Abstract
ABSTRACT For many gamma-ray bursts (GRBs), hardness–intensity correlation (HIC) can be described by a power-law function, Ep ∝ Fκ, where Ep is the peak energy of νFν 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 − Ep in a GRB pulse.
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