# Violation of synchrotron line of death by the highly polarized GRB 160802A

Vikas Chand  Tata Institute of Fundamental Research, Mumbai, India  Tanmoy
Chattopadhyay  Pennsylvania State University, State College, PA, USA  S.
Iyyani  The Inter-University Centre for Astronomy and Astrophysics, Pune,
India  Rupal Basak  The Oskar Klein Centre for Cosmoparticle Physics,
AlbaNova, SE-106 91 Stockholm, Sweden; Department of Physics, KTH Royal
Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm,
Sweden  Aarthy, E  Physical Research Laboratory, Ahmedabad, Gujarat, India  A.
R. Rao  Tata Institute of Fundamental Research, Mumbai, India  Santosh V.
Vadawale  Physical Research Laboratory, Ahmedabad, Gujarat, India  Dipankar
Bhattacharya  The Inter-University Centre for Astronomy and Astrophysics,
Pune, India  V. B. Bhalerao  Indian Institute of Technology, Bombay, India

###### Abstract

GRB 160802A is one of the brightest gamma-ray bursts (GRBs) observed with
Fermi Gamma-ray Burst Monitor (GBM) in the energy range of 10–1000 keV, while
at the same time it is surprisingly faint at energies $\gtrsim 2$ MeV. An
observation with AstroSat/CZT Imager (CZTI) also provides the polarisation
which helps in constraining different prompt emission models using the novel
joint spectra-polarimetric data. We analyze the Fermi/GBM data, and find two
main bursting episodes that are clearly separated in time, one particularly
faint in higher energies and having certain differences in their spectra. The
spectrum in general shows a hard-to-soft evolution in both the episodes. Only
the later part of the first episode shows intensity tracking behaviour
corresponding to multiple pulses. The photon index of the spectrum is hard,
and in over 90 per cent cases, cross even the slow cooling limit
($\alpha=-2/3$) of an optically thin synchrotron shock model (SSM). Though
such hard values are generally associated with a sub-dominant thermal
emission, such a component is not statistically required in our analysis. In
addition, the measured polarisation in 100–300 keV is too high, $\pi=85\pm
29\%$, to be accommodated in such a scenario. Jitter radiation, which allows a
much harder index up to $\alpha=+0.5$, in principle can produce high
polarisation but only beyond the spectral peak, which in our case lies close
to 200–300 keV during the time when most of the polarisation signal is
obtained. The spectro-polarimetric data seems to be consistent with a
subphotospheric dissipation process occurring within a narrow jet with a sharp
drop in emissivity beyond the jet edge, and viewed along its boundary.

gamma-ray burst: general – gamma-ray burst: individual (GRB160802A) –
polarization – radiation mechanisms: non-thermal

##  1 Introduction

One of the putative models invoked to explain the non-thermal spectral shape
in the prompt emission of gamma-ray bursts (GRB) is the synchrotron shock
model (SSM). In this model, electrons gyrating in the magnetic field at
internal shocks generate synchrotron photons that are observed at gamma ray
energies, boosted by the relativistic bulk motion of the jet (Rees & Meszaros
1992, Meszaros & Rees 1993, Rees & Meszaros 1994). One of the predictions of
the SSM is the so-called “synchrotron line of death (LOD)”. The low energy
photon spectral index should not exceed the value $-2/3$ for an optically thin
shocked material. If the effects of the synchrotron cooling are also taken
into consideration (Katz 1994, Sari et al. 1996, Sari & Piran 1997), then the
index can lie in the range of -3/2 to -2/3. The distribution of the indices
was, however, found to violate these limits (Cohen et al. 1997, Crider et al.
1997, Preece et al. 1998, Ghirlanda et al. 2003).

The measurement of the low energy spectral index, however, depends on the
spectral modelling of the GRB prompt emission. For most of the GRBs the shape
of the spectrum could be phenomenologically well described by a Band function
(Band et al., 1993), which consists of two smoothly joined power law
functions. The model parameters are low and high energy indices ($\alpha$ and
$\beta$), the energy where the $\nu F_{\nu}$ spectrum peaks ($E_{p}$) and the
normalization. Besides this empirical model, GRBs are known to show the
evidence of other components in the prompt emission spectrum. These include
one or more thermal components modeled as a blackbody (Ryde 2005; Page et al.
2011, Guiriec et al. 2011, Guiriec et al. 2013, Guiriec et al. 2015a, Basak &
Rao 2015) or a non-thermal component modeled by a power law or cut-off power
law extending up to high energies ($>$100 MeV) that is observed in Fermi LAT
energy band (González et al. 2003, Abdo et al. 2009, Ackermann et al. 2013).
In a unified model for prompt emission from optical to $\gamma-rays$,
deviation from Band model is fit by a three-component model which includes two
non-thermal components and a thermal component (Guiriec et al. 2015b, Guiriec
et al. 2016, Guiriec et al. 2015a).

Some studies show that the spectral evolution of a single emission component
can sometimes make Band + BB artificially fit the data significantly better
than Band alone if the integration time is too long. Thus for an unambiguous
detection of the thermal component, it is generally necessary to verify the
presence of the thermal component in time resolved spectra as well (Burgess &
Ryde, 2015). Hence, though the inclusion of thermal component can alleviate
the problem of line of death (LOD) violation, we must be cautious of such
cases. In addition, Burgess et al. (2015) have used a physical synchrotron
model with a blackbody and found that the problem of LOD violation persists in
many cases. They have also found a more severe LOD $\alpha\sim-0.8$ and
pointed out the need for some other emission mechanisms. One such proposed
mechanism is Jitter radiation. These radiations are emitted by ultra
relativistic electrons in a non-uniform, small-scale magnetic field and
produces a spectral shape that is different from the synchrotron radiation
(Medvedev, 2000). The allowed photon index in a Jitter radiation can reach up
to +0.5.

From data analysis point of view, GRBs with high signal to noise spectral data
are ideal to try out different emission models as the prompt emission shows
rapid spectral evolution and these GRBs provide good enough signal for time
resolved studies. However, the spectral and timing data so far have not been
able to pin down the radiation mechanism. It is thus very important to study
bright GRBs with well defined spectral shapes using other informations such as
X-ray polarisation during the prompt emission phase. As different emission
models predict different degree of polarisation in different energy bands,
this is a powerful technique to provide strong constraints on the possible
models. GRB 160802A is a bright GRB showing significant hard X-ray
polarization (Chattopadhyay et al., 2017). It shows two pulses in its
lightcurve and the spectrum is well fit by a simple Band function and hence it
offers a very good opportunity to carry out a simultaneous timing, spectral
and polarisation study of a class of GRBs violating LOD.

In Section 2 we discuss the joint usage of Fermi and $AstroSat$ for spectral
and polarization studies of GRBs. Then we present the timing and spectral
properties of the GRB in Section 3. We conclude and discuss our results in
Section 4.

##  2 Fermi and AstroSat data

For many years, $Neil$ $Gehrels$ $Swift$ $Observatory$ and $Fermi$ satellites
have been providing detailed information on the prompt emission of GRBs
(Gehrels & Razzaque, 2013). The Burst Alert Telescope (BAT) on-board Swift
(Gehrels et al., 2004) is a dedicated instrument to detect GRBs and the
satellite slews and points towards the location of a GRB during the prompt
emission. BAT, however, has a relatively narrow energy band and hence the
spectrum of the prompt emission for the BAT detected GRBs can be generally
modeled as a simple powerlaw. Gamma-Ray Burst Monitor (GBM) on board _Fermi_
is comprised of 12 sodium iodide (NaI) detectors and 2 bismuth germanate (BGO)
detectors (Meegan et al., 2009). These detectors are sensitive in the 8 keV
$-$ 1 MeV and 150 keV $-$ 40 MeV energy range, respectively. In addition, the
Large Area Telescope (LAT) on board _Fermi_ , is sensitive from 20 MeV to 300
GeV (Atwood et al., 2009). The unprecedented coverage over seven decades in
energy by _Fermi_ has led to the discovery of substantially new science for
GRBs. The _Fermi_ /LAT GRB catalog contains several interesting bright bursts
and _Fermi_ helped revealing a new spectral component that exists up to GeV
energies or spectral breaks existing in the MeV energy ranges (Abdo et al.
2009, Izzo et al. 2012, Ackermann et al. 2010, Vianello et al. 2017, Wang et
al. 2017). Still it is generally felt that the spectral modelling alone is
unable to solve the problem of radiation mechanism of the GRB prompt emission
due to various issues. Some key problems are e.g., (a) the same data can be
fit with a variety of models and the true model cannot be determined based on
the goodness of fit; (b) even if the best-fit model is determined, the models
are generally phenomenological and may not conform with the underlying theory
e.g., the LOD violation; (c) sometimes an additional spectral component e.g.,
a blackbody may change the parameters of the other component e.g., Band
function in such a way that it conforms with the underlying model, but the
additional component is not statistically required. A critical component that
can break these degeneracies inherent in spectral modelling is the measurement
of X-ray polarisation. The Cadmium Zinc Telluride Imager (CZTI) on board
AstroSat is highly sensitive to hard X-ray polarisation (Chattopadhyay et al.
2014, Vadawale et al. 2015, see also Section 4 of Chattopadhyay et al. 2017).

