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

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 $1.0<q\leq1.2$.