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 $T_{90}$ ($△$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 $△$PA$>10^{\circ }$ becomes smaller with the increase of the product value of ${\theta }_j{\Gamma }_0$. The most significant PA rotation with $△$PA$\sim 90^{\circ }$ will happen when ${\theta }_j{\Gamma }_0>50$ and $1.0<q\le 1.2$.

11 pages, 7 figures, 1 table ApJ accepted