_AstroSat_ is a multi-wavelength observatory which was launched on 2015
September 28 (Singh et al., 2014). The CZTI focal plane consists of pixellated
detectors sensitive in the energy range of 20-200 keV, with sensitivity
gradually falling off till about 500 keV. All CZTI data are acquired in “event
mode”, with individual photons time-tagged at 20 $\mu$s resolution (Bhalerao
et al., 2017). CZTI can help the study of GRB prompt emission by measuring
X-ray polarization in the 100 - 300 keV range (Chattopadhyay et al. 2014;
Vadawale et al. 2015). The photons preferentially scattered in the direction
perpendicular to the polarization direction, give rise to an
asymmetry/modulation in an otherwise flat azimuthal angle distribution.
Amplitude of the modulation is directly proportional to the polarization
fraction embedded in the incident radiation. Selection procedure of the
Compton events in CZTI is discussed in detail in Chattopadhyay et al. (2014).

The spectral and temporal properties from _Fermi_ and polarization from the
$AstroSat$/CZTI can give a complete information about a GRB. We need to study
these gathered information individually as well as a statistical sample of it.
GRB 160802A is one of the GRBs observed in both _Fermi_ and $AstroSat$/CZTI.
We present here a combined temporal, spectral, and polarization
characteristics of this GRB.

##  3 GRB 160802A

###  3.1 Observations

Figure 1: Left: Composite light curve with 1 s resolution showing cumulative
rates from two NaI detectors (NaI 2, a) and BGO 0. Bayesian blocks are
overplotted and show the light curves obtained using these blocks of constant
rate. Right: light curve with a higher temporal resolution of 64 ms. The
emission is limited up to energy $\sim$ 2 MeV in the BGO as shown in the top
panel.

GRB 160802A was detected by $Fermi$/GBM at UT 06:13:29.63 (Bissaldi, 2016) as
a very bright GRB with two peaks, and a $T_{90}$ of $16.4\pm 0.4$ s in the
50–300 keV band (see Kouveliotou et al. 1993 for a definition of T90). Both
the peaks showed a Fast Rise Exponential Decay (FRED)-like profile. The peak
energy of the Band function fit to the time–integrated spectrum ($T_{0}-0.3$ s
to $T_{0}+19.4$ s) is $284\pm 7$ keV in the preliminary analysis. The fluence
as observed in the 10-1000 keV band is $1.04\pm 0.08\times 10^{-4}$ erg cm-2.
$AstroSat$/CZTI data show a complex light curve with $T_{90}$ = 16.8 s
(Bhalerao et al., 2016). The burst was also detected by several other
satellites including the Block for X-ray and gamma-radiation detection
Lomonosov, BDRG (Panasyuk et al. 2016), Wind/Konus (Kozlova et al. 2016b) and
the Calorimetric Electron Telescope, CALET (Tamura et al. 2016). No low energy
(X-rays, optical, radio etc.) and high energy ($GeV$) afterglows were reported
for GRB 160802A111https://gcn.gsfc.nasa.gov/other/160802A.gcn3.

###  3.2 Light curves

Lightcurves obtained from NaI and BGO detectors of _Fermi_ -GBM clearly show
two peaks separated by $\sim 8$ s in GRB 160802A (Fig. 1). The left panels
show lightcurves in different energy bins, plotted at 1 second resolution.
Bayesian blocks (Scargle et al., 2013) are obtained using $Fermi$
$science~{}tool$ $gtburstfit$ with $ncpprior$ parameter set to 9. A fit
obtained by Bayesian blocks analysis is overplotted with a solid black line.
We see that the second episode is softer: with a high count rate at low
energies, but rapidly diminishing above 400 keV. We studied lightcurves with
finer energy bands to identify bands with significant emission, and found that
at energies $\gtrsim 2$ MeV, any putative signal in BGO is indistinguishable
from background. To highlight these features, the right panel of Fig. 1 shows
lightcurves with 64 ms time resolution.

###  3.3 Spectral analysis of the prompt emission

We undertake detailed spectral analysis with data from GBM detectors with the
strongest signal: NaI 2 (n2), with the GRB just $20\,^{\circ}$ from its
boresight, and NaI a (na), which detected the GRB at an off-axis angle of
$54\,^{\circ}$. We also select the BGO detector closest to the GRB direction
(BGO 0). We use Time-Tagged-Events (TTE) data provided by the GBM team and
publicly available on the FSSC222Fermi Science Support Center,
https://fermi.gsfc.nasa.gov/ssc/. website. We generate custom response
matrices and spectrum files using the public software
gtburst333https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/gtburst.html
and using best localization available interplanetary network (IPN)
triangulation (Kozlova et al., 2016a). The response file is a weighted
response for an interval split over multiple extensions where each extension
contains response for a particular time interval which can vary within
extensions. The software $gtburst$ assign weights when a selected time-bin for
spectral analysis is split across two or multiple extensions. The spectra were
analyzed in $XSPEC$ (Arnaud, 1996). Spectra reduced using $gtburst$ are PHA 2
files and can be directly used in $XSPEC$ by referencing the spectrum number.
Our data are Poissionian in nature, with a Gaussian background derived from
modelling the spectrum in intervals before and after the GRB emission. Hence,
we use pgstat444https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node293.html
as the data fit estimator. Effective area corrections were applied among the
GBM and BGO detectors and to avoid the k-edge 33-37 keV energy range was
excluded for the analysis of NaI data. There is a trade-off between the
reduction in $pgstat$ and increase in the number of model parameters used to
fit the data. This comparison can be made by using the Bayesian Information
Criterion (BIC). The BIC can be calculated from the $pgstat$ value, the number
of free parameters to be estimated ($k$), and the number of data points ($n$)
as

$\mathrm{BIC}=-2\ln(L)+k\ln(n)$

where $L$ is the likelihood of a model for best fit parameters (Schwarz,
1995). When written in terms of likelihood function we can have
$pgstat=-2\ln(L)$, where $L$ is the likelihood of a model for best fit
parameters (Schwarz, 1995). A model yielding a lower BIC as compared to other
models is taken to be preferred model, based on the magnitude of the reduction
in BIC. A change of $\Delta BIC\geq 6$ is a strong evidence of improvement
(Kass & Rafferty, 1995). An example of using BIC for distinguishing among
different models used to fit the GRB spectrum can be found for the case of GRB
160625B in Wang et al. (2017).

We find that for GRB 160802A, the time-integrated _Fermi_ spectrum is best fit
by a Band function with $E_{p}$ = $276_{-14}^{+15}$ keV, $\alpha$ =
$-0.71_{-0.03}^{+0.03}$ and $\beta$ = $-2.5_{-0.2}^{+0.1}$. Here $\alpha$
satisfies the LOD condition, $\alpha<-2/3$. A thermal blackbody component
added to the spectrum improves the fit: $\Delta pgstat\sim 16~{}(\Delta
BIC=3)$ for 2 more free parameters, although this is only a hint for the
presence of a thermal component and a detailed spectral analysis is further
required.

Then we perform a spectral fitting to the two episodes separately using Band
and cut-off power-law (CPL) models, with or without a blackbody (BB) component
and the results are given in Table 1. We find that for the first episode
$\alpha$ of Band-only fit is $-0.52_{-0.03}^{+0.04}$, violating the
synchrotron LOD for slow cooling. Addition of a blackbody to the Band function
softens the value of $\alpha$ to $-0.73_{-0.05}^{+0.06}$ which is now
consistent with the LOD condition. The addition of the blackbody to either
Band or CPL model significantly improves the fit for the first episode with
$\Delta BIC=16$ and $55$, respectively. For the second episode the addition of
the blackbody component is required only for the CPL model ($\Delta BIC=24$),
while indeed it is disfavoured in case of Band function with $\Delta BIC=-6$.
The spectra for time-integrated analysis are shown in Figure 2. A blackbody in
the integrated spectrum is just a first step towards finding a thermal
component. In order to verify that the added blackbody component is physical
and not an artefact of an evolving Band function, we then resort to time
resolved spectral analysis.

Figure 2: The unfolded time integrated spectrum of GRB 160802A for pulse 1 & 2
are shown along with the residuals (limited between -10 to 10) to the fit. The
Band model (top left), an additional blackbody (top right) and blackbody added
to a powerlaw with an exponential cut-off (bottom left) are for the pulse 1
and a band function fit (bottom right) is shown for pulse 2.

