Monte Carlo simulations of the photospheric process

We present a Monte Carlo (MC) code we wrote to simulate the photospheric process and to study the photospheric spectrum above the peak energy. Our simulations were performed with a photon-to-electron ratio N_γ/N_e = 10⁵, as determined by observations of the Gamma-ray Burst prompt emission. We searched an exhaustive parameter space to determine if the photospheric process can match the observed high-energy spectrum of the prompt emission. If we do not consider electron re-heating, we determined that the best conditions to produce the observed high-energy spectrum are low photon temperatures and high optical depths. However, for these simulations, the spectrum peaks at an energy below 300 keV by a factor of ∼10. For the cases we consider with higher photon temperatures and lower optical depths, we demonstrate that additional energy in the electrons is required to produce a power-law spectrum above the peak energy. By considering electron re-heating near the photosphere, the spectra for these simulations have a peak energy ∼300 keV and a power-law spectrum extending to at least 10 MeV with a spectral index consistent with the prompt emission observations. We also performed simulations for different values of Nγ/Ne and determined that the simulation results are very sensitive to N_γ/N_e. Lastly, in addition to Comptonizing a blackbody spectrum, we also simulate the Comptonization of a f_ν ∝ ν^−1/2 fast cooled synchrotron spectrum. The spectrum for these simulations peaks at ∼10⁴ keV, with a flat spectrum f_ν ∝ ν⁰ below the peak energy.