by simulating an unpolarized stream of photons incident at the off-axis viewing angle of the GRB. The localization of the GRB in the CZTI coordinate system is normally done based on the position provided by Swift/BAT or Fermi/GBM or from observations of X-ray afterglow whenever available. The BAT position is accurate to about 3' whereas the uncertainty in GBM localizations is around 3°.7 (Connaughton et al. 2015). To investigate the effect of the localization uncertainty (in CZTI coordinates) on the estimated modulation amplitude, we did Geant4 simulations for 1 billion photons (the statistical uncertainty is negligible) using the AstroSat mass model in a 5° × 5° region of the sky. We find the variation in modulation amplitude to be within 4% and that in polarization angle within 2.5%. Therefore for the GRBs localized from BAT position, we expect this contribution to the uncertainties of modulation amplitude and polarization angle to be extremely small, while they can be large (~5%) for those localized from GBM position. However, for the 11 GRBs discussed here, the localization uncertainties are small, <1° (see Table 1), contributing very little to the uncertainty in the derived polarization results.

4. We also investigate the dependence of the simulated azimuthal angle distribution on the model spectra. We did mass model simulations for GRB 160821A at the same off-axis angle but for different power-law spectra with index around the reported value. The dependence of the modulation amplitude on energy spectrum is found to be very weak, with ~1% variation in the azimuthal distribution.

5. The other possible systematics in the modulation amplitude is the unequal quantum efficiency of the CZTI pixels. However, since we search for GRB Compton events across the full CZTI plane, the relative quantum efficiencies of the pixels are expected to be averaged out to a large extent. The relative efficiency of the pixels varies only within 5%, which induces negligible false modulation amplitude.

Contributions from each of these sources are properly accounted for in the final estimation of uncertainties in polarization fraction and angle. As an example, for GRB 160821A, the statistical error on modulation amplitude obtained from MCMC analysis is ~0.066. With an additional 8% error introduced by scattering in the satellite structures, the final error on $\mu$ comes out to be ~0.068 by adding the MCMC fitting error and the additional error (8% of $\mu$) in quadrature. Contributions from other sources of uncertainties (e.g., selection of background, localization, GRB spectra, and relative quantum efficiency of the pixels) are negligible. Since the error in polarization angle for GRB 160821A is very small (~4°), the error in $\mu_{100}$ due to uncertainty in polarization angle turns out to be very small, which translates into a negligible contribution to the final error on modulation amplitude (see Equation (4)).

### 2.5.3. Calculation of Bayes Factor and Polarization Chance Probability

In spite of the significant modulations observed for the GRBs (see Figures 8 and 11), any claim on polarization detection requires further investigation of the probability of any unpolarized radiation
mimicking such modulations in the azimuthal angle distribution. This is important because the modulation amplitude is a positive definite quantity, and in particular we are dealing with a very small number of photons for most of the GRBs. We adopt the Bayesian paradigm to estimate such chance probability. We estimate the Bayes factor for the sinusoidal model (for polarized photons) and a constant model (unpolarized photons), where the Bayes factor is defined as the ratio of marginal likelihoods ($P(M|D)$) of the models: $B_{21} = \frac{P(M_1|D)}{P(M_2|D)} = \frac{P(D|M_1)}{P(D|M_2)}$, assuming equal prior probabilities for the models ($M_1$ and $M_2$). $P(D|M)$ or the likelihood function is computed by integrating the posterior probability over the parameter space. There are several methods available in the literature for evaluating the integrals. We have implemented the "Thermodynamic Integration" method (Lartillot & Philippe 2006; Calderhead & Girolami 2009) to compare these two models. This method allows the integration in the parameter space using MCMC. We perform MCMC for each model with $P(D|M, \theta)^3$ defined as the likelihood ($0 < \beta < 1$), at different $\beta$ values and finally integrate the posterior probabilities over $\beta$. The Bayes factor is eventually estimated from the ratio of the respective computed marginal likelihoods. The value of the Bayes factor, $\frac{P(D|M_{\text{pol}})}{P(D|M_{\text{unpol}})}$, required to conclusively favor the polarized model over unpolarized radiation mimicking the polarization signature is subjective, and sometimes a factor >3.2 is considered to be substantial proof in the literature (Kass & Raftery 1995). But in our analysis we have used a Bayes factor of 2 as the threshold for polarization measurements, i.e., that for GRBs with Bayes factor <2, we only estimate the upper limit of polarization.

