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 $N_{ \gamma}/N_{ e} = 10^{ 5}$, as determined by observations of the GRB 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 $\sim 10$. 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 spectrum for these simulations have a peak-energy $\sim \mbox{ 300 keV}$ 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 $N_{ \gamma}/N_{ e}$ and determined that the simulation results are very sensitive to $N_{ \gamma}/N_{ e}$. Lastly, in addition to Comptonizing a Blackbody spectrum, we also simulate the Comptonization of a $f_{ \nu} \propto \nu^{ -1/2}$ fast cooled synchrotron spectrum. The spectrum for these simulations peaks at $\sim 10^{ 4} \mbox{ keV}$, with a flat spectrum $f_{ \nu} \propto \nu^{ 0}$ below the peak energy.
Categories: astro-ph.HE