On the Low Energy Photon Spectral Index and Epeak evolution of Photosphere Model of GRBs

Author: Wei Deng

Abstract: Gamma-ray burst (GRB) spectra are typically described by a smoothly connected broken power law named as "Band" function. The observed typical low energy photon spectral index is α ∼ -1. Theoretically it is challenging to reproduce this value. One popular model for GRB prompt emission is to invoke emission from a dissipative photosphere. The difficulty has been that the predicted low energy photon spectral index is too hard due to the thermal nature of the photosphere emission. It has been speculated that some effects, such as the high latitude emission effect and the temporal smearing effect, may soften the spectrum to make a closer to -1. We perform a detailed analysis of the photosphere emission spectrum by introducing progressively complicated scenarios which finally include probability distribution of photosphere, superposition from all emission layers including on-axis and high-latitude composition, tracing the real finite outer boundary evolution of optical depth and probability function, different initial wind luminosity profile and so on. Based on the results we address how these effects modify the observed spectrum from blackbody and whether the photosphere model can interpret the data. We find that for uniform outflow, during the increasing time interval of initial wind luminosity, The spectrum index below Epeak can only be modified to be around Fν ∼ ν1.5 corresponding to α ∼ 0.5. While during the decreasing time interval of initial wind luminosity, The spectrum index below Epeak can become even smaller depending on the decreasing slope of luminosity. If the decreasing slope of luminosity is steep enough. The spectrum can become high-latitude dominate and reach Fν ∼ ν0 α ∼ corresponding to -1. We also study the evolution of Epeak. We can get either negative correlation (hard-to-soft) or positive correlation (tracing) between Epeak and luminosity profile, which depends on the relationship between dimensionless entropy and initial wind luminosity (η = Lwm). The critical value to separate the two different situation is m=5/32.