Monte Carlo simulations of the photospheric emission in GRBs
  We studied the decoupling of photons from ultra-relativistic spherically
symmetric outflows expanding with constant velocity by means of Monte-Carlo
(MC) simulation. For outflows with finite width we confirm the existence of two
regimes: photon thick and photon thin introduced recently by Ruffini, Siutsou,
Vereshchagin (2011), hereafter RSV. The probability density function of photon
last scattering is shown to be very different in these two cases. We also
obtained spectra as well as light curves. In 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. Its spectrum has Band shape. It is produced when the
outflow is optically thick and its peak is formed at diffusion radius.
