A detailed time-resolved and energy-resolved spectro-polarimetric study of bright GRBs detected by AstroSat CZTI in its first year of operation

GRB 160325A was triggered by Fermi GBM (Meegan et al., 2009) and LAT (Atwood et al., 2009) simultaneously at 06:59:21.51 UT on March 25, 2016 (Roberts, 2016; Axelsson et al., 2016). The GBM light curve of GRB 160325A has two separate emission episodes with a total $T_{\rm 90}$ duration of 43 sec in 50 -300 keV. The gamma-ray/hard X-ray instruments like Swift BAT (Barthelmy et al., 2005; Sonbas et al., 2016), Konus-Wind (Tsvetkova et al., 2016), and AstroSat (Chattopadhyay et al., 2019) also detected GRB 160325A. Previously, we studied the spectro-polarimetric properties of individual episodes of GRB 160325A and noted that both episodes have different spectral and polarimetric properties. The first episode of GRB 160325A is best fitted using Cutoff power-law + Blackbody function and has a low polarization fraction ($<$ 37 %, an upper limit in 100-380 keV), suggesting sub-photospheric model as a dominant radiation model for this episode. On the other hand, the second episode of GRB 160325A is best fitted using Cutoff power-law function and has high polarization fraction ($>$ 43 %, a lower limit in 100-380 keV), suggesting thin shell synchrotron radiation model (Sharma et al., 2020). Our joint spectro-polarimetric analysis indicates a change in the spectral and polarimetric properties of two episodes of GRB 160325A.

GRB 160623A was detected by Fermi GBM at 05:00:34.23 UT on June 23, 2016, (Mailyan et al., 2016). GRB 160623A was also detected by other GRB triggering instruments Konus-Wind (Frederiks et al., 2016a), CALET Gamma-Ray Burst Monitor (Yamaoka et al., 2016), Fermi LAT (Vianello et al., 2016), and AstroSat (Chattopadhyay et al., 2019). We noted that Konus-Wind, CALET, and AstroSat detected a bright emission pulse followed by weaker emission phases. However, GBM could not detect the brighter main emission pulse due to the Earth’s occultation of the source. GBM detected weaker emission of around 50 sec (see Figure 10 of the appendix). Recently, we reported the time-averaged PF of ($<$ 56.51 %, an upper limit) in 100-600 keV using AstroSat/CZTI observations (Chattopadhyay et al., 2022).

For this burst, Swift XRT discovered X-ray afterglow and also observed bright dust-scattered features (radius $\sim$ 3.5 arcmin) around this GRB (Mingo et al., 2016; Tiengo et al., 2016; Pintore et al., 2017). Many ground-based facilities detected the optical/mm/radio afterglows of GRB 160623A.

Utilizing the precise localization of the optical afterglow of GRB 160623A, Malesani et al. (2016) reported the spectroscopic redshift of the burst ($z$ = 0.367). We also conducted observations of the optical afterglow of GRB 160623A using the 10.4m Gran Telescopio Canarias (GTC) as a part of a larger collaboration. Spectra were gathered at various epochs: on June 25 (1.9 days post-burst) and July 3/4, 2016. We utilized both the R1000B and R2500I grisms, covering the wavelength range of 3800-10000 Å. Analysis of the reddest spectrum (2 x 1200 sec with R2500I) at the afterglow position revealed emission lines of H-alpha and [SII], enabling us to determine a redshift of $z$ = 0.367 (see Figure 9 of the appendix), which corroborates the value proposed by Malesani et al. (2016). Additionally, the bluest range spectrum (1200 sec) indicated a marginal detection of H-beta, considering the high foreground Galactic extinction along the line of sight. The faint continuum observed in the spectrum from the first epoch extended down to 3800 Å, with no discernible absorption lines present. Based on these observations, we confirmed that this redshift corresponds to the host galaxy of GRB 160623A (Castro-Tirado et al., 2016).

GRB 160703A was detected by Swift BAT at 12:10:05 UT on July 03, 2016 with a $T_{\rm 90}$ duration of 44.4 $\pm$ 2.8 sec (Cenko et al., 2016; Lien et al., 2016). The prompt emission of GRB 160703A was also observed by Konus-Wind (Frederiks et al., 2016b) and AstroSat (Bhalerao et al., 2016a). Based on AstroSat CZTI observations of GRB 160703A, we reported the high value of time-averaged PF ($<$ 62.64 %, an upper limit) in 100-600 keV (Chattopadhyay et al., 2022).

