Synchrotron Polarization of a Hybrid Distribution of Relativistic Thermal and Nonthermal Electrons in Gamma-Ray Burst Prompt Emission

Synchrotron polarization of relativistic nonthermal electrons in gamma-ray bursts (GRBs) has been widely studied. However, recent numerical simulations of relativistic shocks and magnetic reconnection have found that a more realistic electron distribution consists of a power-law component plus a thermal component, which requires observational validation. In this paper, we investigate synchrotron polarization using a hybrid energy distribution of relativistic thermal and nonthermal electrons within a globally toroidal magnetic field in GRB prompt emission. Our results show that compared to the case of solely nonthermal electrons, the synchrotron polarization degrees (PDs) in these hybrid electrons can vary widely, depending on different parameters, and that the PD decreases progressively with frequency in the gamma-ray, X-ray, and optical bands. The time-averaged PD spectrum displays a significant bump in the gamma-ray and X-ray bands, with the PDs higher than similar to 60% if the thermal peak energy of the electrons is much smaller than the conjunctive energy of the electrons between the thermal and nonthermal distributions. The high-synchrotron PDs (greater than or similar to 60%) in the gamma-ray and X-ray bands, which generally cannot be produced by solely nonthermal electrons with typical power-law slopes, can be achieved by hybrid electrons and primarily originates from the exponential decay part of the thermal component. Moreover, this model can roughly explain the PDs and spectral properties of some GRBs, where GRB 110301A with a high PD ( 70-22+22% ) may be potential evidence for the existence of relativistic thermal electrons.