Time-resolved polarizations of gamma-ray burst prompt emission with observed energy spectra

Time-resolved polarizations carry more physical information about the source of gamma-ray bursts (GRBs) than the time-integrated ones. Therefore, they give more strict constrains on the models of GRB prompt phase. Both time-resolved and time-integrated polarizations are considered here. The model we use is the synchrotron emission in a large-scale ordered aligned magnetic field. Time-resolved polarizations of GRB prompt phase are derived with the corresponding time-resolved energy spectra. We found the time-integrated PDs calculated with two methods are similar. So it is convenient to estimate the time-integrated PD by the time-integrated energy spectrum. Most of the time-resolved PDs calculated in this paper will increase with time. The trend could match the observed time-resolved PD curve of GRB 170114A, but contrary to the predictions of a decaying PD of both the magnetized internal shock and magnetic reconnection models. PAs calculated in this paper, in general, are roughly constants with time. The predicted PAs here can not match with the violent PA changes observed in GRB 100826A and GRB 170114A. Therefore, more accurate time-resolved polarization observations are needed to test models and to diagnose the true physical process of GRB prompt phase.