###  3.4 Time resolved analysis with coarse bins

We divide the GRB lightcurve into coarse bins corresponding to the Bayesian
blocks (BB) obtained from 1 second light-curves (§3.2). The Bayesian blocks
algorithm objectively divides the data into an optimum set of blocks with no
statistically significant variation from a constant rate within each block
(Scargle et al., 2013). The time intervals thus obtained along with the models
tested are given in Table 2. The synchrotron LOD is violated in the first
three intervals as is evident by the contour maps of $\alpha$-$E_{p}$ shown in
Figure 3. In the intervals (i), (ii) & (viii), BB added to Band gives equally
well fit and for intervals (iv), (vii) and (ix), a powerlaw with sharp break
($XSPEC$ model $bknpower$) is at par with Band function. With the addition of
a BB, the value of the spectral index $\alpha$ softens in all the time bins.
The presence of BB can also be an artefact of the evolution of Band function
parameters with time. This can be tested by fitting spectra to smaller time
bins, and requiring the smooth evolution of parameters like the blackbody
temperature with time (see for instance Guiriec et al., 2011, 2013; Burgess &
Ryde, 2015). Motivated by the results from coarse analysis, we explore this
further in §3.5.

Figure 3: The confidence contours of $\alpha$ and $E_{p}$ are shown for the
coarse time bins (i), (ii), (iii) and (viii) clockwise from the top left. For
the first three intervals which spans time interval $0~{}-~{}3~{}s$, the value
of $\alpha$ is greater than what is expected from the popular SSM. For (viii)
however, the $\alpha$ encompasses the allowed value in its $2\sigma$ contour.
Y-axis ($E_{p}$) is drawn at the line of death value $-2/3$.

###  3.5 Detailed time-resolved analysis

The time intervals are obtained by choosing a constant signal to noise ratio
(SNR) of 30 in the light curve obtained from NaI detector $n2$ (which has the
highest observed rates). We found that the addition of a blackbody does not
give a smooth evolution of its parameters, the temperature of BB fluctuates
erratically and in many bins, it remained unconstrained. Moreover the Band
function emerges as the preferred model over BB+Band in all the bins, as
evidenced by the increase in BIC values after adding the blackbody component
(see Table 3). We conclude that we do not detect any significant blackbody
component in the prompt emission of GRB 160802A.

The evolution of the peak energy ($E_{p}$) of GRBs has been found to show hard
to soft evolution with time in some GRBs, $E_{p}$ tracks the intensity
variations in others, while some GRBs show a mixture of both phenomena (Lu et
al., 2012). An exception to this behavior is found in the case of GRB 151006A
(Basak et al., 2017) where a hardening (increase) in $E_{p}$ is found in an
apparently single pulse towards the end of the emission. The variation of the
spectral parameters along with flux (Figure 4) show the $E_{p}$ values for the
first episode initially follow a hard to soft (HTS) trend, and then track the
8–900 keV flux. In particular, the evolution of $E_{p}$ is very fast in the
first second: showing an order of magnitude change as it decreases from $\sim
1000$ keV to 200 keV. The fast evolution is likely to have manifested itself
as a curvature in the spectrum, which was incorrectly modeled as a blackbody
in the coarse analysis (§3.4).

From the evolution of $\alpha$ we find that the values are crossing the LOD as
shown in Figure 4. The results are unaltered if we use only one of the
detectors $n2$ that has pointing angle $<50^{\circ}$. The value of $\alpha$
and $E_{p}$ are determined by the data below the break energy, while the
$\beta$ is determined from data at the energies above that. Although Fermi GBM
covers the whole of the burst, the number of photons are very few at energies
in the BGO band. Therefore $\beta$ remains unconstrained in most of the bins
and is manifested as a steep high energy power law component of the Band
function (in $\nu F_{\nu}$ representation) because of large magnitudes of the
nominal best-fit values.

Figure 4: The $E_{p}$ evolves with time like a hard to soft (HTS) evolution
initially and then intensity tracking for the first episode. Second episode
has HTS evolution of its $E_{p}$. The photon flux calculated in 8 - 1000 keV
is also shown in the background. The three horizontal lines in the second
panel are lines of death for synchrotron fast cooling ($\alpha=-3/2$, dotted
red line), synchrotron slow cooling ($\alpha=-2/3$, blue dash-dot line), and
Jitter radiation ($\alpha=+1/2$, solid red line).

###  3.6 Polarization analysis

Chattopadhyay et al. (2017) made a systematic analysis of the GRBs detected by
CZTI during the first year of its operation and have reported positive
polarisation detection (chance probability $<$0.1) for 5 of the 11 GRBs having
sufficient number of Compton events for polarisation analysis. GRB 160802A
shows a high degree of polarisation ($85\pm 30~{}\%$) and it has the second
highest Bayes factor for the polarized model as compared to the unpolarized
model among all the GRBs. We have explored the polarisation characteristics of
this GRB with an aim to optimise the polarisation measurement in terms of the
selected energy and time windows.

GRB 160802A shows two distinct peaks and, further, it also shows two distinct
phases of spectra in the first peak: the first phase (covering 0 – 2.5 s, see
Figure 4) having high $E_{p}$ and hard low energy spectral index, and the
second phase with more modest values of $E_{p}$ and a softer low energy
spectral index. Most of the time $E_{p}$ is above 200 keV. CZT Imager is
sensitive for polarisation in the 100 – 400 keV range, the efficiency peaking
at lower energies. Hence, for this analysis we restrict ourselves to the
energy range of 110 – 175 keV, consistently below the spectral peak ($E_{p}$).
To investigate the variation of the polarisation characteristics with the
pulse characteristics, we undertook polarisation measurements in three
distinct time intervals: (i) $\Delta t<$ 2.74 s (measured from the Fermi
trigger time), (ii) 2.74 s $<\Delta t<$ 5.64 s, and (iii) 15.65 s $<\Delta t<$
20.34 s (second pulse). The results are shown in Figure 5.

It is interesting to note that in spite of a large variation in the flux as
well as low energy spectral index, the polarisation value remains high
throughout the burst.

Figure 5: The Compton double events (top panel), polarisation fraction (middle
panel) and the polarisation angle (bottom panel) of GRB 160802A as a function
of time (§3.6).

##  4 Discussion and Conclusions

We have carried out systematic analysis of spectral and polarisation data from
_Fermi_ and AstroSat/CZTI respectively for GRB 160802A. Our analysis derives a
number of important constraints as follows.

  1. (a)

We obtain hard $\alpha$ values most of which lie above $-0.67$, the line of
death of synchrotron emission in slow cooling limit (Cohen et al., 1997;
Crider et al., 1997; Ghirlanda et al., 2003; Preece et al., 1998; Goldstein et
al., 2013), throughout the burst duration including the first and second
episodes (0–7 s and 12–20 s). In coarse time bins though the spectra show a
hint of a Black Body (BB) component, this is most probably an artefact of
evolving peak energy (Burgess & Ryde, 2015). In the finer resolved time bins,
the BB component is never statistically required and $\alpha$ still remains
above the line of death (Crider et al., 1997; Preece et al., 1998; Ghirlanda
et al., 2003).

  2. (b)

During the initial part of the first pulse $\alpha$ is found to get harder
with time, even reaching values $>0$.

  3. (c)

The peak energy $E_{p}$ in general shows a decreasing trend across each major
episodes of emission. However, note that the first episode possesses multiple
pulses in the light curve (Fig. 1), in contrast to the second episode which is
a smooth single pulse. Thereby, the $E_{p}$ evolution in the first episode is
more complex, starting with a hard-to-soft (HTS) evolution, followed by an
intensity tracking behaviour at later times.

  4. (d)

Interestingly, it can also be noted that across the first episode
(significantly in the first pulse of the episode), the time evolution of
$E_{\rm peak}$ and $\alpha$ have a negative correlation in contrast to what is
typically observed in bursts (Kaneko et al., 2006), whereas a positive
correlation can be observed in the second episode.

  5. (e)

No high energy emission above 2 MeV is observed which suggests a cutoff above
this energy.

  6. (f)

Finally, strong polarisation, $\pi=85\pm 29\%$ in energy range 100–175 keV is
observed, in both the episodes.

On an average the $\beta$ of the Band function fit to the spectrum is $-3.4$
with standard deviation $<\sigma>~{}=~{}1.9$ for the burst (Table 3). This
indicates a strong curvature at the high energy end of the spectrum. In such a
scenario a negative correlation between $E_{p}$ and $\alpha$ implies the
following: i) The decrease in $E_{p}$ with time is accompanied by a narrowing
of the spectrum. ii) As the $E_{p}$ values are well constrained and are
located well within the energy window, the inferred hardening of $\alpha$ is
real, and not an artefact caused by $E_{p}$ being close to the edge of the
observing band. iii) This behaviour also suggests that the overlapping of
spectra in each time bin due to time integration is minimum. If significant
overlapping of spectra with decreasing $E_{p}$ did occur, then it would result
in an average spectrum with softer $\alpha$. Also note that in segments of
evolution where $E_{p}$ is not found to be decreasing, the corresponding
$\alpha$ values are relatively soft, indicating that such segments may consist
of overlap of several pulses Ryde & Svensson (1999).

