Is gamma-ray burst polarization from photosphere emission?

TL;DR

This work tests whether GRB prompt emission polarization can be explained by photosphere emission, by combining spectral data with POLAR and AstroSAT polarization measurements. It finds a power-law X-ray afterglow and a $T_{90} \propto (L_{\text{iso}})^{-0.5}$ relation, along with unusually hard $\alpha$ values, all aligning with a thermal photosphere origin. A key result is the positive correlation between $\alpha$ and the polarization degree (PD), which the authors show can be reproduced by a photosphere model in a structured jet viewed off-axis, where the angular Lorentz-factor distribution controls both $\alpha$ and PD. These findings provide a diagnostic criterion favoring photospheric emission for the polarization sample and outline testable predictions for future wide-band polarization missions.

Abstract

Context: Despite more than half a century of research, the dominant radiation mechanism of gamma-ray burst (GRB) prompt emission remains unsolved. Some progress has been made through the analyses of the observational spectra of Swift/BAT, Konus/Wind, and Fermi/GBM, as well as the spectra of the photosphere or synchrotron models, but it is still insufficient to pin down the answer. Aims: Combining the spectral and polarization observations, we seek new criteria for model evaluation. Methods: We thoughtfully investigate the polarization samples of POLAR and AstroSAT, combining the light curve, the spectral and the polarization parameters. Results: The power-law shape of the X-ray afterglows, the $T_{90} \propto (L_{\text{iso}})^{-0.5}$ correlation, and the hard low-energy spectral index $α$ are revealed, thus supporting the photosphere origin. Furthermore, we discover the positive correlation of the $α$ and the polarization degree (PD), which can be consistently explained by the photosphere polarization scenario involving the jet asymmetry from a moderate viewing angle of $θ_{v}$=0.015.

Figures (7)

• Figure 1: The roughly power-law shape (without a significant plateau) for the X-ray afterglow light curves of the GRBs with reported polarization detections. This fits well with the prediction of the hot fireball model. The slight deviation from the power law (breaks) can arise from the moderate viewing angle $\theta_{v} \sim 1.5/\Gamma$ for the polarization sample (see Rossi2002). The early flares in GRB 140206A are inherited from the prompt emission, considering a very close match for the light curves of Swift/BAT and Swift/XRT, during this period.
• Figure 2: The $T_{90}\propto (L_{\text{iso}})^{-0.5}$ correlation (blue solid line) for the GRBs with reported polarization detections (red stars), along with the high-efficiency sample (orange stars; Meng2022) and the high-energy sample (cyan stars; $E_{\gamma,\text{beam}}$$\gtrsim 10^{52}$ erg and obtaining GeV/TeV detection; Sharma2021). Notably, all three samples exhibit a roughly power-law shape in their X-ray afterglows. The dashed green lines mark a $T_{90}$ deviation of a factor of two, from the best-fit log ($T_{\text{90}}$) = 1.67 - 0.5 log ($L_{\text{iso}}$) relationship. This $T_{90}\propto (L_{\text{iso}})^{-0.5}$ correlation aligns closely with the predictions made by the NDAF model (red solid line), which is under the hot fireball framework.
• Figure 3: The distribution of the low-energy spectral index $\alpha$, for the GRBs with reported polarization degree (the red and blue boxes, excluding the upper and lower limits). The $\alpha$ is quite close to or larger than the “synchrotron line of death” $\alpha$= $-$2/3 (the orange line). Note that GRB 170101A is only detected by POLAR and Swift/BAT, thus the $\alpha \equiv -1.55$ is doubtful.
• Figure 4: The apparently positive correlation of the low-energy spectral index $\alpha$ and the polarization degree (left) and the possible photosphere explanation (right, polarization degree $\Pi =\left\vert Q\right\vert /I$). (a) Notably, this positive correlation can be obtained from the POLAR sample (blue circles, with Pearson correlation coefficient r=0.69) and the AstroSAT bursts (green triangles, r=0.85), both. The P values standing for the significance level are both $\sim$ 0.06, thus the correlation is almost significant (combining POLAR and AstroSAT, P $\sim$ 0.03 can be achieved). (b) For the photosphere polarization, the polarization degree is shown to be positively correlated with the p value (the power-law decreasing index of the $\Gamma$, for the jet angular distribution), for the smaller $\theta_{c,\Gamma}$ case available for bursts with higher energy. Also, for $\Gamma \cdot \theta_{c,\Gamma} \simeq 1$, $\alpha$ is positively correlated with the p value, $\alpha \simeq (-1/4) (1+3/p)$. The predicted positive correlation of $\alpha$ and the polarization degree for $\theta_v$=0.015 (red pluses in the left panel) can match the observations of POLAR and the slope of the AstroSAT sample, approximately. Notice that the GRB 170127C in POLAR may have larger $\theta_{c,\Gamma}$, thus possessing larger $\alpha$ of 0.25 and smaller polarization degree (see Figure \ref{['fig:theta_c']} (a), maybe two to three times smaller).
• Figure 5: Correlations of photosphere polarization degree ($\Pi =\left\vert Q\right\vert /I$), $\theta_{c,\Gamma}$ (or $\theta _{\text{jet}}$) and $E_{\text{iso}}$. (a) Comparison of the photosphere polarization degree for smaller $\theta_{c,\Gamma}$ ($\Gamma \cdot \theta_{c,\Gamma}=1$, solid lines; predicting much larger polarization degree) and larger $\theta_{c,\Gamma}$ ($\Gamma \cdot \theta_{c,\Gamma}=2$, dashed lines; predicting much smaller polarization degree). (b) The smaller $\theta _{\text{jet}}$ (likely $\theta_{c,\Gamma}$ also) is found for the high-energy sample ($E_{\text{iso}} \gtrsim 10^{53}$ erg), indicating the polarization detection.