The X-ray and optical counterpart of GRB 160703A was detected by Swift XRT and UVOT instruments (D’Elia et al., 2016; Hagen & Cenko, 2016). The UVOT detected the afterglow of GRB 160703A in all its seven filters, based on this Hagen & Cenko (2016) constrained the redshift of the burst ($z~{}<$ 1.5). Later follow-up observations using the Giant Metrewave Radio Telescope (GMRT) telescope detected a faint potential radio counterpart of GRB 160703A (Nayana et al., 2016).

At 06:13:29.63 UT on August 02, 2016, GRB 160802A was triggered by Fermi GBM with $T_{\rm 90}$ of 16.4 sec (in 50-300 keV). GBM provides the localization as RA= 35.29, DEC = +72.69 (J2000) with uncertainty radius of 1 degree (Bissaldi, 2016). The GBM light curve of GRB 160802A has two clearly separated emission episodes (see Figure 10 of the appendix). GRB 160802A was one of the brightest (energy fluence 1.04 $\times$ 10^-4 erg $\rm s^{-2}$ in 10-1000 keV) Fermi GBM detected bursts. The burst was independently detected by other gamma-ray detecting satellites/instruments such as AstroSat CZTI (Bhalerao et al., 2016b), Konus-Wind (Kozlova et al., 2016a), Lomonosov BDRG (Panasyuk et al., 2016), and CALET Gamma-ray Burst Monitor (Tamura et al., 2016).

We in Chand et al. (2018) studied the spectro-polarimetric study of GRB 160802A using joint Fermi and AstroSat observations. We performed spectral analysis using empirical functions and XSPEC software. We noted that the evolution of low-energy photon indices of the Band function is harder than those theoretically expected from thin shell synchrotron slow and fast cooling model, indicating photospheric origin. Additionally, we calculated the time-averaged PF = 85 $\pm$ 29 % using previous polarization tools in 100-300 keV (Chand et al., 2018). A high value of the time-averaged PF ($<$ 51.89 %, an upper limit) was also measured 100-600 keV in Chattopadhyay et al. (2022) for GRB 160802A using improved polarimetric techniques. Such a high value of PF indicates a synchrotron model if the source was observed on-axis. On the other hand, the photospheric model can also produce such high PF if the source is viewed along the edge. Based on our joint Fermi and AstroSat spectro-polarimetric observations, we suggested that GRB 160802A might have originated due to subphotospheric dissipation viewed along the edge (Chand et al., 2018).

GRB 160821A was detected by Swift BAT and Fermi GBM at 20:34:30 UT on 21 August 2016 (Siegel et al., 2016; Stanbro & Meegan, 2016). The prompt emission of the burst was also discovered independently using Fermi LAT (McEnery et al., 2016), Konus-Wind (Kozlova et al., 2016b), CALET (Marrocchesi et al., 2016), and AstroSat (Bhalerao et al., 2016c). The burst is extremely bright which provides a unique opportunity for detailed spectro-polarimetric analysis using Fermi-AstroSat observations. We performed the spectro-polarimetric analysis of GRB 160821A and noted a high PF (66${}^{+26}_{-27}$ %) in the time-averaged polarization measurements (in 100-300 keV). Additionally, the time-resolved polarization measurements give evidence of a change in polarization angle by twice during the entire emission phase of GRB 160821A (Sharma et al., 2019). Recently, for this burst, we reported the time-averaged PF ($<$ 33.87 %, an upper limit) in 100-600 keV utilizing the improved polarization measurement tools (Chattopadhyay et al., 2022).