The obtained hard values of $\alpha>-0.67$ lead to the inference that the
observed spectra are inconsistent with the optically thin fast ($\alpha=-1.5$)
and slow cooling ($\alpha=-0.67$) synchrotron emission models (Katz 1994, Rees
& Meszaros 1994, Tavani 1996, Sari et al. 1998) as well as with the fast
cooling synchrotron emission model from a decaying magnetic field
($\alpha\leq-0.8$) (Uhm & Zhang, 2014). A smooth Band function with a hard
$\alpha$ may suggest a photospheric emission scenario wherein continuous
dissipation occurs at high optical depths extending till the photosphere
(Beloborodov, 2010). If so, then the spectral peak would be unpolarised as it
corresponds to the Wien peak formed at higher optical depths. However, during
the interval 1.6 s to 5.64 s post trigger, the $E_{p}$ lies between 100–300
keV, within the CZTI band where high polarisation is observed. This
observation is thus incongruous with the above model. Polarisation imparted by
scattering does not help either, since at large optical depths multiple
scatterings tend to wash out the directionality. Therefore the observed high
polarisation cannot be expected from the subphotospheric dissipation model
based on Comptonisation (see Lundman et al. 2016 for more details).

Another non-thermal process which could be compatible with the observed hard
values of $\alpha$ is Jitter radiation (Medvedev, 2000), wherein small scale
random magnetic turbulence (correlation length, $\lambda_{B}<$ Larmor radius
of the electron) can result in deflection of the electrons on scales less than
the beaming angle. The emission thus produced can result in hard spectra
($\alpha>-0.67$) and can in principle be as large as $+0.5$. The Jitter
emission spectrum, however, is better modeled by a sharp broken power law
instead of a smooth function such as Band function. Jitter radiation, in
contrast to synchrotron emission, extends to frequencies well beyond the
synchrotron critical frequency: up to $a^{3}\omega_{c}$ where
$a=R_{L}/\lambda$, $R_{L}$ the Larmor radius, $\lambda$ the characteristic
scale of turbulence in the outflow, and $\omega_{c}$ is the characteristic
synchrotron frequency. Since $a\gg 1$, emission extending to high energy gamma
rays are expected (Aharonian et al. 2002, Kelner et al. 2013). However, here
we find a cutoff in emission around 2 MeV. High polarisation in case of Jitter
radiation can be achieved only in a specific geometry where the magnetic field
turbulence is constrained within a slab (or plane) that is viewed nearly edge
on. This can result in polarisation degrees as high as $90\%$ (Prosekin et
al., 2016). However, it is important to note that irrespective of the
observing angle the degree of polarisation is highest at energies much beyond
the spectral peak. Around the spectral peak, the polarisation is expected to
be relatively low with values $\leq 40\%$ (see Fig 1 of Prosekin et al. 2016).

Hard $\alpha$ values also suggests that our line of sight is not significantly
off the burst axis (Lundman et al., 2013), and that the central engine is
active throughout the burst duration. At large off-axis angles and when the
central engine is off, the observed emission would be dominated by high
latitude emissions, resulting in a softer spectrum both in terms of $E_{p}$
and $\alpha$ due to lower Doppler boost and superposition of spectra
respectively. This would result in an average spectrum with region below the
spectral peak $-1\geq\alpha\leq-0.5$ (Lundman et al., 2013; Pe’er, 2008),
softer than what is observed here. Both the emission models discussed above,
while being capable of generating spectra nearly compatible with those
observed, find it difficult to explain the high degree of polarisation around
the spectral peak. The observed high polarisation therefore results most
likely from the viewing geometry, as envisaged by Waxman (2003), who showed
that bright and highly polarised emission can be seen when the observer’s line
of sight makes an angle $\theta_{\rm j}\leq\theta_{\rm v}\leq\theta_{\rm
j}+1/\Gamma$ from the jet axis, where $\theta_{j}$ is the jet opening angle,
$\theta_{v}$ is the viewing angle with respect to the axis of the jet and
$\Gamma$ is the Lorentz factor of the outflow. This also requires a strong
asymmetry in observed emission within the off-axis viewing cone as could be
obtained in a “top-hat” jet model, but not in “structured jet” models where
emissivity drops slowly away from the jet axis. A sharp drop in emissivity
beyond the edge of the jet is also suggested by the observed hard $\alpha$
values. In case of structured jets, the emission viewed off-axis would be
dominated by that from high latitudes, resulting in a softer spectrum both in
terms of $E_{\rm peak}$ and $\alpha$ due to lower Doppler boost and
superposition of spectra respectively, contrary to what is observed. On the
other hand, in case of a ”top-hat” jet, hardly any high latitude emission is
expected and the hard spectrum can survive even when observed close to the
edge of the jet. The hard $\alpha$ then suggests subphotospheric dissipation
to be the underlying emission mechanism. In this model Comptonisation can
yield high polarisation since orthogonal Thomson scattering in the rest frame
dominates near the edge of the jet. In contrast, regardless of the geometry,
Jitter radiation cannot produce the observed high level of polarisation near
the spectral peak.

In our current analysis, a spectral cutoff is observed beyond $2\,{\rm MeV}$.
By using the argument of $\gamma-\gamma$ attenuation (Lithwick & Sari, 2001),
we can constrain the lower limit of Lorentz factor of the outflow for the
first and second episodes to be $\geq 78\pm 23$ and $74\pm 23$ respectively.
This in turn gives an upper limit on the beaming angle for the first episode
(second episode), $1/\Gamma\leq 0.73\pm 0.22$ degrees ($0.77\pm 0.24$
degrees). This value is consistent with the viewing angle geometry
($\theta_{v}/\theta_{j}$) suggested by Waxman (2003). Alternatively, under the
assumption of a narrow jet, the jet opening angle is inferred to be
$\theta_{j}\sim 1/\Gamma\sim 1^{\circ}$, similar to the lowest $\theta_{j}$
deduced from jet breaks observed in afterglows (Racusin et al., 2009).

Thus, combining the spectral analysis and the polarisation measurements, we
deem it the most likely that the observed emission from GRB 160802A is due to
subphotospheric dissipation taking place within a narrow GRB jet viewed along
its boundary, with jet emissivity dropping sharply away from its edge.

To summarize, the spectral and timing properties are rich sources of
information about emission mechanisms. Polarization of the prompt emission
helped us to further narrow down the emission mechanisms. It also helped us to
infer the jet geometry as high polarization is observed in case of this GRB.
However, by the combined constraints given by spectro-polarimetric properties
we need a narrow jet viewed along its edge. It is, however, on our radar to
see in future for similar bright bursts whether we obtain a high polarization
always by geometric effects only. Observation of afterglows is also a deciding
factor as then we can measure the jet opening angles and even rule out such
geometries when coupled with harder values of low energy spectral indices.

