Multi-wavelength Emission of Gamma-ray Burst Prompt Phase. I. Time-resolved and Time-integrated Polarizations

The time-integrated polarization degree (PD) at prompt optical band of gamma-ray burst (GRB) was predicted to be less than $20\%$, while the time-resolved one can reach as high as $75\%$ in photosphere model. Polarizations in optical band during GRB prompt phase had not been studied under framework of the magnetic reconnection model. Here, a three-segment power laws of the energy spectrum is used to reconstruct the Stokes parameters of the magnetic reconnection model. The multi-wavelength light curves and polarization curves from the optical band to MeV gamma-rays in GRB prompt phase are studied. We found depending mainly on the jet dynamics there is a long lasting high PD phase at all calculated energy bands for the typical parameter sets. The time-resolved PD could be as high as $50\%$, while the time-integrated one is roughly $17\%$) in optical band. It can reach $60\%$ for the time-resolved PD in X-rays and the time-integrated one is around $(30-40)\%$. The polarization angle (PA) evolution is random in both optical and gamma-ray bands for the photosphere model, while it is roughly a constant in the synchrotron models. Therefore, future time-resolved PA observations in the prompt optical or gamma-ray band could distinguish between the photosphere and the synchrotron models.