Modeling the Linear Polarization of GRB Afterglows Across the Electromagnetic Spectrum

TL;DR

This paper develops a numerical model to calculate and analyze the polarization of GRB afterglows across the electromagnetic spectrum, considering relativistic effects and magnetic field configurations.

Contribution

It introduces a new computational tool for modeling polarization in GRB afterglows, incorporating relativistic motion, magnetic field geometry, and electron cooling effects.

Findings

Polarization varies across wavelengths and time, influenced by magnetic field structure.

Constraints on jet and viewing angles can be derived from polarization data.

A radial magnetic field component is necessary to explain observed polarization levels.

Abstract

Linear polarization measurements in the optical band show polarization degrees of a few percent at late times. Recently, polarization at sub-percent level was also detected in radio by ALMA, opening the window for multi-wavelength polarimetry and stressing the importance of properly modeling 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 analyze 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 degrees respectively and conclude that a non-negligible component of radial magnetic field is required to explain the 1% polarization level observed 3.5 days after the burst.