Monte Carlo Simulations of the Photospheric Emission in Gamma-Ray Bursts

We studied the decoupling of photons from ultra-relativistic spherically symmetric outflows expanding with constant velocity by means of Monte Carlo simulations. For outflows with finite widths we confirm the existence of two regimes: photon-thick and photon-thin, introduced recently by Ruffini et al. (RSV). The probability density function of the last scattering of photons is shown to be very different in these two cases. We also obtained spectra as well as light curves. In the photon-thick case, the time-integrated spectrum is much broader than the Planck function and its shape is well described by the fuzzy photosphere approximation introduced by RSV. In the photon-thin case, we confirm the crucial role of photon diffusion, hence the probability density of decoupling has a maximum near the diffusion radius well below the photosphere. The time-integrated spectrum of the photon-thin case has a Band shape that is produced when the outflow is optically thick and its peak is formed at the diffusion radius.