The AstroSat CZTI mainly serves as a hard X-ray imaging/spectroscopy detector with a wide field of view. Notably, its ground calibration has revealed polarization measurement capabilities for on-axis sources. Recent experimentation by Vaishnava et al. (2022) has further validated CZTI’s ability to measure off-axis hard X-ray polarization for bright sources such as GRBs. Above 100 keV, CZTI exhibits a notable probability of Compton scattering. Leveraging the pixilated nature of CZT detectors, it functions as a Compton Polarimeter. Given its distinctive hard X-ray polarization measurement capabilities, the CZTI team has reported polarization measurements of both persistent (such as the Crab pulsar and nebula) and transient (including GRBs) X-ray sources (Rao et al., 2016; Vadawale et al., 2018; Chattopadhyay et al., 2019). Despite moderate brightness, energetic transient sources like GRBs are the potential hard X-ray for polarization measurements due to the simultaneous availability of pre and post-burst backgrounds with higher signal-to-noise ratios. For a comprehensive understanding of the prompt emission polarization analysis of GRBs using CZTI data, we in Chattopadhyay et al. (2022) present detailed techniques. In this study, we present a concise overview of the steps and recent enhancements in the polarization analysis tool for CZTI data.

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  Selection of Compton events: To conduct polarization analysis using CZTI data, we initially chose double events detected within a 20 $\mu$s temporal window. Subsequently, we applied Compton criteria, assessing the ratio of energies received on neighboring pixels, to filter out double events resulting from chance coincidence.

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  Creation of Background-Subtracted Azimuthal Angle Distribution: Compton events were selected within both the GRB emission region and the pre-and post-burst background regions. To define the latter, we excluded instances of spacecraft crossing the South Atlantic Anomaly. Following this, we subtracted the raw azimuthal angle distribution of the GRB emission region from that of the background, resulting in the final background-subtracted azimuthal angle distribution for the GRB.

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  Correction for geometric effects: Systematic errors stemming from geometric effects and off-axis detection of GRBs impact the background-subtracted azimuthal angle distribution. To address this, we employed the Geant4 toolkit and the AstroSat mass model to simulate an unpolarized azimuthal angle distribution. This simulation considered the distribution of photons observed from GRB spectra at the same orientation as the AstroSat spacecraft. Subsequently, we normalized the observed background-subtracted azimuthal angle distribution of the GRB using the simulated unpolarized azimuthal angle distribution.

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  Calculation of Modulation Amplitude and Polarization Angle: We employed a sinusoidal function to fit the observed background-subtracted and geometry-corrected azimuthal angle distribution of the GRB. This fitting process enabled us to determine the modulation factor ($\mu$) and polarization angle within the AstroSat CZTI plane. For the sinusoidal function fitting, we utilized the Markov chain Monte Carlo (MCMC) method.

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  Calculation of Polarization Fraction: To ascertain the polarization fraction, normalization of the modulation factor ($\mu$) with the simulated modulation amplitude for 100% polarized radiation $\mu_{100}$ is required. This value is obtained through Geant4 toolkit simulations using the AstroSat mass model for the same direction and observed spectral parameters. Subsequently, the PF is calculated by normalizing $\mu$ with $\mu_{100}$ for those bursts exhibiting a Bayes factor greater than 2. In instances where the Bayes factor is below 2, we establish a constraint on the polarization fraction by setting a 2$\sigma$ upper limit (refer to Chattopadhyay et al. 2022 for further details).

Furthermore, we have implemented the following enhancements in the polarization data analysis of the AstroSat CZTI for this study. This upgraded CZTI pipeline is being utilized for the first time for executing time and energy-resolved polarization measurements of bursts detected by the AstroSat CZTI.

The temporal profiles of GRBs exhibit distinct characteristics attributed to the erratic behavior of the central engine. To extract temporal information from Fermi GBM data, we employed the Fermi GBM Data Tools (Goldstein et al., 2022). Furthermore, to extract spectra from Fermi GBM data, we employed the gtburst tool¹¹1https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/gtburst.html. For BAT data, both temporal and spectral analyses were carried out using HEASOFT, utilizing the most recent BAT calibration files. For detailed insights into the technique employed for BAT data analysis, refer to Gupta et al. (2021). It is important to note that 3ML plugin for the simultaneous fitting of BAT data with data from other instruments, such as Konus-Wind, AstroSat, etc, is not currently available. Consequently, for GRBs observed with BAT, we have relied exclusively on the spectral parameters derived from the Konus-Wind instrument, as reported in Chattopadhyay et al. (2022). Below, we have provided details of our spectral analysis (empirical and physical synchrotron model). However, we did not explore the physical photospheric models due to the lack of a publicly available robust and validated photospheric model (compatible with 3ML).

