Impact of the ISM magnetic field on GRB afterglow polarization

Abstract

Linear polarization has been measured in several GRB afterglows. After a few days, polarization arises from the forward shock emission which depends on the post-shock magnetic field. The latter can originate both from compression of existing fields, here the ISM magnetic field, and from shock generated instabilities. For short GRBs, previous modelling of the polarization arising from the forward shock considered a random field fully or partially confined to the shock plane. However, the ISM magnetic field likely consists of both random and ordered components. Here we study the impact of a more realistic magnetic field having both ordered and random components. We present our semi-analytical model and compute polarization curves arising for different magnetic field configurations. We find that the presence of an ordered component, even significantly weaker than the random one, has distinct signatures that could be detectable. In the presence of an ordered component not in the observer plane, we show that: i) for an observer inside the jet, the polarization angle $\theta_p$ either remains constant during all the afterglow phase or exhibits variations smaller than the 90\textdegree swing expected from a random component solely, ii) for an observer outside the jet, the polarization angle evolves from $\theta_p^{\max}$, before the jet break to its opposite after the jet break. We also find that the upper limit polarization for GRB170817 requires a random field not fully confined to the shock plane and is compatible with an ordered component as large as half the random one.