To investigate this further, we estimate the probability of false polarization detection by simulating 100% unpolarized radiation in the Geant4 AstroSat mass model. We repeatedly simulate unpolarized photon streams a large number of times ($10^4$) with a varying number of Compton events and estimate the modulation amplitude following the same method as mentioned in Section 2.5. We define the false detection probability as the probability of the Bayes factor being ≥2 for an estimated modulation amplitude equal to or greater than a given value. Figure 10 shows the probability of false polarization detection as a function of detected modulation amplitude and the number of Compton events. The results shown here are obtained by simulating for off-axis viewing angle of GRB 160821A. We have repeated the analysis for other viewing angles and the results are found to be similar. We expect the number of Compton events to be ~300–4000 for bright GRBs in CZTI (~2500 for GRB 160821A) and therefore the simulations are done for Compton events in the range 300–4000. The false detection probability is found to be as large as ~20% for Compton events <500 for a detected modulation amplitude of 0.2. The plateau at lower modulation amplitudes (particularly for the smaller number of Compton events) implies that the number of false detections does not vary below a critical value of modulation amplitude. The plateau level increases for Bayes factors <2. For any true polarization detection in highly polarized GRBs, we expect the modulation amplitude to be greater than 0.2. The number of Compton events expected for moderately bright GRBs is around 700, which makes the false detection probability very small. It is to be noted that actual observed azimuthal angle distributions have larger errors due to the background subtraction. The simulated azimuthal distributions do not require any background subtraction and therefore have comparatively smaller error bars, because of which the Bayes

<figure><img src="image_13.png" /><figcaption>Figure 10. Probability of false polarization detection as a function of modulation amplitude and the number of detected Compton events. The false probability is defined as the probability of unpolarized radiation resulting in a modulation amplitude greater than a reference value with Bayes factor (sinusoidal to constant fit) greater than 2 (see text for details).</figcaption></figure>

factors are slightly overestimated. Therefore the false detection probabilities obtained here represent the worst-case scenario.

### 2.5.4. Calculation of Upper Limit of Polarization

Upper limits on polarization are estimated for GRBs for which the values of the Bayes factor are found to be less than 2. We estimate the upper limit following the method given in Kashyap et al. (2010). The calculations are done in two steps. The first step involves the estimation of polarization detection threshold, which we determine by limiting the probability of false detection, i.e.,

$$ \mathrm{Pr}(\mu > \mu_{\alpha}|P = 0, N_{\text{Compt}}, N_{\text{bkg}}, \mathrm{BF} > 2) \le \alpha, \quad (5) $$

where $\alpha$ is the maximum allowed probability of false detection, $P$ is the fraction of polarization, $N_{\text{Compt}}$ and $N_{\text{bkg}}$ are the observed numbers of Compton events and background events for a given burst respectively, and BF is the Bayes factor, the minimum value of which should be equal to 2 according to our chosen criteria. The false probability is estimated using Geant4 simulation of the AstroSat mass model for the observed Compton and background events for a given GRB with 100% unpolarized photons (as described in Section 2.5.3). We therefore estimate the modulation amplitude, $\mu_{\alpha}$, for the maximum allowed probability of a false detection ($\alpha$). This is called the $\alpha$-level detection threshold. In the next step, we calculate the probability of detection of polarization such that

$$ \mathrm{Pr}(\mu > \mu_{\alpha}|P > 0, N_{\text{Compt}}, N_{\text{bkg}}, \mathrm{BF} > 2) \ge \beta, \quad (6) $$

where $\beta$ is the minimum probability of detection. We simulate the GRB for the given number of source and background events with varying polarization fractions (from 0% to 100%) and estimate $\mathrm{Pr}(\mu > \mu_{\alpha})$ as a function of polarization fraction. The polarimetric sensitivity of CZTI depends on the polarization angle in the CZTI plane. Therefore, we simulate the polarized photons in Geant4 at a polarization angle of 22°5, which corresponds to $\mu_{100}$ averaged over the polarization angles 0°–45°. The polarization fraction ($P$) for which $\mathrm{Pr}(\mu > \mu_{\alpha})$ exceeds $\beta$ gives the upper limit of polarization. We use values of $\beta = 0.5$ in conjunction with $\alpha = 0.05$ or
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Geometrically corrected modulation curves (similar to the right panel of Figure 8) for the remaining 10 GRBs. The blue solid line is the sinusoidal fit to the modulation curve, while the green dashed line is the simulated azimuthal distribution for 100% polarized radiation for the same observed polarization angle. Values of modulation factor and polarization angle shown within the figure are obtained from MCMC simulations. The uncertainties are obtained for one parameter of interest at the 68% confidence level.</figcaption></figure>
0.01 to estimate the upper limit. It is to be noted that $\beta = 0.5$ actually corresponds to the $\alpha$-level detection threshold if we assume that the sampling distribution of the estimated modulation amplitude follows smooth Gaussian statistics with median equal to $P$ (Kashyap et al. 2010). A higher value of $\beta$ would correspond to a higher upper limit of polarization.

