2023MNRAS.523.4583M

We compute the linear polarization during the afterglow phase of gamma-ray bursts, for both on-axis and off-axis observers. We use numerical simulations of the deceleration of a relativistic jet, and compute the polarization by post-processing the results of the numerical simulations. In our simulations, we consider a magnetic field that is chaotic in the plane of the shock, in addition to a magnetic field component that is parallel to the shock velocity. While the linear polarization computed for on-axis observers is consistent with previous analytical estimates, we found that lateral expansion, which is accurately handled in our simulations, plays a crucial role in determining the linear polarization for off-axis observers. Our results show that the off-axis linear polarization, as seen by off-axis observers, exhibits a single peak, in contrast to the two peaks inferred by previous analytical studies. The maximum polarization degree is 40 per cent at an observing angle θ_obs = 0.4 rad, and it decreases as the observing angle increases, which is opposite to that predicted by analytical models, where polarization increases with larger observing angles. From the upper limit of 12 per cent in the linear polarization obtained at 244 d for the GRB 170817A, we also infer an anisotropy factor of B_∥/B_⊥ = 0.5-0.9, consistent with the post-shock magnetic field being amplified by turbulence.