We present new simulations of GRB photospheric emission that are able to quantitatively reproduce important observational correlations. Two key observational constraints on GRB emission are that the more energetic events are characterized by photons of higher frequency (Amati et al. 2002) and they are produced by outflows with higher velocity (Liang et al. 2012, Ghirlanda et al. 2012). Earlier work indicated that photospheric emission can qualitatively account for the former constraint but is unable to quantitatively reproduce the photon frequency of a burst of given energy. Simulated bursts were found to be softer than their observed counterparts.

Here we report simulations that produce both the observed relations. The key physics not previously captured is that the photospheric spectrum is formed at the surface of last energy exchange between the radiation and the electrons rather than at the surface of last scattering (Giannios 2011). We find that simulated GRBs are relatively insensitive to the details of the progenitor star and injected jet. However, their characteristics are strongly dependent on the angle between the jet axis and the line of sight to the observer. This implies that the observed correlations are mainly due to the polar stratification of the outflow induced by its interaction with the progenitor star. We also find that the radiative efficiency of simulated bursts is correlated to the burst energetics, a prediction that can potentially be tested against observations.