### 3. Results

Figure 11 shows the modulation curves for the remaining 10 GRBs. The modulation curves are obtained in the energy range ~100–300 keV. We see a clear polarization signature in most of the GRBs, while for a few GRBs the lack of a sufficient number of photons leads to a large uncertainty in the estimated modulation amplitude and the polarization angle. The fitted values of the modulation amplitudes and polarization angles are given in the text inside the figures along with the estimated uncertainties. The green dashed lines are the simulated modulation for 100% polarized radiation for the GRBs at the observed polarization angles. Except for GRB 160325A and GRB 160802A, all the GRBs manifest a single broad pulse. These two GRBs show two clear pulses in their light curves. The modulation curves shown here are for the combined Compton events from both peaks in order to enhance the signal-to-noise ratio. However, we have seen no significant change in the modulation amplitudes and polarization angles across the pulses in both the GRBs. It is to be noted that previously we presented polarization analysis for GRB 151006A in Rao et al. (2016). The analysis was done without the use of a detailed AstroSat mass model. With the implementation of the mass model the new result is more accurate and the estimated modulation amplitude is slightly less than that reported earlier. It is to be noted that we do not see any significant modulation for GRB 160623A in the full energy range of 100–300 keV. The modulation amplitude is estimated to be low with large uncertainties on both modulation amplitude and polarization angle, signifying that the radiation is unpolarized or has low polarization in the 100–300 keV band. Interestingly, at energies below 200 keV, we find significant modulation in the azimuthal angle distribution for GRB 160623A. This is either due to a change in the polarization angle or the unpolarized nature of the radiation at higher energies, which leads to a net low polarization in the full 100–300 keV band. Currently, it is not possible to distinguish these two scenarios due to poor statistics at higher energies.

Figure 12 shows the estimated Bayes factors for the GRBs. We obtain high values of Bayes factor for six GRBs, for which we can definitely claim the detection of polarization. GRB 151006A, GRB 160509A, and GRB 160703A have Bayes factor slightly higher than 1; therefore the possibility that these GRBs are unpolarized cannot be completely ruled out. The probabilities of GRB 160607A and GRB 160623A being unpolarized are high as shown in Figure 12. For the GRBs with Bayes factors $\le 2$, we estimate the upper limit of polarization as discussed earlier. Figure 13 shows the estimated polarization fractions and the contours for 68% (red), 90% (green), and 99% (blue) confidence levels estimated from MCMC simulations. For GRB 151006A, GRB 160509A, GRB 160607A, GRB 160623A, and GRB 160703A, we see that the polarization fractions and angles are hardly constrained. This is consistent with the fact that Bayes factors for these bursts are <2, indicating that these GRBs are either intrinsically unpolarized or the degree of polarization is below the polarimetric

<figure><img src="image_15.png" /><figcaption>Figure 12. Bayes factors for the polarized model (sinusoidal fit) to the unpolarized (constant fit) for all the GRBs. The Bayes factors are estimated using combined MCMC and “Thermodynamic Integration” methods (see text for details). For bursts with Bayes factor less than 2, we estimate the upper limit of polarization (shown in red).</figcaption></figure>

sensitivity of the instrument. We estimate the upper limits of polarization for these GRBs following the method described in Section 2.5.4 for $\alpha = 0.05$ and $0.01$ with $\beta = 0.5$. The derived polarization fractions and angles for the GRBs with Bayes factor $>2$ along with the estimated uncertainties (for one parameter of interest with 68% confidence level) are given in Table 2. The uncertainties on the polarization fraction reported here are estimated after incorporating the systematic errors as discussed in Section 2.5. Polarization fraction is estimated by normalizing the estimated modulation amplitude with $\mu_{100}$. We estimate $\mu_{100}$ from the Geant4 simulations of the AstroSat mass model. $\mu_{100}$ depends on the energy of the photons, polarization angle, and the incident direction. Chattopadhyay et al. (2014) describe the dependence of $\mu_{100}$ on photon energy and polarization angle for on-axis sources. Higher values of $\mu_{100}$ are expected when the polarization is along the corner pixels, whereas $\mu_{100}$ is low when it is aligned along the edge pixels. For off-axis angles, we find that the dependence of $\mu_{100}$ on polarization angle is not as significant as for on-axis sources. $\mu_{100}$, however, strongly depends on the incident direction of the photons. For larger off-axis angles, the value of $\mu_{100}$ is found to be lower than for smaller off-axis angles. In order to take these effects into account, we estimate $\mu_{100}$ by simulating the same GRB spectra at the same viewing angle for the observed polarization angle. Values of $\mu_{100}$ for the 11 bursts are given in Table 2 with the azimuthal distributions shown in Figure 11.

For estimations of the upper limit, we use $\mu_{100}$ values averaged over polarization angles $0^\circ-45^\circ$ (given inside the brackets in Table 2). It is to be noted that the estimated polarization angles in the CZTI plane for the GRBs lie between $-45^\circ$ and $+45^\circ$. In order to make sure that this is not because of any systematic effect causing a preferred polarization direction in detector coordinates, we did multiple cross-checks by analyzing the GRBs in different energy ranges and time intervals. We find the results to be consistent with what is reported here. We also note that the sky polarization angles (after converting the polarization angles in the CZTI plane to the sky frame) as shown in the fifth column are randomly oriented in the full angle space of $0^\circ-180^\circ$ as expected for a
<figure><img src="image_16.png" /><figcaption>**Figure 13.** Contour plots of polarization angle and fraction for all the GRBs as obtained from the MCMC method. The red, green, and blue areas represent the 68%, 90%, and 99% confidence levels respectively (two parameters of interest, polarization fraction and polarization angle).</figcaption></figure>