Table 1: Summary of spectral fitting for the two emission episodes in GRB 160802A Episode 1: |  |  |  |
---|---|---|---|---
($0~{}-~{}7$ s) |  |  |  |
Parametersa |  B |  BB+B |  CPL |  BB+ CPL
$\alpha$ |  $-0.52_{-0.03}^{+0.04}$ |  $-0.73_{-0.05}^{+0.06}$ |  – |  –
$\beta$ |  $-2.6_{-0.1}^{+0.1}$ |  $-3.8_{-\infty}^{+0.7}$ |  – |  –
$E_{\rm{p}}$ (keV) |  $297_{-14}^{+15}$ |  $429_{-36}^{+37}$ |  – |  –
$E_{c}$ (MeV) |  – |  – |  $247_{-12}^{+13}$ |  $348_{-34}^{+41}$
$kT_{BB}$ (keV) |  – |  $35_{-4}^{+3}$ |  – |  $35_{-3}^{+3}$
$\Gamma_{c}$ |  – |  – |  $0.60_{-0.03}^{+0.03}$ |  $0.70_{-0.05}^{+0.05}$
Fluxb |  $7.7$ |  $8.0$ |  $7.9$ |  $8.0$
pgstat/dof/BIC |  395/341/430 |  367/339/414 |  435/342/464 |  368/340/409
$\Delta$(BIC)c |  – |  16 |  |  55
Episode 2: |  |  |  |
$15~{}-~{}20$ s |  |  |  |
$\alpha$ |  $-0.78_{-0.11}^{+0.11}$ |  $-1.1_{-0.1}^{+0.2}$ |  – |  –
$\beta$ |  $-2.4_{-0.2}^{+0.1}$ |  $-3.8_{-\infty}^{+3.0}$ |  – |  –
$E_{\rm{p}}$ (keV) |  $122_{-13}^{+17}$ |  $267_{-86}^{+74}$ |  – |  –
$E_{c}$ (MeV) |  – |  – |  $173_{-20}^{+24}$ |  $326_{-83}^{+139}$
$kT_{BB}$ (keV) |  – |  $17_{-4}^{+3}$ |  – |  $17_{-3}^{+3}$
$\Gamma_{c}$ |  – |  – |  $1.00_{-0.06}^{+0.06}$ |  $1.2_{-0.1}^{+0.1}$
Fluxb |  $2.3$ |  $2.4$ |  $2.2$ |  $2.4$
pgstat/dof/BIC |  399/341/434 |  393/339/440 |  423/342/458 |  393/340/434
$\Delta$(BIC)c |  – |  -6 |  |  24
aParameters are $\alpha$, $\beta$ and Ep for Band (B) model, kTBB for the
black body (BB) model, cut-off energy, Ec, and
index $\Gamma_{c}$ for the cut-off power law (CPL) model.
bFlux in the units of 10-6 erg cm-2 in 8 - 1000 keV.
c $\Delta$BIC is the decrease in BIC with respect to the Band model or the CPL
model.
Table 2: Spectral fit to GBM data in the coarse time intervals described in §3.4. Errors on the parameters are corresponding to a 90% confidence region. Interval |  Model | $\alpha$ | $\beta$ | $E_{\rm p}$ | $kT_{\rm BB}$ | PGstat/dof/BIC | Prefered model
---|---|---|---|---|---|---|---
|  | $\Gamma_{1}$ | $\Gamma_{2}$ | $E_{break}$ |  |  |
[s] |  |  |  | [keV] | [keV] |  |
$i$ |  B | $-0.42_{-0.05}^{+0.05}$ | $-3.45_{-\infty}^{+0.60}$ | $546_{-37}^{+38}$ |  | 386/343/409 |
$(0.0,~{}1.0)$ |  BB+B | $-0.51_{-0.04}^{+0.04}$ | $-3.0_{-3.0}^{+9.2}$ | $680_{-66}^{+46}$ | $47_{-9}^{+9}$ | 375/341/411 | Band/BB+Band
|  bknpower | $0.64_{-0.04}^{+0.04}$ | $2.31_{-0.09}^{+0.09}$ | $274_{-20}^{+21}$ |  | 469/343/492 |
$ii$ |  B | $-0.21_{-0.06}^{+0.06}$ | $-2.76_{-0.28}^{+0.19}$ | $307_{-18}^{+19}$ | — | 360/345/383 |
$(1.0,~{}2.0)$ |  BB+B | $-0.40_{-0.12}^{+0.12}$ | $-3.5_{-\infty}^{+0.6}$ | $412_{-49}^{+61}$ | $37_{-7}^{+6}$ | 345/341/380 | Band/BB+Band
|  bknpower | $0.57_{-0.04}^{+0.04}$ | $2.32_{-0.07}^{+0.08}$ | $178_{-10}^{+11}$ |  | 446/343/469 |
$iii$ |  B | $-0.31_{-0.09}^{+0.10}$ | $-2.79_{-0.49}^{+0.27}$ | $213_{-24}^{+18}$ | — | 402/345/426 |
$(2.0,~{}3.0)$ |  BB+B | $-0.63_{-0.16}^{+0.23}$ | $-4.34_{-\infty}^{+1.55}$ | $304_{-67}^{+57}$ | $33_{-6}^{+5}$ | 398/341/433 | Band
|  bknpower | $0.72_{-0.05}^{+0.05}$ | $2.39_{-0.11}^{+0.12}$ | $136_{-11}^{+11}$ |  | 426/343/450 |
$iv$ |  B | $-0.6_{-0.1}^{+0.2}$ | $-2.8_{-2.5}^{+0.4}$ | $192_{-30}^{+26}$ | — | 387/345/410 |
$(3.0,4.0)$ |  BB + B | $-0.81_{-0.21}^{+0.21}$ | $-3.26_{-\infty}^{+0.85}$ | $258_{-43}^{+90}$ | $26_{-7}^{+7}$ | 383/341/418 | Band/bknpower
|  bknpower | $0.90_{-0.07}^{+0.07}$ | $2.21_{-0.10}^{+0.12}$ | $104_{-10}^{+12}$ |  | 341/343/414 |
$v$ |  B | $-0.76_{-0.20}^{+0.20}$ | $-2.48_{-\infty}^{+0.28}$ | $133_{-23}^{+37}$ |  | 338/345/362 |
$(4.0,5.0)$ |  BB + B | $-1.05_{-0.29}^{+1.78}$ | $-2.94_{-\infty}^{+0.94}$ | $190_{-123}^{+121}$ | $21_{-21}^{+71}$ | 337/343/372 | Band
|  bknpower | $1.12_{-0.17}^{+0.09}$ | $2.32_{-0.25}^{+0.24}$ | $94_{-26}^{+19}$ |  | 341/343/364 |
$vi$ |  B | $-0.76_{-0.08}^{+0.08}$ | $-9.36_{-\infty}^{+6.64}$ | $252_{-31}^{+25}$ | — | 414/345/437 |
$(5.0,6.0)$ |  BB + B | $-0.95_{-0.20}^{+0.21}$ | $-10_{-\infty}^{+0}$ | $304_{-74}^{+109}$ | $36_{-36}^{+74}$ | 411/343/446 | Band
|  bknpower | $1.00_{-0.06}^{+0.06}$ | $2.44_{-0.16}^{+0.26}$ | $151_{-17}^{+27}$ |  | 421/343/444 |
$vii$ |  B | $-0.17_{-0.80}^{+1.83}$ | $-2.13_{-0.45}^{+0.23}$ | $58_{-21}^{+35}$ | — | 323/345/347 |
$(6.0,7.0)$ |  BB + B | $0.28_{-1.72}^{+\infty}$ | $-1.90_{-0.54}^{+0.28}$ | $38_{-21}^{+181}$ | $17_{-17}^{+\infty}$ | 323/343/358 | Band/bknpower
|  bknpower | $0.72_{-0.58}^{+0.57}$ | $2.06_{-0.18}^{+0.35}$ | $36_{-8}^{+31}$ |  | 324/343/348 |
$viii$ |  B | $-0.60_{-0.11}^{+0.12}$ | $-2.22_{-0.13}^{+0.10}$ | $143_{-16}^{+19}$ | — | 389/345/413 |
$(15.0,17.0)$ |  BB + B | $-0.96_{-0.13}^{+0.14}$ | $-2.74_{-\infty}^{+0.36}$ | $280_{-57}^{+79}$ | $19_{-3}^{+3}$ | 375/343/410 | Band/BB+Band
|  bknpower | $1.00_{-0.06}^{+0.05}$ | $2.12_{-0.06}^{+0.07}$ | $88_{-8}^{+8}$ |  | 410/343/432 |
$ix$ |  B | $-1.0_{-0.3}^{+0.7}$ | $-2.4_{-0.6}^{+0.3}$ | $65_{-23}^{+18}$ | — | 364/345/387 |
$(17.0,~{}18.0)$ |  BB + B | $1.2_{-1.4}^{+\infty}$ | $-2.1_{-0.2}^{+0.1}$ | $24_{-6}^{+22}$ | $20_{-5}^{+6}$ | 359/343/394 | Band/bknpower
|  bknpower | $1.40_{-0.36}^{+0.15}$ | $2.32_{-0.22}^{+0.25}$ | $53_{-20}^{+23}$ |  | 394/343/391 |
