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

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, σ, of the outflow is unknown. If σ 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 σ values. For a given density fluctuation, we discover a clear power-law relationship between the relative PD reduction and the σ value of the outflow. Such a relation may be applied to estimate σ of the GRB outflows using the polarization data of early afterglows.