large sample. The sixth column shows the estimated probabilities of false polarization detection for the bursts. False detection probabilities are estimated from the modulation amplitudes and Bayes factors of the bursts as described in Section 2.5.3. False probabilities are found to be negligible for the GRBs that are bright and have significant detection of modulation. We see that most of the GRBs are highly polarized, corroborating earlier reports for a few GRBs from RHESSI, INTEGRAL, and GAP. For GRB 160106A, GRB 160131A, GRB 160802A, GRB 160821A, and GRB 160910A, the polarization fractions are estimated with ≳3σ detection

significance (for one parameter of interest at 68% confidence level). On the other hand for GRB 160325A, polarization fraction is constrained within ~2.2σ significance. It is to be noted that the uncertainties quoted in Table 2 are obtained at the 68% confidence level for only one parameter of interest, that is by looking only at the variation in the azimuthal angle distribution rather than the measurement of both polarization fraction and angle simultaneously. The latter is resorted to while determining the contours presented in Figure 13. The estimated errors differ in these two methods. The chance probability is also estimated from the variation in the azimuthal
<table><caption>**Table 3**
Parameters of GRB Jets Derived from Observed Prompt and Afterglow Properties</caption><thead><tr><th>GRB</th><th>Redshift (z)</th><th>E<sub>γ,iso,52</sub><br>(erg)</th><th>Lorentz Factor (Γ<sub>0</sub>)</th><th>Jet Opening Angle (θ<sub>j</sub>)<br>(deg)</th><th>θ<sub>j</sub>Γ<sub>0</sub></th><th>E<sub>γ,j,50</sub><br>(erg)</th></tr></thead><tbody><tr><td>160131A</td><td>0.972<sup>a</sup></td><td>~40</td><td>459<sup>+54</sup><sub>-49</sub></td><td>3<sup>+3</sup><sub>-1.8</sub></td><td>25</td><td>60<sup>+18</sup><sub>-5</sub></td></tr><tr><td>160509A</td><td>1.17<sup>b</sup></td><td>250</td><td>724<sup>+130</sup><sub>-111</sub></td><td>4.0<sup>+4.3</sup><sub>-2.3</sub></td><td>51</td><td>63<sup>+203</sup><sub>-51</sub></td></tr><tr><td>160623A</td><td>0.367<sup>c</sup></td><td>8.5</td><td>311<sup>+21</sup><sub>-19</sub></td><td>6<sup>+4</sup><sub>-3</sub></td><td>32</td><td>5</td></tr></tbody></table>

**Notes.**

a Ugarte et al. (2016) (GCN 18966).

b Tanvir et al. (2016) (GCN 19419).

c Malesani et al. (2016) (GCN 19708).

angle distribution for unpolarized radiation. Since upper limits are estimated from these chance probabilities, we still obtain meaningful upper limits on the degree of polarization for certain bursts even though the polarization fractions are unconstrained at the 68% level.

## 4. Discussions and Conclusions

In the fireball scenario (Piran 2004; Mészáros 2006), interaction of highly relativistic material within the jet causes the prompt emission, whereas the interaction of the jet with the ambient medium leads to the afterglow phase. 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 of such high-energy radiation are inverse Compton scattering, blackbody radiation, and sometimes a mixture of all these processes. The time-integrated high polarization observed in many GRBs so far (as shown in this work and the previously reported GRBs) demands the magnetic field to be uniform and time-independent (Granot & Königl 2003; Nakar et al. 2003; Waxman 2003) if the emission is of synchrotron origin. Both conditions are satisfied if we assume a toroidal magnetic field geometry at large distances from the compact object where the radiation is emitted. This requires the field to be generated very close to the compact object and then carried by the wind, which could be either dominated by Poynting flux, converting the field energy to the kinetic energy of electrons (Lyutikov et al. 2003) or dominated by the plasma particle density, where the particle energy is dissipated to the energy of the electrons. High polarization (~40%-70%) can be achieved even from a random magnetic field generated in the shock plane itself, if the jet is narrow (Γθ<sub>j</sub> ~ 1, where θ<sub>j</sub> is the jet opening angle and Γ is the bulk Lorentz factor of the jet) and viewed along the edge (Medvedev 2007), or from jitter radiation by turbulence-accelerated electrons in a planar magnetic field as recently shown by Mao & Wang (2013, 2017).

Lazzati et al. (2004) demonstrated that inverse Compton emission from relativistic electrons in a jet propagating within an external photon field (Shaviv & Dar 1995) can result in high observed polarization (60%-100%) if the jet is narrow and is observed along the edge similar to the case of a random magnetic field. The possibility of such a geometric configuration favorable for high polarization is relatively small for both the Compton drag model and the random synchrotron radiation model. GRBs without such favorable viewing geometry are expected to be unpolarized according to the geometric models. Gill et al. (2018) discuss these proposed radiation mechanisms and the expected levels of linear polarization for various jet geometries, viewing angles, magnetic field structures, and

