Monte Carlo Simulations of Photospheric Emission in Relativistic Outflows

We study the spectra of photospheric emission from highly relativistic gamma-ray burst outflows using a Monte Carlo code. We consider the Comptonization of photons with a fast-cooled synchrotron spectrum in a relativistic jet with a realistic photon-to-electron number ratio {N}_γ /{N}_{{e}}={10}⁵, using mono-energetic protons that interact with thermalized electrons through Coulomb interaction. The photons, electrons, and protons are cooled adiabatically as the jet expands outward. We find that the initial energy distributions of the protons and electrons do not have any appreciable effect on the photon peak energy {E}_{γ ,{peak}} and the power-law spectrum above {E}_{γ ,{peak}}. The Coulomb interaction between the electrons and the protons does not affect the output photon spectrum significantly as the energy of the electrons is elevated only marginally. {E}_{γ ,{peak}} and the spectral indices for the low- and high-energy power-law tails of the photon spectrum remain practically unchanged even with electron-proton coupling. Increasing the initial optical depth {τ }_{in} results in a slightly shallower photon spectrum below {E}_{γ ,{peak}} and fewer photons at the high-energy tail, although {f}_ν \propto {ν }^-0.5 above {E}_{γ ,{peak}} and up to ∼1 MeV, independent of {τ }_{in}. We find that {E}_{γ ,{peak}} determines the peak energy and the shape of the output photon spectrum. Finally, we find that our simulation results are quite sensitive to {N}_γ /{N}_{{e}}, for {N}_{{e}}=3× {10}³. For almost all our simulations, we obtain an output photon spectrum with a power-law tail above {E}_{γ ,{peak}} extending up to ∼1 MeV.