The expected polarization fraction from different radiation models depends on the jet viewing geometry, and this can be further verified by investigating the $\Gamma\theta_{\rm j}$ condition, where $\Gamma$ represents the bulk Lorentz factor and $\theta_{\rm j}$ denotes the jet opening angle (see section 5.1 for more information). $\Gamma$ and $\theta_{\rm j}$ could be calculated using the Liang relation (the correlation between isotropic gamma-ray energy and $\Gamma$, Liang et al. 2010) and the jet breaks observed in the afterglow light curve, respectively. However, both of these parameters depend on the redshift. Therefore, redshift is a very important parameter to verify the $\Gamma\theta_{\rm j}$ condition and predict the possible radiation mechanism based on the observed value of polarization fraction. We observed that only two GRBs (GRB 160623A and GRB 160703A) in our sample have redshift constraints. No redshift measurements were found in the literature for the remaining GRBs. To determine their photometric redshift, we attempted to locate the associated host galaxies of the bursts with sub-arcsecond localization in our sample (GRB 160703A and GRB 160821A) using the 3.6m Devasthal Optical Telescope (DOT, Gupta et al. 2023). We conducted observations of GRB 160703A using TANSPEC (in i-filter, Sharma et al. 2022) on 2022-11-11, with a total exposure time of 5700 seconds. Similarly, observations of GRB 160821A were carried out using a 4K $\times$ 4K IMAGER (in R-filter, Pandey et al. 2018, 2023) on 2022-12-20, with a total exposure time of 5100 seconds (see Figure 9 of the appendix). The methods for the optical data reduction of host images taken using TANSPEC and IMAGER are presented in Gupta et al. (2022b); Gupta (2023). However, despite our efforts, we were unable to detect any associated host galaxies of these bursts within the best available error circles. Our observations yielded limiting magnitudes of $\sim$ 23 mag for GRB 160703A and 23.6 mag for GRB 160821A, respectively. This suggests that the host galaxies of these GRBs may be intrinsically faint or highly obscured, reflecting the diverse nature of GRB host environments.

The prompt light curve profiles of Fermi detected (GRB 160325A, GRB 160623A, GRB 160802A, and GRB 160821A) and Swift detected (GRB 160703A) GRBs in our sample are presented in Figure 10 of the appendix. The light curves of GRB 160325A (depicted in red) and GRB 160802A (in green) exhibit similar temporal profiles, characterized by two distinct episodes: a prominent pulse followed by a softer pulse, with a quiescent temporal gap in between. In contrast, GRB 160623A (highlighted in blue) showcases a primary pulse succeeded by weaker emission. Notably, Fermi could not detect the main emission of GRB 160623A due to Earth occultation during the burst’s main emission, with the Fermi trigger occurring approximately 50 seconds post-burst (Mailyan et al., 2016). The light curve of GRB 160821A (depicted in pink) illustrates a faint initial emission followed by a very brighter emission. Meanwhile, GRB 160703A presents multiple overlapping profiles (in grey).

We employed the Bayesian block method on the CZTI Compton light curves to determine the time intervals for the time-integrated spectral analysis of GRBs in our sample. These selected time segments were also utilized for time-integrated polarization measurements, as detailed in section 2.2 of Chattopadhyay et al. 2022. The time-integrated Fermi spectra of GRB 160325A and GRB 160623A were optimally fitted using the Bkn2pow function. Conversely, the time-integrated Fermi spectra of GRB 160802A and GRB 160821A exhibited the best fits with the Band + Blackbody function. For the Swift BAT-detected GRB 160703A, the time-integrated spectrum was most effectively described by the Cutoff power-law function, considering the limitation of energy coverage of BAT. Detailed information regarding the best fit time-integrated spectral parameters for all five GRBs in our sample can be found in Table 5 of the appendix.