Table 3: Detailed time-resolved Spectral fitting Sr. no. | (t1,t2) | $kT_{BB}$ | $\alpha$ | $\beta$ | Ep (keV) | PGSTAT/dof/BIC | Prefered model
---|---|---|---|---|---|---|---
|  |  | $\Gamma_{1}$ | $\Gamma_{2}$ | $E_{break}$ |  |
1 | (-0.26, 0.32) |  | $-0.55_{-0.09}^{+0.05}$ | $-5.0_{-\infty}^{+2.0}$ | $951_{-127}^{+168}$ | $343/343/366$ | Band/bknpower
|  | $4.3_{-4.3}^{+3.0}$ | $-0.40_{-0.15}^{+0.17}$ | $-10_{-\infty}^{+20}$ | $850_{-115}^{+9055}$ | $335/341/370$ |
|  |  | $0.84_{-0.05}^{+0.05}$ | $7_{-3}^{+\infty}$ | $1020_{-188}^{+135}$ | $341/343/364$ |
2 | (0.32, 0.48) |  | $-0.41_{-0.08}^{+0.08}$ | $-8.0_{-\infty}^{+5.0}$ | $685_{-71}^{+84}$ | $325/343/349$ | Band
|  | $48_{-48}^{+460}$ | $-0.43_{-0.15}^{+0.14}$ | $-10_{-\infty}^{+20}$ | $746_{-78}^{+167}$ | $324/341/359$ |
|  |  | $0.72_{-0.19}^{+0.06}$ | $2.9_{-0.7}^{+0.6}$ | $504_{-212}^{+106}$ | $353/343/376$ |
3 | (0.48, 0.64) |  | $-0.36_{-0.12}^{+0.13}$ | $-3.4_{-\infty}^{+0.8}$ | $491_{-62}^{+74}$ | $357/343/381$ | Band
|  | $47_{-20}^{+21}$ | $-0.5_{-0.2}^{+0.2}$ | $-9.4_{-\infty}^{+9.5}$ | $586_{-123}^{+142}$ | $352/341/388$ |
|  |  | $0.64_{-0.13}^{+0.08}$ | $2.4_{-0.3}^{+0.3}$ | $278_{-72}^{+45}$ | $374/343/398$ |
4 | (0.64, 0.83) |  | $-0.20_{-0.15}^{+0.17}$ | $-3.36_{-\infty}^{+0.80}$ | $326_{-44}^{+48}$ | $318/343/341$ | Band
|  | $25_{-11}^{+26}$ | $-0.18_{-0.27}^{+0.54}$ | $-6_{-\infty}^{+16}$ | $372_{-58}^{+79}$ | $315/341/350$ |
|  |  | $0.61_{-0.18}^{+0.10}$ | $2.5_{-0.4}^{+0.4}$ | $213_{-58}^{+48}$ | $339/343/362$ |
5 | (0.83, 0.98) |  | $-0.02_{-0.20}^{+0.22}$ | $-2.34_{-0.45}^{+0.20}$ | $283_{-41}^{+61}$ | $412/343/435$ | Band
|  | $17_{-6}^{+7}$ | $1.8_{-2.2}^{+\infty}$ | $-2.3_{-1.1}^{+0.2}$ | $245_{-40}^{+166}$ | $408/341/443$ |
|  |  | $0.50_{-0.11}^{+0.10}$ | $2.2_{-0.2}^{+0.2}$ | $181_{-25}^{+23}$ | $421/343/444$ |
6 | (0.98, 1.1) |  | $-0.03_{-0.18}^{+0.20}$ | $-2.36_{-0.33}^{+0.20}$ | $316_{-46}^{+55}$ | $368/343/392$ | Band
|  | $18_{-5}^{+23}$ | $0.5_{-1.0}^{+4.0}$ | $-2.4_{-1.1}^{+0.2}$ | $314_{-78}^{+450}$ | $365/341/400$ |
|  |  | $0.40_{-0.12}^{+0.11}$ | $2.2_{-0.1}^{+0.2}$ | $181_{-25}^{+30}$ | $382/343/405$ |
7 | (1.1, 1.2) |  | $-0.16_{-0.21}^{+0.48}$ | $-2.82_{-1.06}^{+0.38}$ | $372_{-55}^{+90}$ | $310/343/333$ | Band
|  | $8_{-8}^{+\infty}$ | $-0.15_{-0.60}^{+0.50}$ | $-2.8_{-0.9}^{+0.4}$ | $361_{-55}^{+322}$ | $310/341/345$ |
|  |  | $0.6_{-0.1}^{+0.1}$ | $2.4_{-0.2}^{+0.2}$ | $226_{-35}^{+38}$ | $321/343/344$ |
8 | (1.2, 1.3) |  | $-0.11_{-0.17}^{+0.20}$ | $-2.63_{-0.80}^{+0.32}$ | $290_{-42}^{+48}$ | $333/343/356$ | Band
|  | $29_{-14}^{+13}$ | $-0.2_{-0.3}^{+0.7}$ | $-3.3_{-\infty}^{+0.9}$ | $401_{-120}^{+125}$ | $329/341/364$ |
|  |  | $0.4_{-0.1}^{+0.2}$ | $2.2_{-0.1}^{+0.2}$ | $145_{-16}^{+42}$ | $352/343/375$ |
9 | (1.3, 1.5) |  | $-0.20_{-0.13}^{+0.17}$ | $-3.3_{-\infty}^{+0.7}$ | $345_{-48}^{+39}$ | $364/343/388$ | Band
|  | $37_{-12}^{+13}$ | $-0.30_{-0.23}^{+0.24}$ | $-3.6_{-\infty}^{+1.0}$ | $427_{-78}^{+126}$ | $360/341/395$ |
|  |  | $0.5_{-0.1}^{+0.1}$ | $2.3_{-0.2}^{+0.2}$ | $175_{-23}^{+27}$ | $379/343/402$ |
10 | (1.5, 1.6) |  | $-0.23_{-0.13}^{+0.18}$ | $-3.4_{-\infty}^{+0.9}$ | $364_{-56}^{+45}$ | $315/343/338$ | Band
|  | $38_{-16}^{+15}$ | $-0.34_{-0.23}^{+0.26}$ | $-10_{-\infty}^{+0}$ | $455_{-75}^{+128}$ | $311/341/346$ |
|  |  | $0.50_{-0.12}^{+0.15}$ | $2.3_{-0.2}^{+0.3}$ | $183_{-25}^{+55}$ | $333/343/356$ |
11 | (1.6, 1.72) |  | $-0.36_{-0.19}^{+0.18}$ | $-3.2_{-\infty}^{+0.8}$ | $288_{-47}^{+50}$ | $309/343/332$ | Band
|  | $13_{-8}^{+37}$ | $-0.1_{-0.6}^{+1.6}$ | $-3.2_{-\infty}^{+0.8}$ | $288_{-76}^{+117}$ | $306/341/341$ |
|  |  | $0.72_{-0.09}^{+0.08}$ | $2.5_{-0.2}^{+0.3}$ | $186_{-30}^{+26}$ | $321/343/344$ |
12 | (1.72, 1.9) |  | $-0.3_{-0.2}^{+0.2}$ | $-3.5_{-\infty}^{+0.9}$ | $250_{-34}^{+37}$ | $348/343/371$ | Band
|  | $41_{-6}^{+8}$ | $-0.5_{-0.3}^{+0.5}$ | $-10_{-\infty}^{+0}$ | $306_{-49}^{+93}$ | $346/341/381$ |
|  |  | $0.68_{-0.15}^{+0.11}$ | $2.5_{-0.3}^{+0.4}$ | $157_{-31}^{+36}$ | $355/343/378$ |
13 | (1.9, 2.05) |  | $-0.12_{-0.18}^{+0.21}$ | $-2.8_{-1.2}^{+0.4}$ | $236_{-32}^{+35}$ | $337/343/360$ | Band/bknpower
|  | $41_{-7}^{+7}$ | $-0.7_{-0.3}^{+0.3}$ | $-10_{-\infty}^{+0}$ | $438_{-122}^{+241}$ | $333/341/368$ |
|  |  | $0.5_{-0.1}^{+0.1}$ | $2.4_{-0.2}^{+0.2}$ | $142_{-15}^{+19}$ | $336/343/359$ |
14 | (2.05, 2.2) |  | $-0.06_{-0.20}^{+0.20}$ | $-2.4_{-0.4}^{+0.2}$ | $216_{-32}^{+43}$ | $319/343/342$ | Band
|  | $32_{-8}^{+7}$ | $-0.5_{-0.2}^{+0.3}$ | $-3.5_{-\infty}^{+1.1}$ | $402_{-124}^{+149}$ | $315/341/350$ |
|  |  | $0.52_{-0.14}^{+0.12}$ | $2.2_{-0.1}^{+0.2}$ | $129_{-19}^{+24}$ | $326/343/350$ |
15 | (2.2, 2.4) |  | $-0.37_{-0.15}^{+0.18}$ | $-3.0_{-\infty}^{+0.5}$ | $225_{-30}^{+34}$ | $332/343/355$ | Band
|  | $60_{-60}^{+\infty}$ | $-0.1_{-0.9}^{+4.7}$ | $-2.1_{-1.6}^{+0.3}$ | $95_{-41}^{+211}$ | $331/341/366$ |
|  |  | $0.82_{-0.12}^{+0.08}$ | $2.7_{-0.4}^{+0.4}$ | $173_{-37}^{+26}$ | $338/343/361$ |
16 | (2.4, 2.74) |  | $-0.2_{-0.2}^{+0.2}$ | $-2.8_{-\infty}^{+0.4}$ | $181_{-26}^{+34}$ | $413/343/436$ | Band
|  | $27_{-22}^{+\infty}$ | $-0.50_{-0.37}^{+2.42}$ | $-9.4_{-\infty}^{+7.1}$ | $246_{-87}^{+88}$ | $412/341/447$ |
