Impact of the ISM magnetic field on GRB afterglow polarization

Linear polarization has been measured in several gamma-ray burst (GRB) afterglows. After a few days, polarization arises from the forward shock emission that depends on the post-shock magnetic field. The latter can originate both from compression of existing fields, here the interstellar medium (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 θp either remains constant during all the afterglow phase or exhibits variations smaller than the 90° swing expected from a random component solely; (ii) for an off-axis observer, the polarization angle evolves from $\theta _\mathrm{ p}^{\max }$, before the jet break to its opposite after the jet break. We also find that the upper limit polarization for GRB 170817 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.