Time-Resolved and Energy-Resolved Polarizations of GRB Prompt Emission

Besides light curves and spectra, polarization provides a different powerful tool of studying the $\gamma-$ray burst (GRB) prompt phase. Compared with the time-integrated and energy-integrated polarization, time-resolved and energy-resolved polarization can deliver more physical information about the emitting region. Here we investigate time-resolved and energy-resolved polarization of GRB prompt emission using the synchrotron models. We find that the equal arrival time surface effect is very important in shaping the PD curves when the physical conditions of emitting region changes violently with radius. Polarization properties are neither correlated with the spectral lag nor the peak energy evolution patterns. Polarization properties with a mixed magnetic field are very similar to those for a corresponding ordered magnetic field but the former has a smaller polarization degree. The emission at the MeV peak can be highly polarized for a synchrotron model while it is unpolarized as predicted by a dissipative photosphere model. Future energy-resolved polarization observations can distinguish between these two models.