|  |  | $0.64_{-0.12}^{+0.13}$ | $2.3_{-0.2}^{+0.3}$ | $109_{-12}^{+27}$ | $421/343/444$ |
17 | (2.74, 3) |  | $-0.51_{-0.16}^{+0.22}$ | $-3.40_{-\infty}^{+1.0}$ | $214_{-40}^{+36}$ | $356/343/380$ | Band
|  | $31_{-20}^{+\infty}$ | $-0.8_{-0.3}^{+0.2}$ | $-10_{-\infty}^{+0}$ | $279_{-27}^{+146}$ | $354/341/389$ |
|  |  | $0.9_{-0.1}^{+0.1}$ | $2.5_{-0.3}^{+0.4}$ | $142_{-26}^{+32}$ | $362/343/386$ |
Table 3: Detailed time-resolved Spectral fitting (continued) Sr. no. | (t1,t2) | $kT_{BB}$ | $\alpha$ | $\beta$ | Ep (keV) | PGSTAT/dof/BIC | Preferred model
---|---|---|---|---|---|---|---
|  |  | $\Gamma_{1}$ | $\Gamma_{2}$ | $E_{break}$ |  |
18 | (3, 3.45) |  | $-0.60_{-0.20}^{+0.24}$ | $-2.5_{-\infty}^{+0.3}$ | $155_{-30}^{+41}$ | $379/343/402$ | Band/bknpower
|  | $27_{-16}^{+\infty}$ | $-1.0_{-0.4}^{+0.6}$ | $-2.6_{-\infty}^{+0.7}$ | $231_{-166}^{+309}$ | $378/341/413$ |
|  |  | $1.0_{-0.1}^{+0.1}$ | $2.3_{-0.2}^{+0.2}$ | $103_{-16}^{+20}$ | $378/343/401$ |
19 | (3.45, 3.86) |  | $-0.51_{-0.14}^{+0.15}$ | $-10_{-\infty}^{+20}$ | $204_{-20}^{+21}$ | $407/343/430$ | Band
|  | $21_{-21}^{+\infty}$ | $-0.55_{-0.30}^{+0.30}$ | $-10_{-\infty}^{+0}$ | $224_{-36}^{+70}$ | $405/341/441$ |
|  |  | $0.80_{-0.13}^{+0.14}$ | $2.3_{-0.2}^{+0.4}$ | $107_{-15}^{+38}$ | $418/343/441$ |
20 | (3.86, 4.2) |  | $-0.6_{-0.1}^{+0.2}$ | $-2.8_{-\infty}^{+0.5}$ | $204_{-36}^{+38}$ | $321/343/345$ | Band/bknpower
|  | $29_{-16}^{+\infty}$ | $-0.8_{-0.5}^{+0.8}$ | $-2.8_{-\infty}^{+0.9}$ | $235_{-171}^{+337}$ | $321/341/356$ |
|  |  | $0.9_{-0.1}^{+0.1}$ | $2.24_{-0.18}^{+0.29}$ | $115_{-20}^{+32}$ | $325/343/348$ |
21 | (4.2, 5) |  | $-0.75_{-0.22}^{+0.26}$ | $-2.38_{-0.64}^{+0.25}$ | $111_{-30}^{+28}$ | $368/343/391$ | Band/bknpower
|  | $69_{-69}^{+408}$ | $3.7_{-4.7}^{+\infty}$ | $-2.2_{-0.3}^{+0.2}$ | $75_{-9}^{+75}$ | $367/341/402$ |
|  |  | $1.1_{-0.1}^{+0.1}$ | $2.2_{-0.1}^{+0.3}$ | $72_{-10}^{+25}$ | $368/343/391$ |
22 | (5, 5.4) |  | $-0.6_{-0.1}^{+0.1}$ | $-9.2_{-\infty}^{+\infty}$ | $246_{-19}^{+35}$ | $366/343/390$ | Band/bknpower
|  | $39_{-9}^{+\infty}$ | $-1.0_{-0.3}^{+0.7}$ | $-10_{-\infty}^{+0}$ | $338_{-107}^{+186}$ | $364/341/399$ |
|  |  | $0.91_{-0.09}^{+0.08}$ | $2.5_{-0.2}^{+0.3}$ | $152_{-21}^{+26}$ | $367/343/391$ |
23 | (5.4, 5.6) |  | $-0.60_{-0.12}^{+0.10}$ | $-3.5_{-\infty}^{+0.9}$ | $277_{-35}^{+43}$ | $369/343/392$ | Band
|  | $27_{-27}^{+\infty}$ | $-0.58_{-0.32}^{+0.35}$ | $-3.61_{-\infty}^{+0.9}$ | $282_{-46}^{+123}$ | $369/341/404$ |
|  |  | $0.90_{-0.08}^{+0.08}$ | $2.6_{-0.3}^{+0.3}$ | $184_{-31}^{+30}$ | $377/343/401$ |
24 | (15.7, 15.9) |  | $-0.40_{-0.17}^{+0.24}$ | $-2.3_{-0.5}^{+0.3}$ | $247_{-54}^{+56}$ | $340/343/363$ | Band
|  | $22_{-8}^{+10}$ | $-0.48_{-0.30}^{+0.47}$ | $-2.6_{-\infty}^{+0.4}$ | $347_{-100}^{+179}$ | $335/341/370$ |
|  |  | $0.62_{-0.14}^{+0.20}$ | $2.0_{-0.1}^{+0.3}$ | $109_{-15}^{+55}$ | $351/343/374$ |
25 | (15.9, 16.0) |  | $-0.48_{-0.17}^{+0.25}$ | $-2.9_{-\infty}^{+0.5}$ | $191_{-38}^{+36}$ | $337/343/360$ | Band/bknpower
|  | $27_{-8}^{+7}$ | $-0.8_{-0.3}^{+0.3}$ | $-4.4_{-\infty}^{+2.0}$ | $289_{-91}^{+136}$ | $333/341/369$ |
|  |  | $0.76_{-0.11}^{+0.11}$ | $2.3_{-0.1}^{+0.2}$ | $104_{-11}^{+15}$ | $337/343/360$ |
26 | (16.0, 16.15) |  | $-0.36_{-0.26}^{+0.40}$ | $-2.40_{-0.51}^{+0.25}$ | $127_{-29}^{+32}$ | $338/343/362$ | Band/bknpower
|  | $48_{-12}^{+81}$ | $-0.07_{-0.90}^{+0.50}$ | $-2.2_{-0.4}^{+0.2}$ | $86_{-22}^{+191}$ | $336/341/371$ |
|  |  | $0.76_{-0.15}^{+0.13}$ | $2.18_{-0.12}^{+0.14}$ | $75_{-10}^{+11}$ | $340/343/363$ |
27 | (16.15, 16.3) |  | $-0.2_{-0.3}^{+0.4}$ | $-2.4_{-0.3}^{+0.2}$ | $102_{-20}^{+20}$ | $332/343/356$ | Band
|  | $15_{-3.3}^{+4.3}$ | $-0.7_{-0.3}^{+0.1}$ | $-10_{-\infty}^{+0}$ | $214_{-30}^{+15}$ | $329/341/364$ |
|  |  | $1.1_{-0.1}^{+0.1}$ | $2.2_{-0.1}^{+0.3}$ | $72_{-10}^{+25}$ | $368/343/365$ |
28 | (16.3, 16.5) |  | $-0.6_{-0.2}^{+0.3}$ | $-2.5_{-0.5}^{+0.2}$ | $99_{-16}^{+21}$ | $281/343/305$ | Band/bknpower
|  | $78_{-51}^{+\infty}$ | $-0.5_{-0.2}^{+0.4}$ | $-3.4_{-\infty}^{+1.1}$ | $82_{-18}^{+25}$ | $281/343/316$ |
|  |  | $1.15_{-0.14}^{+0.11}$ | $2.5_{-0.2}^{+0.3}$ | $86_{-18}^{+17}$ | $286/343/310$ |
29 | (16.5, 16.9) |  | $-0.6_{-0.2}^{+0.3}$ | $-2.5_{-0.4}^{+0.3}$ | $86_{-13}^{+14}$ | $356/343/379$ | Band/bknpower
|  | $8.5_{-8.5}^{+\infty}$ | $-0.6_{-0.8}^{+1.8}$ | $-2.6_{-\infty}^{+0.5}$ | $106_{-23}^{+137}$ | $355/341/390$ |
|  |  | $1.15_{-0.14}^{+0.11}$ | $2.5_{-0.2}^{+0.3}$ | $86_{-18}^{+17}$ | $286/343/380$ |
30 | (16.9, 17.6) |  | $-1.0_{-0.2}^{+0.3}$ | $-2.6_{-1.4}^{+0.3}$ | $72_{-14}^{+17}$ | $367/343/390$ | Band/bknpower
|  | $5_{-5}^{+1.7}$ | $0.9_{-1.9}^{+\infty}$ | $-2.5_{-0.4}^{+0.2}$ | $82_{-13}^{+17}$ | $365/341/400$ |
|  |  | $1.15_{-0.14}^{+0.11}$ | $2.5_{-0.2}^{+0.3}$ | $86_{-18}^{+17}$ | $286/343/394$ |
31 | (17.6, 20.34) |  | $0.05_{-1.01}^{+2.30}$ | $-2.4_{-0.6}^{+0.3}$ | $36_{-11}^{+15}$ | $276/343/299$ | bknpower
|  | $5_{-5}^{+6}$ | $-0.5_{-0.8}^{+5.0}$ | $-2.7_{-1.4}^{+0.3}$ | $78_{-17}^{+24}$ | $273/341/308$ |
|  |  | $1.15_{-0.14}^{+0.11}$ | $2.5_{-0.2}^{+0.3}$ | $86_{-18}^{+17}$ | $286/343/302$ |

