Rotation of Polarization Angle in Gamma-Ray Burst Prompt Phase. III. The Influence of the Magnetic Field Orientation

TL;DR

This work investigates how the orientation of a large-scale aligned magnetic field, quantified by $δ$, influences polarization-angle (PA) rotations during the GRB prompt phase using a parametric magnetic reconnection model. It computes time- and energy-resolved polarization across optical-to-MeV bands, analyzing dependence on off-axis parameter $q$, jet opening angle $θ_j$, and initial bulk Lorentz factor $Γ_0$. The main finding is that PA rotation behavior is robust to field orientation: the region with significant $\Delta$PA shrinks as $δ$ grows in $0^ op°<δ<90^ op°$, complementary orientations give identical $\Delta$PA, and for $δ=0^ op°$ or $90^ op°$ rotations are restricted within the burst. These results support robust PA predictions across plausible magnetic-field geometries, aiding interpretation of polarization measurements from instruments such as POLAR-2 and IXPE and constraining magnetic-field geometry in GRB jets.

Abstract

Polarization is very sensitive to the configuration of the magnetic field in the radiation region. In addition to polarization curve and polarization spectrum, studies of polarization angle (PA) rotation spectrum is also crucial. In this paper, we use a simple parametric magnetic reconnection model with a large-scale aligned magnetic field in the radiation region to study the effects of field orientation on the PA rotations. Under different field orientations, variations of the PA rotation with parameters and the PA rotation spectra are studied. We find that the conclusions obtained in our previous works are almost independent of the field orientations. The area of the parameter space with $Δ$PA $>10^\circ$ will shrink as the value of field orientation ($δ$) increases for $0^\circ<δ<90^\circ$. The $Δ$PA values would be the same for two complementary field orientations. For two particular magnetic field orientations ($δ=0^\circ$ and $90^\circ$), the $Δ$PA would also only be $0^\circ$ or $90^\circ$ within the burst duration.

Figures (1)

• Figure 1: The variations of $\Delta$PA with key parameters and the PA rotation spectra for various $\delta$ values. The (a), (b), (c) panels correspond to the variations of $\Delta$PA with $q$, $\theta_j$ and $\Gamma_0$, respectively. And the (d), (e), (f) panels correspond to the $\Delta$PA spectra with $q=2/3,\,1.2$ and $1.3$, respectively. In each panel, the different colored lines correspond to different $\delta$ values.