Cheng Kangfa, Mao Jirong, Zhao Xiaohong, Liu Hongbang, Chen Zhegeng, Yu Gaojin, Chen Zhifu

Synchrotron circular polarization of a non-thermal power-law electron distribution in gamma-ray bursts (GRBs) has been studied. However, some numerical simulations have shown that the resulting distribution of electrons is a combination of a thermal component and a non-thermal power-law component. In this paper, we investigate synchrotron circular polarization using such a hybrid energy distribution of relativistic thermal and nonthermal electrons within a globally toroidal magnetic field in GRB prompt optical emission. Our results show that compared to the solely nonthermal electron model, the synchrotron circular polarization degree (PD) in the hybrid electron model can vary widely in the optical band, depending on different parameters. The lower the electron temperature, the higher the circular PD. The time-averaged circular PD in the hybrid electron model can be higher than $\sim 1\%$ when the electron temperature is as low as $\sim 10^{10}$ K, while in the solely nonthermal electron model is usually lower than $\sim 1\%$. We further calculate the radiative transfer of the circular and linear polarization in the optical band. Our results show that both of the circular and linear PDs decrease with the increase of optical depth, but the linear PDs decline faster than the circular PDs. To further examine the physical mechanisms of both radiation and particle acceleration, we expect that instruments will be capable of measuring the circular polarization of GRB prompt optical emission in the future.