## Acknowledgements

This research has made use of data obtained through the HEASARC Online
Service, provided by the NASA/GSFC, in support of NASA High Energy
Astrophysics Programs. This publication also uses the data from the AstroSat
mission of the Indian Space Research Organisation (ISRO), archived at the
Indian Space Science Data Centre (ISSDC). 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.

## References

  * Abdo et al. (2009) Abdo, A. A., Ackermann, M., Ajello, M., et al. 2009, ApJ, 706, L138
  * Ackermann et al. (2010) Ackermann, M., Asano, K., Atwood, W. B., et al. 2010, ApJ, 716, 1178
  * Ackermann et al. (2013) Ackermann, M., Ajello, M., Asano, K., et al. 2013, ApJS, 209, 11
  * Aharonian et al. (2002) Aharonian, F. A., Belyanin, A. A., Derishev, E. V., Kocharovsky, V. V., & Kocharovsky, V. V. 2002, Phys. Rev. D, 66, 023005
  * Arnaud (1996) Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17
  * Atwood et al. (2009) Atwood, W. B., Abdo, A. A., Ackermann, M., et al. 2009, ApJ, 697, 1071
  * Band et al. (1993) Band, D., Matteson, J., Ford, L., et al. 1993, ApJ, 413, 281
  * Basak et al. (2017) Basak, R., Iyyani, S., Chand, V., et al. 2017, MNRAS, 472, 891
  * Basak & Rao (2015) Basak, R., & Rao, A. R. 2015, ApJ, 812, 156
  * Beloborodov (2010) Beloborodov, A. M. 2010, MNRAS, 407, 1033
  * Bhalerao et al. (2016) Bhalerao, V., Kumar, V., Bhattacharya, D., Rao, A. R., & Vadawale, S. 2016, GRB Coordinates Network, Circular Service, No. 19782, #1 (2016), 19782
  * Bhalerao et al. (2017) Bhalerao, V., Bhattacharya, D., Vibhute, A., et al. 2017, Journal of Astrophysics and Astronomy, 38, 31
  * Bissaldi (2016) Bissaldi, E. 2016, GRB Coordinates Network, Circular Service, No. 19754, #1 (2016), 19754
  * Burgess & Ryde (2015) Burgess, J. M., & Ryde, F. 2015, MNRAS, 447, 3087
  * Burgess et al. (2015) Burgess, J. M., Ryde, F., & Yu, H.-F. 2015, MNRAS, 451, 1511
  * Chattopadhyay et al. (2014) Chattopadhyay, T., Vadawale, S. V., Shanmugam, M., & Goyal, S. K. 2014, Astrophysical Journal Supplement, 212, 12
  * Chattopadhyay et al. (2017) Chattopadhyay, T., Vadawale, S. V., Aarthy, E., et al. 2017, ArXiv e-prints, arXiv:1707.06595
  * Cohen et al. (1997) Cohen, E., Katz, J. I., Piran, T., et al. 1997, ApJ, 488, 330
  * Crider et al. (1997) Crider, A., Liang, E. P., Smith, I. A., et al. 1997, ApJ, 479, L39
  * Gehrels & Razzaque (2013) Gehrels, N., & Razzaque, S. 2013, Frontiers of Physics, 8, 661
  * Gehrels et al. (2004) Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ, 611, 1005
  * Ghirlanda et al. (2003) Ghirlanda, G., Celotti, A., & Ghisellini, G. 2003, A&A, 406, 879
  * Goldstein et al. (2013) Goldstein, A., Preece, R. D., Mallozzi, R. S., et al. 2013, ApJS, 208, 21
  * González et al. (2003) González, M. M., Dingus, B. L., Kaneko, Y., et al. 2003, Nature, 424, 749
  * Guiriec et al. (2016) Guiriec, S., Gonzalez, M. M., Sacahui, J. R., et al. 2016, ApJ, 819, 79
  * Guiriec et al. (2015a) Guiriec, S., Mochkovitch, R., Piran, T., et al. 2015a, ApJ, 814, 10
  * Guiriec et al. (2011) Guiriec, S., Connaughton, V., Briggs, M. S., et al. 2011, ApJ, 727, L33
  * Guiriec et al. (2013) Guiriec, S., Daigne, F., Hascoët, R., et al. 2013, ApJ, 770, 32
  * Guiriec et al. (2015b) Guiriec, S., Kouveliotou, C., Daigne, F., et al. 2015b, ApJ, 807, 148
  * Izzo et al. (2012) Izzo, L., Ruffini, R., Penacchioni, A. V., et al. 2012, A&A, 543, A10
  * Kaneko et al. (2006) Kaneko, Y., Preece, R. D., Briggs, M. S., et al. 2006, ApJS, 166, 298
  * Kass & Rafferty (1995) Kass, R. E., & Rafferty, A. E. 1995, J. Am. Stat. Assoc., 90, 773
  * Katz (1994) Katz, J. I. 1994, ApJ, 432, L107
  * Kelner et al. (2013) Kelner, S. R., Aharonian, F. A., & Khangulyan, D. 2013, ApJ, 774, 61
  * Kouveliotou et al. (1993) Kouveliotou, C., Meegan, C. A., Fishman, G. J., et al. 1993, ApJ, 413, L101
  * Kozlova et al. (2016a) Kozlova, A., Golenetskii, S., Aptekar, R., et al. 2016a, GRB Coordinates Network, Circular Service, No. 19535, #1 (2016), 19535
  * Kozlova et al. (2016b) —. 2016b, GRB Coordinates Network, Circular Service, No. 19767, #1 (2016), 19767
  * Lithwick & Sari (2001) Lithwick, Y., & Sari, R. 2001, ApJ, 555, 540
  * Lu et al. (2012) Lu, R.-J., Wei, J.-J., Liang, E.-W., et al. 2012, ApJ, 756, 112
  * Lundman et al. (2013) Lundman, C., Pe’er, A., & Ryde, F. 2013, MNRAS, 428, 2430
  * Lundman et al. (2016) Lundman, C., Vurm, I., & Beloborodov, A. M. 2016, ArXiv e-prints, arXiv:1611.01451
  * Medvedev (2000) Medvedev, M. V. 2000, ApJ, 540, 704
  * Meegan et al. (2009) Meegan, C., Lichti, G., Bhat, P. N., et al. 2009, ApJ, 702, 791
  * Meszaros & Rees (1993) Meszaros, P., & Rees, M. J. 1993, ApJ, 405, 278
  * Page et al. (2011) Page, K. L., Starling, R. L. C., Fitzpatrick, G., et al. 2011, MNRAS, 416, 2078
  * Panasyuk et al. (2016) Panasyuk, M. I., Svertilov, S. I., Bogomolov, V. V., et al. 2016, GRB Coordinates Network, Circular Service, No. 19759, (2016), 19759
  * Pe’er (2008) Pe’er, A. 2008, ApJ, 682, 463
  * Preece et al. (1998) Preece, R. D., Briggs, M. S., Mallozzi, R. S., et al. 1998, ApJ, 506, L23
  * Prosekin et al. (2016) Prosekin, A. Y., Kelner, S. R., & Aharonian, F. A. 2016, ArXiv e-prints, arXiv:1607.01522
  * Racusin et al. (2009) Racusin, J. L., Liang, E. W., Burrows, D. N., et al. 2009, ApJ, 698, 43
  * Rees & Meszaros (1992) Rees, M. J., & Meszaros, P. 1992, MNRAS, 258, 41P
  * Rees & Meszaros (1994) —. 1994, ApJ, 430, L93
  * Ryde (2005) Ryde, F. 2005, ApJ, 625, L95
  * Ryde & Svensson (1999) Ryde, F., & Svensson, R. 1999, Astrophysical Letters and Communications, 39, 285
  * Sari et al. (1996) Sari, R., Narayan, R., & Piran, T. 1996, ApJ, 473, 204
  * Sari & Piran (1997) Sari, R., & Piran, T. 1997, MNRAS, 287, 110
  * Sari et al. (1998) Sari, R., Piran, T., & Narayan, R. 1998, ApJL, 497, L17
  * Scargle et al. (2013) Scargle, J. D., Norris, J. P., Jackson, B., & Chiang, J. 2013, ApJ, 764, 167
  * Schwarz (1995) Schwarz, G. 1995, AnSta, 6, 461
  * Singh et al. (2014) Singh, K. P., Tandon, S. N., Agrawal, P. C., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9144, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series
  * Tamura et al. (2016) Tamura, T., Yoshida, A., Sakamoto, T., et al. 2016, GRB Coordinates Network, Circular Service, No. 19778, #1 (2016), 19778
  * Tavani (1996) Tavani, M. 1996, ApJ, 466, 768
  * Uhm & Zhang (2014) Uhm, Z. L., & Zhang, B. 2014, Nature Physics, 10, 351
  * Vadawale et al. (2015) Vadawale, S. V., Chattopadhyay, T., Rao, A. R., et al. 2015, Astronomy & Astrophysics, 578, 73
  * Vianello et al. (2017) Vianello, G., Gill, R., Granot, J., et al. 2017, ArXiv e-prints, arXiv:1706.01481
  * Wang et al. (2017) Wang, Y.-Z., Wang, H., Zhang, S., et al. 2017, ApJ, 836, 81
  * Waxman (2003) Waxman, E. 2003, Nature, 423, 388