Rotation of Polarization Angle in Gamma-Ray Burst Prompt Phase$-$\uppercase\expandafter{\romannumeral2}. The Influence of The Parameters

TL;DR

This study investigates how parameters like jet angle, observational angle, and Lorentz factor influence polarization angle rotation in GRB prompt emission, revealing significant impacts and conditions for large rotations.

Contribution

It introduces a magnetic reconnection model analyzing PA rotations in GRBs, highlighting the roles of jet and viewing angles, and Lorentz factor, which were less explored before.

Findings

PA rotation depends on jet opening angle, observational angle, and Lorentz factor.

Typical PA change within T90 ranges from 12° to 66° for off-axis observations.

Maximum PA rotation (~90°) occurs when the product of jet angle and Lorentz factor exceeds 50.

Abstract

In addition to the light curve and energy spectrum, polarization is also important for inferring the physical properties of the Gamma-ray burst (GRB). Rotation of the polarization angle (PA) with time will cause depolarization of the time-integrated polarization degree. However, it is rarely studied before. Here, we use a magnetic reconnection model with a large-scale ordered aligned magnetic field in the emitting region to study the influence of the parameters on the PA rotations in GRB prompt phase. We find that half-opening angle of the jet $\theta_{j}$, the observational angle $\theta_{V}$, and the bulk Lorentz factor $\Gamma$ all have significant impacts on the PA rotations. The PA rotations are affected by the product value of $\theta_{j}\Gamma_{0}$ ($\Gamma_{0}$ is the normalization factor of $\Gamma$ with $\Gamma(r)=\Gamma_{0}(r/r_{0})^{s}$), but are roughly independent of the concrete values of both $\theta_{j}$ and $\Gamma_{0}$. For the typical parameters, the changes of the PA within $T_{90}$ ($\triangle$PA) would be within ($12^\circ$, $66^\circ$) for slight off-axis observations, where $T_{90}$ is the duration of the burst with the accumulated flux density ranging from $5\%$ to $95\%$. The $q$ range for $\triangle$PA$>10^{\circ}$ becomes smaller with the increase of the product value of $\theta_{j}\Gamma_{0}$. The most significant PA rotation with $\triangle$PA$\sim90^{\circ}$ will happen when $\theta_{j}\Gamma_{0}>50$ and $1.0<q\leq1.2$.