Rotation of Polarization Angle in Gamma-Ray Burst Prompt Phase. II. 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 has rarely been 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 the GRB prompt phase. We find that the half-opening angle of the jet θ j , the observational angle θ V , and the bulk Lorentz factor Γ all have significant impacts on the PA rotations. The PA rotations are affected by the product value of θ j Γ 0 (Γ 0 is the normalization factor of Γ with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Γ</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>r</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msup> </mml:math> ), but are roughly independent of the concrete values of both θ j and Γ 0 . For the typical parameters, the changes of the PA within T 90 (△PA) would be within (12°, 66°) 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 &gt; 10° becomes smaller with the increase of the product value of θ j Γ 0 . The most significant PA rotation with △PA ∼ 90° will happen when θ j Γ 0 &gt; 50 and 1.0 &lt; q ≤ 1.2.