Modelling the linear polarization of GRB afterglows across the electromagnetic spectrum

ABSTRACT Linear polarization measurements in the optical band show polarization degrees of a few per cent at late times. Recently, polarization at sub-per-cent level was also detected in radio by ALMA, opening the window for multiwavelength polarimetry and stressing the importance of properly modelling polarization in GRB afterglows across the EM spectrum. We introduce a numerical tool that can calculate the polarization from relativistically moving surfaces by discretizing them to small patches of uniform magnetic field, calculating the polarized emission from each cell assuming synchrotron radiation and summing it to obtain the total degree of polarization. We apply this tool to afterglow shocks with random magnetic fields confined to the shock plane, considering electron radiative cooling. We analyse the observed polarization curves in several wavelengths above the cooling frequency and below the minimal synchrotron frequency and point to the characteristic differences between them. We present a method to constrain the jet opening angle and the viewing angle within the context of our model. Applying it to GRB 021004, we obtain angles of ∼10○ and ∼8○ respectively and conclude that a non-negligible component of radial magnetic field is required to explain the ${\sim}1{{\ \rm per\ cent}}$ polarization level observed 3.5 days after the burst.