spectral parameters. In our analysis, GRB 160623A is found to have low modulation with large errors in both polarization fraction and angle, suggesting that the burst has low or no polarization. On the other hand, we see that most of the GRBs are nominally highly polarized (>70%), which apparently favors the Compton drag model. This can be further verified by investigating Γθ<sub>j</sub> and the view angle condition for the Compton drag model. We try to test the Γθ<sub>j</sub> condition for the GRBs with known redshifts (GRB 160131A, GRB 160509A, and GRB 160623A). The isotropic energy E<sub>γ,iso</sub> in the γ-ray band is found by integrating the time-integrated spectra over the energy range 1 keV–10 MeV. The cosmological parameters chosen were Ω<sub>λ</sub> = 0.73, Ω<sub>m</sub> = 0.27, and H<sub>0</sub> = 70 km s<sup>-1</sup> Mpc<sup>-1</sup> (Komatsu et al. 2009). We can find bulk Lorentz factors of the jetted emission from the prompt and the afterglow properties by several methods (Wang et al. 2017). We relied here on the E<sub>iso</sub>–Γ<sub>0</sub> correlation (Liang et al. 2010). The Lorentz factor decays during the afterglow phase, so we derived it from a prompt emission correlation. The initial Lorentz factor Γ<sub>0</sub> is constrained from the limits in the normalization and slope of the correlation. From Γ<sub>0</sub> we found the beaming angle of the emission (~1/Γ<sub>0</sub>). The jet half-opening angles are calculated from the jet breaks observed in Swift/XRT X-ray light curves<sup>18</sup> (Sari 1999; Frail et al. 2001). The limits on θ<sub>j</sub> are set by selecting the radiation efficiency and the circumburst density (η, n (cm<sup>-3</sup>)) in the range between (0.1, 0.001) and (0.9, 10). We could thus find the collimation-corrected emission energy of the bursts E<sub>j</sub> = E<sub>iso</sub>(1 – cosθ<sub>j</sub>). The calculated values for these GRBs are given in Table 3. Such estimates for a large number of GRBs with polarization measurements would be very useful for a detailed understanding of the GRB prompt emission. For the remaining GRBs with no redshift measurements, we plan to use the Yonetoku correlation (Yonetoku et al. 2004) to estimate the redshifts of the bursts. The Lorentz factor (Γ<sub>0</sub>) can be calculated in the same way by making use of the E<sub>iso</sub>–Γ<sub>0</sub> correlation. We plan to estimate the jet breaks and thereby the jet opening angles from the available afterglow measurements. However, given the uncertainties associated with these correlations and those in the measured polarization fractions, it is difficult to constrain any of these models for the bursts individually. Alternatively, statistical analysis of the prompt emission polarization for a very large sample of GRBs is expected to give a better insight into the mechanisms behind the prompt emission (Toma et al. 2009). In Figure 14 we show the estimated polarization fractions of the GRBs as a function of their peak energies (E<sub>peak</sub>). For the GRBs detected only in BAT, we use the E<sub>peak</sub> values estimated from Konus/Wind

<footnote n="18"><sup>18</sup> http://www.swift.ac.uk/xrt_curves/</footnote>
<figure><img src="image_17.png" /><figcaption>**Figure 14.** Polarization fraction as a function of peak energies, $E_{\text{peak}}$, for the GRBs for which polarizations have been estimated. The black points represent the GRBs detected by CZTI (see Table 2), while the red points stand for those detected by GAP, *INTEGRAL*, and COSI. The blue dots and upper limits are the polarization degree and polarization upper limits (99%) for the five GRBs detected by POLAR (see text for details).</figcaption></figure>

time-integrated data (see Table 1). The black data points refer to the bursts studied in this work while the blue points represent the measurements for GRB 161218A, GRB 170101A, GRB 170127C, GRB 170206A, GRB 170114A by POLAR (Zhang et al. 2019). The 99% upper limits are also shown for these GRBs. The red points stand for GRB 100826A, GRB 110301A, GRB 110721A by GAP (Yonetoku et al. 2011, 2012), GRB 160530A by COSI (Lowell et al. 2017), and GRB 041219A by IBIS on board *INTEGRAL* (Götz et al. 2009). The recent POLAR results indicate that GRBs are in general weakly polarized, perhaps due to the evolution of polarization angle across the burst (Zhang et al. 2019). In our results, we find most of the GRBs to be highly polarized. In this respect, a bigger sample of GRB polarization measurements in future will be interesting. However, it is to be noted that we optimize the selection of energy and GRB regions slightly in order to get best detection of polarization (see Figure 2). For example, GRB 160821A shows a change in polarization angle from the initial few seconds to the peak region of the burst (selected here for polarization analysis), giving rise to a net zero polarization (Sharma et al. 2019). GRB 171010A also shows a change in PA across the burst (Chand et al. 2019). On the other hand, from energy-resolved analysis of GRB 1710101A (Chand et al. 2019) and GRB 160802A (Chand et al. 2018), we also note that polarization properties seem to change across the peak energy of the bursts, which yields an unpolarized distribution when the individual distributions are integrated over the energies. For all the GRBs reported here except GRB 160607A, we note that the peak energies are beyond the CZTI sensitivity range. It is interesting to note that four out of the five GRBs in Zhang et al. (2019) have peak energies in the POLAR energy range of analysis (80–500 keV). However, any concrete conclusion requires a bigger sample of polarization measurements. Given the lifetime of *AstroSat* of at least five years, CZTI is expected to detect polarization for a large sample of GRBs (>60). We also plan to include the low-gain pixels in the polarization analysis (shown in the Compton spectrum of GRB 160821A) in order to extend the energy range to 600 keV or more, which will enable us to investigate the changes in polarization properties with peak energy in addition to the enhanced sensitivity because of slightly larger

collecting area. CZTI polarimetry measurements are therefore expected to provide critical inputs to distinguish the prompt emission models.

