We study the spectra of photospheric emission from highly relativistic gamma-ray burst outflows using a Monte Carlo ( MC ) code .
We consider the Comptonization of photons with a fast cooled synchrotron spectrum in a relativistic jet with realistic photon to electron number ratio N _ { \gamma } / N _ { e } = 10 ^ { 5 } , using mono-energetic protons which interact with thermalised electrons through Coulomb interaction .
The photons , electrons and protons are cooled adiabatically as the jet expands outwards .
We find that the initial energy distribution of the protons and electrons do not have any appreciable effect on the photon peak energy E _ { \gamma,peak } and the power-law spectrum above E _ { \gamma,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 _ { \gamma,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 \tau _ { in } results in slightly shallower photon spectrum below E _ { \gamma,peak } and fewer photons at the high-energy tail , although f _ { \nu } \propto \nu ^ { -0.5 } above E _ { \gamma,peak } and up to \sim 1 MeV , independent of \tau _ { in } .
We find that E _ { \gamma,peak } determines the peak energy and the shape of the output photon spectrum .
Lastly , we find that our simulation results are quite sensitive to N _ { \gamma } / N _ { e } , for N _ { e } = 3 \times 10 ^ { 3 } .
For almost all our simulations , we obtain an output photon spectrum with power-law tail above E _ { \gamma,peak } extending up to \sim 1 MeV .