2022MNRAS.512.5693S

For many gamma-ray bursts (GRBs), hardness-intensity correlation (HIC) can be described by a power-law function, E_p ∝ F^κ, where E_p is the peak energy of νF_ν spectrum, and F is the instantaneous energy flux. In this paper, HIC of the non-dissipative photospheric emission from a structured jet is studied in different regimes. An intermediate photosphere, which contains both of unsaturated and saturated emissions is introduced, and we find positive κ < 1/4 in this case. The same conclusion could be generalized to the photospheric emission from a hybrid jet without magnetic dissipations, or that with sub-photospheric magnetic dissipations and fully thermalized. This may imply that the contribution peaking at ∼1/2 in the distribution of observed κ are mainly from the prompt emission of GRBs with synchrotron origin. Besides, emissions of the intermediate photosphere could give a smaller low-energy photon index α than that in the unsaturated regime, and naturally reproduce anticorrelation in α - E_p in a GRB pulse.