We analyzed the spectral (obtained using time-integrated analysis) and temporal parameters of GRBs in our sample and compared them with a larger sample of Fermi GBM detected GRBs (see Figure 1). Such comparison provides valuable insights into the spectral properties and diversity of these cosmic sources. The distribution of the low energy photon index is useful for characterizing the power-law behavior of the photon spectrum at lower energies and identifying the emission mechanisms. The distribution of $\alpha_{\rm pt}$ reveals that a significant number of bursts deviates from the synchrotron emission mechanism. The distribution of $E_{\rm p}$ value is crucial and indicates the energy at which the GRB spectrum reaches its maximum intensity. We noted all the bursts in our sample have a harder peak energy than the mean peak value obtained for Fermi GBM detected GRBs. The distribution of high-energy photon indices signifies the steepness of the spectral slope in the high-energy regime. The high energy spectral index ($\beta_{\rm pt}$) values (calculated using the time-integrated spectral measurement) for GRB 160325A, GRB 160623A, and GRB 160802A are steeper than the mean value obtained for Fermi GBM detected GRBs. On the other hand, GRB 160821A has a shallower $\beta_{\rm pt}$ value. Further, we studied the distribution of $T_{\rm 90}$ duration using Fermi GBM data, and the distribution indicates that all the bursts in our sample belong to the long GRBs class.

The GRBs spectrum shows strong evolution within the burst; therefore, the derived time-integrated spectral parameters may not provide intrinsic spectral behavior and can be artifacts due to strong spectral evolution. Thus, time-resolved spectral measurements are needed to verify the underlying radiation mechanisms of GRBs. We studied the time-resolved spectral analysis of those bursts (GRB 160325A, GRB 160802A, and GRB 160821A) for which Fermi GBM observations were available. Fermi GBM wide spectral coverage is crucial for detailed spectral analysis.

We selected the temporal bins for time-resolved spectral analysis using the Bayesian Block method. After selecting bins, we calculated the significance of individual bins and only selected those with a signification greater than 10. Further, we fitted all these bins with Band and CPL models and calculated the difference of DIC values to identify the best-fit model for individual bins. The comparison between DIC values of Band and CPL models for all three GRBs are plotted with red squares in Figure 11 of the appendix. The DIC comparison indicates that individual bins of GRB 160325A, GRB 160802A, and GRB 160821A are preferred Band function over CPL model (no bins have $\Delta$ DIC $\leq$ -10). For some of the bins, CPL model has $\Delta$ DIC value in between zero and -10, indicating that Band and CPL both models have an equivalent fit. After selecting the best-fit function between Band and CPL models, we added the additional Blackbody (BB) function. We again selected the best-fit model between Band or CPL with Band+BB or CPL+BB using the difference of DIC values obtained for the two models. A detailed selection method for the different empirical functions is present in Caballero-García et al. (2023). Furthermore, we have also compared the fits between the best fit empirical and physical models. However, there are some time bins for which the physical synchrotron parameters are not very well constrained (due to the low signification).

We used the derived spectral parameters using time-resolved spectral analysis to study their evolution and correlation among them. The spectral evolution of empirical parameters $E_{\rm p}$, low and high energy photon indices for GRB 160325A, GRB 160802A, and GRB 160821A is presented in Figures 3, 4, and 5, respectively. The evolution of physical parameters (electron spectral index and magnetic field strength) obtained using synchrotron modeling is also shown in these figures. We observed that $E_{\rm p}$ evolution of all three GRBs has an intensity tracking behavior. Additionally, $\alpha_{\rm pt}$ evolution for GRB 160802A and GRB 160821A have the same tracking behavior, supporting a double-tracking nature. The correlation among different empirical and physical spectral parameters of time-resolved spectral parameters was also studied. The correlation results between different model parameters are listed in the appendix in Table 15. Our correlation analysis indicates that the peak energy of the burst (obtained using empirical fitting) is strongly correlated with flux evolution for all three GRBs. We also observed that $\alpha_{\rm pt}$ is strongly correlated with flux evolution for GRB 160802A and GRB 160821A. However, it is anti-correlated for GRB 1603025A (correlation analysis for GRB 160325A is not statistically significant due to less number of available bins). The physical parameters B and $p$ calculated using synchrotron modeling are found to be correlated with each other for GRB 160802A and GRB 160821A. Moreover, the physical parameters B and $p$ strongly correlate with empirical parameters $E_{\rm p}$, $\alpha_{\rm pt}$, and flux for GRB 160802A and GRB 160821A.

