The hardness-intensity correlation of photospheric emission from a structured jet for gamma-ray bursts

For many gamma-ray bursts (GRBs), hardness-intensity correlation (HIC) can be described by a power-law function, E-p proportional to F-kappa, where E-p is the peak energy of nu F-nu 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 kappa < 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 similar to 1/2 in the distribution of observed kappa 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 alpha than that in the unsaturated regime, and naturally reproduce anticorrelation in alpha - E-p in a GRB pulse.

Automated summary

This paper studies the hardness-intensity correlation (HIC) of photospheric emissions from a structured jet in different regimes. The findings suggest that positive kappa values less than 1/4 can be observed in an intermediate photosphere, and can be generalized to other cases. Additionally, the emissions from the intermediate photosphere have a smaller low-energy photon index compared to the unsaturated regime, and can naturally reproduce the anticorrelation in alpha - E-p in GRB pulses.