# Magnetized Reverse Shock: Density-fluctuation-induced Field Distortion, Polarization Degree Reduction, and Application to GRBs

## TL;DR

This paper investigates how density fluctuations in the environment of gamma-ray bursts can distort magnetic fields in reverse shocks, reducing polarization, and proposes a method to estimate the outflow's magnetization parameter from polarization data.

## Contribution

It introduces relativistic MHD simulations of magnetized jets in clumpy media to quantify polarization reduction and relates it to the outflow's magnetization parameter, σ.

## Key findings

- Density fluctuations cause a power-law reduction in polarization degree.
- A relationship between polarization reduction and σ allows estimation of outflow magnetization.
- Simulations demonstrate the impact of environmental inhomogeneities on magnetic field order.

## Abstract

The early optical afterglow emission of several gamma-ray bursts (GRBs) shows a high linear polarization degree (PD) of tens of percent, suggesting an ordered magnetic field in the emission region. The light curves are consistent with being of a reverse shock (RS) origin. However, the magnetization parameter, $\sigma$, of the outflow is unknown. If $\sigma$ is too small, an ordered field in the RS may be quickly randomized due to turbulence driven by various perturbations so that the PD may not be as high as observed. Here we use the "Athena++" relativistic MHD code to simulate a relativistic jet with an ordered magnetic field propagating into a clumpy ambient medium, with a focus on how density fluctuations may distort the ordered magnetic field and reduce PD in the RS emission for different $\sigma$ values. For a given density fluctuation, we discover a clear power-law relationship between the relative PD reduction and the $\sigma$ value of the outflow. Such a relation may be applied to estimate $\sigma$ of the GRB outflows using the polarization data of early afterglows.