Though synchrotron emission is widely believed to be the dominant emission mechanism behind prompt emission of GRBs, the inverse Compton scattering process and thermal emission from an expanding photosphere also appear to be important in many GRBs (Lundman et al. 2014). A potential way to distinguish these various models is by investigating the dependence of polarization on the spectral and time evolution of the GRBs. A detailed spectropolarimetric study is currently in progress for all the GRBs reported here. The preliminary spectral analysis shows a deviation from the Band model and the need for an additional thermal blackbody to model the spectrum more precisely for four GRBs (160106A, 160509A, 160802A, and 160910A). The GRBs 160106A, 160509A, and 160910A are peculiar because the required blackbody component attains a temperature higher than the peak energy ($E_{\text{peak}}$) of these GRBs. We have nine GRBs with afterglow observations and seven of these have both optical and X-ray afterglows. Among them, five GRBs also have radio afterglows. A multi-band spectral and timing analysis of the prompt and afterglows emissions together with the polarization measurements can reveal more about the physics of these sources (Troja et al. 2017).

## 5. Summary

This work describes the polarimetric analysis method for GRBs using the CZTI instrument of *AstroSat* and presents the polarization measurements of prompt emission for 11 bright GRBs detected during the first year of operation of CZTI. A good polarization measurement in hard X-rays is very difficult for two reasons: first, the measurements are prone to high systematic errors, and second, the measurement itself is of an extreme photon-starved nature. For the measurement of the polarization of the prompt emission of GRBs, both these aspects are significantly amplified due to the short duration of the prompt emission and the unknown position of the GRBs. These aspects are evident from the fact that, despite multiple efforts for more than a decade and a half, there has not been any firm detection of polarization apart from a few measurements made by POLAR (Zhang et al. 2019) and GAP (Yonetoku et al. 2011, 2012). In most cases (about 10 GRBs), only some hints of polarization have been reported (RHESSI, Coburn & Boggs 2003; IBIS, Götz et al. 2013, 2014; SPI, McGlynn et al. 2007, 2009; Kalemci et al. 2007; BATSE, Willis et al. 2005; AstroSat, Rao et al. 2016; Basak et al. 2017; Chand et al. 2018, 2019; see review by McConnell 2017) and in many cases the measurements are of not very high significance.

In this context, the present work is of considerable significance because it has almost doubled the number of GRBs with measured polarization in its first year of operation. Similar measurements have been carried out for a number of additional GRBs and will be reported later. It is to be noted that POLAR stopped operating in 2017 and there are currently no GRB polarimetric mission scheduled in the near future. This makes the measurements from CZTI even more important.

An important point to note here is that the results presented here (or GRB polarization measurements with CZTI in general) critically depend on the simulation for unpolarized and polarized radiation through the *AstroSat* satellite. For this purpose, we have made the *AstroSat* mass model, painstakingly
collecting the details of all the parts and materials that have gone into making the satellite. This is implemented in the Geant4 code and the resultant products (DPH, spectra, localization) are shown to agree quite well with the real data. The residual systematics from the mass model might contribute toward the estimation of $\mu_{100}$ but it may not have a significant effect on the detection of polarization. For the GRBs with detected polarization, additional confirmation can come from comparing the polarization properties with the other observables of GRBs. We have already started this exercise (Chand et al. 2018, 2019; Sharma et al. 2019).

We find most of the bursts to be highly polarized, implying either synchrotron emission in a time-independent ordered magnetic field or Compton drag as the mechanism for the prompt emission. However, in order to draw such “firm” conclusions, it is necessary to have a much larger sample. Given the fact that most of the GRBs in the present sample are moderately bright, CZTI is expected to continue GRB polarization measurements at a similar rate for several years to come. The availability of a large number of such measurements from CZTI is likely to significantly enhance our understanding of GRB prompt emission.

This publication uses data from the AstroSat mission of the Indian Space Research Organization (ISRO), archived at the Indian Space Science Data Centre (ISSDC). The CZT Imager is built by a consortium of Institutes across India including Tata Institute of Fundamental Research, Mumbai, Vikram Sarabhai Space Centre, Thiruvananthapuram, ISRO Satellite Centre, Bengaluru, Inter University Centre for Astronomy and Astrophysics, Pune, Physical Research Laboratory, Ahmedabad, Space Application Centre, Ahmedabad: contributions from the vast technical team from all these institutes are gratefully acknowledged. T.C. is thankful for the helpful discussions with D. N. Burrows (PSU), P. Meszaros (PSU), D. Fox (PSU), K. Frank (PSU), C. B. Markward (NASA/GSFC), V. Kashyap (Harvard), and Carson Chow (UPenn). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 664931. This research has also made use of data obtained through the High Energy Astrophysics Data Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center.