Previous studies on the polarization of a few GRBs, such as GRB 100826A, GRB 160821A, and GRB 170114A, have suggested that their polarization properties could exhibit temporal evolution (Yonetoku et al., 2011a; Sharma et al., 2019; Burgess et al., 2019). However, it’s important to note that these GRBs were observed using different instruments and analyzed through distinct pipelines. The observed hints regarding the evolution in polarization properties of GRB 100826A, GRB 160821A, and GRB 170114A were obtained using the GAP, AstroSat/CZTI, and POLAR instruments, respectively. These findings imply that the polarization properties of GRBs may undergo intrinsic changes over time, potentially resulting in null or low polarization fractions in time-integrated polarization measurements.

In our recent five-year catalog paper (Chattopadhyay et al., 2022), we highlighted a notable observation: approximately 75% of GRBs exhibit low or null polarization fractions in our time-integrated polarization analysis. However, to ascertain whether these bursts are intrinsically unpolarized or if their polarization properties undergo changes within the bursts, leading to null or low polarization, a detailed time-resolved polarization analysis is imperative. In the present work, we studied a detailed time-resolved polarization analysis of five GRBs detected in the first year of operation of AstroSat. We applied two distinct binning techniques to the GRB light curves and subsequently conducted polarization measurements. In case the GRB light curve has more than one pulse (for example, GRB 160325A and GRB 160802A), we selected individual pulses for time-resolved polarization measurement. Conversely, for GRBs exhibiting a single pulse, namely GRB 160623A, GRB 160703A, and GRB 160821A, we selected the peak duration of the burst. The results of our time-resolved polarization measurement are tabulated in Table 2. Additionally, we present an illustrative example of the posterior probability distribution obtained through polarization analysis of GRB 160623A (during the peak duration) in Figure 6.

Further, we also selected the time bins using the sliding mode temporal binning method (since the GRB light curves exhibit rapid or irregular variations) with a bin width of 10 sec (for GRB 160325A, GRB 160623A, GRB 160703A, and GRB 160821A) or 5 sec (for GRB 160802A) for the time-resolved polarization measurements. We initially divided the light curve into smaller time intervals of the bin width from 0-10 sec or 0-5 sec and slid these average intervals across the entire duration of the burst with increasing order of 1 sec (GRB 160325A, GRB 160623A, GRB 160703A, and GRB 160802A) or 2 sec (GRB 160821A). Using the sliding mode binning, we calculated the average values of polarization parameters within each bin. The polarization results obtained using the temporal sliding binning along with pulsed/peak-wise binning algorithms are displayed in Figures 3, 4, 5, and 7, respectively. The time-resolved (pulsed-wise) analysis of the first pulses of GRB 160325A and GRB 160802A constrains the higher PF values (see Table 2), although sliding mode analysis of the same pulses indicates lower PF values. We noted that the polarization angles of GRB 160325A, GRB 160623A, GRB 160703A, and GRB 160802A obtained for different burst intervals remain within their respective error bars. This suggests that there is no substantial change in the polarization properties as these bursts evolve. However, we noted that the polarization angles of GRB 160821A changed twice within the burst, consistent with our previous results reported in 100-300 keV with the previous polarization pipeline (Sharma et al., 2019). Our time-resolved polarization analysis gives a hint that the polarization properties of GRB 160821A depend on the temporal window of the burst.

In addition to conducting time-resolved polarization measurements, we also performed an energy-resolved polarization analysis. A comparison of the polarization fraction obtained using the AstroSat CZTI and POLAR missions catalog revealed that AstroSat CZTI detected approximately 20 % higher polarization compared to POLAR measurements (Chattopadhyay et al., 2022). We suggested that the discrepancy between the observed time-integrated and energy-integrated polarization fractions of prompt emission by AstroSat CZTI and POLAR missions could be attributed to the fact that both instruments report the polarization fractions values in different energy channels (CZTI values in 100-600 keV, and POLAR values in 50-500 keV).

In this work, we carried out energy-resolved polarization measurements to investigate the energy-dependent behavior of polarized radiation (polarization degree and angle) during the prompt phase of GRBs. We have employed two methods for selecting energy bins of individual bursts. Initially, we selected the bins based on observed peak energy calculated from the time-averaged spectral analysis. We created two bins: one ranging from 100-$E_{\rm p}$ keV and the other from $E_{\rm p}$-600 keV. In cases where the observed peak energy exceeded 600 keV (the maximum allowed energy range for the polarization measurements using CZTI), we selected the following bins: 100-300 keV and 300-600 keV, considering that the mean value of peak energy for long GRBs is approximately 200-300 keV (refer to Figure 1). The calculated values of the energy-resolved polarization fraction of all five bursts are listed in Table 3.

