Time-integrated Polarization of Structured Jets in Gamma-Ray Burst Prompt Emission

Abstract The structure of gamma-ray burst (GRB) jets remains one of the most significant open questions in high-energy astrophysics. Observations of events like GRB 170817A, associated with gravitational waves, and the exceptionally bright GRB 221009A suggest that jets may be structured rather than uniform. Polarization studies offer a powerful tool to probe jet structures, complementing traditional spectral analyses. This study examines the polarization degree (PD) of two types of structured jets under different magnetic field configurations (MFCs). The first type features a core with constant energy per unit solid angle, transitioning to a power-law decay at the edges. The second type exhibits a continuous decay of both energy per unit solid angle and Lorentz factor, controlled by a decay index. Additionally, motivated by jet-ambient medium interactions, we introduce a structured magnetic field model: the jet core region is dominated by an ordered magnetic field, while the ratio of ordered to random field strengths in the jet outer region follows a power-law decay. The results show that structured jets with ordered magnetic fields exhibit higher PD than uniform jets, especially when viewed off-axis, while random magnetic fields have minimal impact on structured jet PD. The PD difference between on-axis and off-axis observations decreases for jets with a shallow decay index, contrasting with uniform jets. If observed, PD shows little variation with fluence ratio, which strongly indicates a structured jet. Furthermore, within the structured magnetic field framework, random fields generally suppress polarization, but the random MFC can enhance off-axis polarization to some extent.