## ORCID iDs

Tanmoy Chattopadhyay https://orcid.org/0000-0001-9856-1866

Santosh V. Vadawale https://orcid.org/0000-0002-2050-0913

Rupal Basak https://orcid.org/0000-0001-5488-7258

A. R. Rao https://orcid.org/0000-0003-0833-0533

Varun Bhalerao https://orcid.org/0000-0002-6112-7609

V. Sharma https://orcid.org/0000-0002-4394-4138

## References

Agostinelli, S., Allison, J., Amako, K., et al. 2003, NIMPA, 506, 250

Band, D., Matteson, J., Ford, L., et al. 1993, ApJ, 413, 281

Barthelmy, S. D., Barbier, L. M., Cummings, J. R., et al. 2005, SSRv, 120, 143

Basak, R., Iyyani, S., Chand, V., et al. 2017, MNRAS, 472, 891

Basak, R., & Rao, A. R. 2015, ApJ, 807, 34

Bhalerao, V., Bhattacharya, D., Rao, A. R., & Vadawale, S. 2015, GCN, 18422, 1

Bhalerao, V., Bhattacharya, D., Vibhute, A., et al. 2017, JApA, 38, 31

Calderhead, B., & Girolami, M. 2009, Computational Statistics and Data Analysis, 53, 4028

Chand, V., Chattopadhyay, T., Iyyani, S., et al. 2018, ApJ, 862, 154

Chand, V., Chattopadhyay, T., Oganesyan, G., et al. 2019, ApJ, 874, 70

Chattopadhyay, T., Vadawale, S. V., Rao, A. R., Sreekumar, S., & Bhattacharya, D. 2014, E&A, 37, 555

Chattopadhyay, T., Vadawale, S. V., Rao, A. R., et al. 2016, Proc. SPIE, 9905, 99054D

Chib, S., & Greenberg, E. 1995, The American Statistician, 49, 327

Chiu, J.-L., Boggs, S. E., Chang, H.-K., et al. 2015, NIMPA, 784, 359

Coburn, W., & Boggs, S. E. 2003, Natur, 423, 415

Connaughton, V., Briggs, M. S., Goldstein, A., et al. 2015, ApJS, 216, 32

Covino, S., & Gotz, D. 2016, A&AT, 29, 205

Eichler, D., Livio, M., Piran, T., & Schramm, D. N. 1989, Natur, 340, 126

Frail, D. A., Kulkarni, S. R., Sari, R., et al. 2001, ApJL, 562, L55

Frederiks, D., Golenetskii, S., Aptekar, R., et al. 2016a, GCN, 19649, 1

Frederiks, D., Golenetskii, S., Aptekar, R., et al. 2016b, GCN, 19554, 1

Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ, 611, 1005

Gehrels, N., & Mészáros, P. 2012, Sci, 337, 932

Geyer, C. J. 2011, Handbook of Markov Chain Monte Carlo (London, Boca Raton, FL: Chapman and Hall/CRC Press), 3

Ghisellini, G., & Celotti, A. 1999, ApJL, 511, L93

Ghisellini, G., Lazzati, D., Celotti, A., & Rees, M. J. 2000, MNRAS, 316, L45

Gill, R., Granot, J., & Kumar, P. 2018, arXiv:1811.11555

Götz, D., Covino, S., Fernández-Soto, A., Laurent, P., & Bošnjak, Ž 2013, MNRAS, 431, 3550

Götz, D., Laurent, P., Antier, S., et al. 2014, MNRAS, 444, 2776

Götz, D., Laurent, P., Lebrun, F., Daigne, F., & Bošnjak, Ž 2009, ApJL, 695, L208

Granot, J., & Königl, A. 2003, ApJL, 594, L83

Hakkila, J., & Preece, R. D. 2014, ApJ, 783, 88

Hastings, W. K. 1970, Biometrika, 57, 97

Iwamoto, K., Mazzali, P. A., Nomoto, K., et al. 1998, Natur, 395, 672

Iyyani, S., Ryde, F., Ahlgren, B., et al. 2015, MNRAS, 450, 1651

Kaaret, P. 2014, arXiv:1408.5899

Kalemci, E., Boggs, S. E., Kouveliotou, C., Finger, M., & Baring, M. G. 2007, ApJ, 169, 75

