Afterglow Linear Polarization Signatures from Shallow GRB Jets: Implications for Energetic GRBs

TL;DR

This paper develops a semi-analytical model to analyze afterglow polarization signatures of shallow GRB jets, revealing lower polarization levels than classical models and providing tools to interpret observations like GRB 221009A.

Contribution

It introduces a new analytical framework for afterglow polarization in shallow jets, linking polarization peaks to jet structure and viewing angles, and applies it to real GRB data.

Findings

Lower polarization in shallow jets compared to top-hat models

Analytical expression for peak polarization degree based on jet parameters

Early-time polarization can distinguish jet structures and magnetization

Abstract

Gamma-ray bursts (GRBs) are powered by ultra-relativistic jets. The launching sites of these jets are surrounded by dense media, which the jets must cross before they can accelerate and release the high energy emission. Interaction with the medium leads to the formation of a mildly relativistic sheath around the jet resulting in an angular structures in the jet's asymptotic Lorentz factor and energy per solid angle, which modifies the afterglow emission. We build a semi-analytical tool to analyze the afterglow light curve and polarization signatures of jets observed from a wide range of viewing angles, and focus on ones with slowly declining energy profiles known as shallow jets. We find overall lower polarization compared to the classical top-hat jet model. We provide an analytical expression for the peak polarization degree as a function of the energy profile power-law index, magnetic field configuration and viewing angle, and show that it occurs near the light curve break time for all viewers. When applying our tool to GRB 221009A, suspected to originate from a shallow jet, we find that the suggested jet structures for this event agree with the upper limits placed on the afterglow polarization in the optical and X-ray bands. We also find that at early times the polarization levels may be significantly higher, allowing for a potential distinction between different jet structure models and possibly constraining the magnetization in both forward and reverse shocks at that stage.