Synchrotron Polarization of Gamma-Ray Burst Afterglow Shocks with Hydrodynamic-scale Turbulent Magnetic Field

Abstract

Afterglows of gamma-ray bursts (GRBs) are emitted from expanding forward shocks, which are expected to have magnetic fields much stronger than the interstellar field, although the origin of the field is a long-standing problem. Two field amplification mechanisms, plasma kinetic instabilities and magnetohydrodynamic instabilities, have been discussed so far. The coherence-length scales of the fields amplified by these two processes are different by 7–10 orders of magnitude, and the polarimetric observations may distinguish them. We construct a semi-analytic model of the forward-shock afterglow polarization under the assumption of hydrodynamic-scale turbulent magnetic field. We perform numerical calculations of synchrotron polarization for the isotropic turbulence and the zero viewing angle. We find that the polarization degrees are ∼1% when the field coherence-length scale in the fluid co-moving frame is of the order of the thickness of the shocked regions. This range of polarization degree is comparable to that of the observed late-phase optical afterglows. Our model also shows that the radio polarization degrees are comparable to the optical ones on average but can be higher than the optical ones at some time intervals. The polarization angles are shown to vary randomly and continuously. These polarimetric properties are clearly different from the case of plasma kinetic instability. Simultaneous polarimetric observations of GRB afterglows at the radio and optical bands have recently started, which will help us constrain the magnetic field amplification mechanism.

The IXPE View of GRB 221009A

“…Observations of polarization in the afterglow phase can also provide insight into jet physics and structure (Rossi et al 2004). Models in the literature (Kuwata et al 2023) predict a progressive loss of coherence of the propagating jet magnetic fields, which results in an expected low PD (below 5%-3%) of the late phases of the GRB afterglow emission. These predictions are largely consistent with results from time-resolved GRB afterglow measurements of optical polarization (Mundell et al 2013;Covino & Gotz 2016;Stringer & Lazzati 2020).…”