Kashyap, V. L., van Dyk, D. A., Connors, A., et al. 2010, ApJ, 719, 900

Kass, R. E., & Raftery, A. E. 1995, J. Am. Stat. Assoc., 90, 773

Komatsu, E., Dunkley, J., Nolta, M. R., et al. 2009, ApJS, 180, 330

Kumar, P., & Zhang, B. 2015, PhR, 561, 1

Lartillot, N., & Philippe, H. 2006, Systematic Biology, 55, 195

Lazzati, D., Rossi, E., Ghisellini, G., & Rees, M. J. 2004, MNRAS, 347, L1

Lei, F., Dean, A. J., & Hills, G. L. 1997, SSRv, 82, 309

Liang, E.-W., Yi, S.-X., Zhang, J., et al. 2010, ApJ, 725, 2209

Lowell, A. W., Boggs, S. E., Chiu, C. L., et al. 2017, ApJ, 848, 120

Lundman, C., Pe'er, A., & Ryde, F. 2014, MNRAS, 440, 3292

Lyutikov, M., Pariev, V. I., & Blandford, R. D. 2003, ApJ, 597, 998

MacFadyen, A. I., & Woosley, S. E. 1999, ApJ, 524, 262

Malesani, D., de Ugarte Postigo, A., Pasquale, M., et al. 2016, GCN, 19708

Mao, J., & Wang, J. 2013, ApJ, 776, 17

Mao, J., & Wang, J. 2017, ApJ, 838, 78

McConnell, M. L. 2017, NewAR, 76, 1

McGlynn, S., Clark, D. J., Dean, A. J., et al. 2007, A&A, 466, 895

McGlynn, S., Foley, S., McBreen, B., et al. 2009, A&A, 499, 465

Medvedev, M. V. 2007, Ap&SS, 307, 245

Meegan, C., Lichti, G., Bhat, P. N., et al. 2009, ApJ, 702, 791

Mészáros, P. 2006, RPPH, 69, 2259

Meszaros, P., & Rees, M. J. 1993, ApJ, 405, 278

Nakar, E., Piran, T., & Waxman, E. 2003, JCAP, 10, 005

Narayan, R., Paczynski, B., & Piran, T. 1992, ApJL, 395, L83

Orsi, S. & Polar Collaboration 2011, ASTRA, 7, 43

Pe'er, A., & Ryde, F. 2011, ApJ, 732, 49

Piran, T. 2004, RvMP, 76, 1143

Poole, C. M., Cornelius, I., Trapp, J. V., & Langton, C. M. 2012, Australas. Phys. Eng. Sci. Med., 35, 329

Rao, A. R., Chand, V., Hingar, M. K., et al. 2016, ApJ, 833, 86

Rees, M. J., & Meszaros, P. 1994, ApJL, 430, L93

Rutledge, R. E., & Fox, D. B. 2004, MNRAS, 350, 1288

Ryde, F. 2004, ApJ, 614, 827

Sari, R. 1999, ApJL, 524, L43

Sari, R., Piran, T., & Narayan, R. 1998, ApJL, 497, L17

Sharma, V., Iyyani, S., Bhattacharya, D., et al. 2019, ApJL, 882, L10

Shaviv, N. J., & Dar, A. 1995, ApJ, 447, 863

Singh, K. P., Tandon, S. N., Agrawal, P. C., et al. 2014, Proc. SPIE, 9144
Sun, J. C., Wu, B. B., Bao, T. W., et al. 2016, Proc. SPIE, 9905, 99052P

Tanvir, N. R., Levan, A. J., Cenko, S. B., et al. 2016, GCN, 19419, 1

Toma, K., Sakamoto, T., Zhang, B., et al. 2009, ApJ, 698, 1042

Troja, E., Lipunov, V. M., Mundell, C. G., et al. 2017, Natur, 547, 425

Tsvetkova, A., Golenetskii, S., Aptekar, R., et al. 2016a, GCN, 18974, 1

Tsvetkova, A., Golenetskii, S., Aptekar, R., et al. 2016b, GCN, 19511, 1

Ugarte, A. D., Thoene, C. C., Sanchez-Ramirez, R., Velarde, G. G., & Herrera, V. 2016, GCN, 18966, 1

Vadawale, S. V., Chattopadhyay, T., Mithun, N. P. S., et al. 2018, NatAs, 2, 50

Vadawale, S. V., Chattopadhyay, T., Rao, A. R., et al. 2015, A&A, 578, 73

Vadawale, S. V., Rao, A. R., Bhattacharya, D., et al. 2016, Proc. SPIE, 9905, 99051G

Vaillancourt, J. E. 2006, PASP, 118, 1340

Wang, Y.-Z., Wang, H., Zhang, S., et al. 2017, ApJ, 836, 81

Waxman, E. 2003, Natur, 423, 388

Wigger, C., Hajdas, W., Arzner, K., Güdel, M., & Zehnder, A. 2004, ApJ, 613, 1088

Willis, D. R., Barlow, E. J., Bird, A. J., et al. 2005, A&A, 439, 245

Woosley, S. E. 1993, ApJ, 405, 273

Yonetoku, D., Murakami, T., Gunji, S., et al. 2011, ApJL, 743, L30

Yonetoku, D., Murakami, T., Gunji, S., et al. 2012, ApJL, 758, L1

Yonetoku, D., Murakami, T., Masui, H., et al. 2006, Proc. SPIE, 6266

Yonetoku, D., Murakami, T., Nakamura, T., et al. 2004, ApJ, 609, 935

Zhang, S.-N., Kole, M., Bao, T.-W., et al. 2019, NatAs, 3, 258