Interpreting time-integrated polarization data of gamma-ray burst prompt emission

Abstract: Aims. With the accumulation of polarization data in the gamma-ray burst (GRB) prompt phase, polarization models can be tested. Methods. We predicted the time-integrated polarizations of 37 GRBs with polarization observation. We used their observed spectral parameters to do this. In the model, the emission mechanism is synchrotron radiation, and the magnetic field configuration in the emission region was assumed to be large-scale ordered. Therefore, the predicted polarization degrees (PDs) are upper limits. Results. For most GRBs detected by the Gamma-ray Burst Polarimeter (GAP), POLAR, and AstroSat, the predicted PD can match the corresponding observed PD. Hence the synchrotron-emission model in a large-scale ordered magnetic field can interpret both the moderately low PDs ($\sim10\%$) detected by POLAR and relatively high PDs ($\sim45\%$) observed by GAP and AstroSat well. Therefore, the magnetic fields in these GRB prompt phases or at least during the peak times are dominated by the ordered component. However, the predicted PDs of GRB 110721A observed by GAP and GRB 180427A observed by AstroSat are both lower than the observed values. Because the synchrotron emission in an ordered magnetic field predicts the upper-limit of the PD for the synchrotron-emission models, PD observations of the two bursts challenge the synchrotron-emission model. Then we predict the PDs of the High-energy Polarimetry Detector (HPD) and Low-energy Polarimetry Detector (LPD) on board the upcoming POLAR-2. In the synchrotron-emission models, the concentrated PD values of the GRBs detected by HPD will be higher than the LPD, which might be different from the predictions of the dissipative photosphere model. Therefore, more accurate multiband polarization observations are highly desired to test models of the GRB prompt phase.