Further, we also selected the energy bins using the sliding mode spectral binning method (since the GRB spectra exhibit rapid variations) with a bin width of 50 keV for the energy-resolved polarization of all five GRBs in our sample. We initially divided the spectrum into smaller energy intervals of the bin width from 100-300 keV and slid these average energy intervals across the total energy range of the CZTI with an increasing order of 50 keV. Using the sliding mode binning, we calculated the average values of polarization parameters within each spectral bin. The polarization results obtained using the energy sliding binning algorithm are shown in Figure 8. We noted that the polarization angles of GRB 160325A, GRB 160703A, and GRB 160802A, GRB 160821A obtained for different energy segments remain mostly consistent (no substantial change in the polarization angles); however, we noted that the polarization angles of GRB 160623A changed with energy. Additionally, we noted that the polarization fraction values have increasing trends with energy, although the analysis might be limited due to fewer Compton counts in later energy bins. The energy-resolved polarization analysis gives a hint that polarization measurements depend on the energy channels of the detectors.

The main objective of this study is to investigate the possible jet composition and emission mechanisms of GRBs through time-resolved and energy-resolved spectro-polarimetric analysis. Different radiation models in GRBs are associated with different polarization fraction values. However, it is important to note that the observed polarization fraction values also depend on the viewing geometry of the bursts. To assess the viewing geometry of individual bursts, we employed the $\Gamma\theta_{\rm j}$ condition. By applying this condition, we sought to gain insights into the viewing perspective of the bursts and their implications on their polarization properties. When viewing the jet from an on-axis perspective, the value of $\Gamma\theta_{\rm j}$ is significantly greater than 1. Conversely, for off-axis observations, $\Gamma\theta_{\rm j}$ is expected to be much smaller than 1. In the case of a narrow jetted view, the $\Gamma\theta_{\rm j}$ value is expected to be approximately 1. The value of $\Gamma$ of the fireball can be derived from prompt emission as well as afterglow features of GRBs (Liang et al., 2010; Ghirlanda et al., 2018). In this work, we constrain the value of bulk Lorentz factor using well-studied Liang correlation³³3$\Gamma_{0}$ $\approx$ 182 $\times$ $E_{\gamma,\rm iso,52}^{0.25\pm 0.03}$, the strong correlation between bulk Lorentz factor and isotropic gamma-ray energy of the fireball (Liang et al., 2010). The derived values of bulk Lorentz factor are tabulated in Table 4. For GRB 160623A, we obtained $E_{\gamma,\rm iso}$ value using Konus-Wind observations (Tsvetkova et al., 2017) as the main emission was not detected using Fermi GBM. Additionally, we derive the jet opening angle (lower limits) using the X-ray afterglow light curves observed using Swift XRT and equation 4 of Frail et al. (2001). The $\theta_{\rm j}$ value depends on micro-physical afterglow parameters (medium number density ($n_{0}$) and electrons thermal energy fraction ($\epsilon_{e}$)). We assume typical values of $n_{0}$ = 1 and $\epsilon_{e}$ = 0.2 to constrain $\theta_{\rm j}$ values (Gupta et al., 2022c). However, detailed afterglow modeling and a good data set will be needed to constrain these parameters better (Gupta et al., 2022a). For GRB 160623A, we obtained the $\theta_{\rm j}$ value from Chen et al. (2020). However, in the case of GRB 160802A and GRB 160821A, no Swift XRT observations are available, so we used $\theta_{\rm j}$ = 2.1 degree, which is the mean value of jet opening angle for typical Fermi-detected long GRBs (Sharma et al., 2021). After calculating the bulk Lorentz factor and jet opening angle values for individual bursts, we determine the viewing geometry ($\Gamma\theta_{\rm j}$). The calculated values of $\Gamma\theta_{\rm j}$ are tabulated in Table 4. We noted that the calculated for all five bursts in our sample have $\Gamma\theta_{\rm j}$ $>>$ 1, suggesting that the jet from these GRBs is observed from an on-axis perspective. Further, we utilized $\Gamma\theta_{\rm j}$ condition and our spectro-polarimetric results for each of the five GRBs in our sample to investigate GRBs’ possible jet composition and emission mechanisms.