Time-integrated polarizations in the prompt phase of gamma-ray bursts via the multi-window interpretation

Aims. We used multi-window observations, including the light curve and evolutions of the spectral peak energy ( E p ), the polarization degree (PD), and the polarization angle (PA), to infer the model parameters for predicting the time-integrated PD in the prompt phase of gamma-ray bursts (GRBs). Methods. We selected 23 GRBs that were codetected by Fermi/GBM and polarization detectors (i.e., GAP, POLAR, and AstroSat). In our multi-window fitting, the light curve, E p curve, PD curve, and PA curve were interpreted simultaneously under the synchrotron radiation model in ordered magnetic fields (i.e., the aligned-field case and the toroidal-field case). Results. For bursts with strong (∼90°) PA rotations, the predicted time-integrated PD of the aligned-field case roughly matches the corresponding observed best-fit value, while it is higher for the toroidal-field case. For bursts without strong (∼90°) PA rotation(s), the predicted PDs of the aligned-field case and the toroidal-field case are comparable and can interpret the observational data equally well. The observed time-resolved and time-integrated PDs for GRB 170206A are comparable and are both lower than our predicted upper limits in ordered magnetic fields. This means that mixed magnetic fields, that is, magnetic fields with both ordered and random components, probably reside in the radiation regions of this burst. Except for one out of the total 23 bursts, the predicted time-integrated PDs, which are ∼44% for the aligned-field case and around 49% for the toroidal-field case, are consistent with the corresponding observed values. Consistent with previous study, the models with synchrotron radiation in ordered magnetic fields can therefore interpret most of the current polarization data within an error bar of 1 σ .