Numerical simulations of polarisation in gamma-ray burst afterglows

We compute the linear polarisation 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 polarisation 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 polarisation 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 polarisation for off-axis observers. Our results show that the off-axis linear polarisation, as seen by off-axis observers, exhibits a single peak, in contrast to the two peaks inferred by previous analytical studies. The maximum polarisation degree is 40 per cent at an observing angle θobs = 0.4 rad, and it decreases as the observing angle increases, which is opposite to what predicted by analytical models, where polarisation increases with larger observing angles. From the upper limit of 12 per cent in the linear polarisation obtained at 244 days 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.