Realistic model for the prompt and high latitude emissions in GRBs

There is good observationnal evidence that the Steep Decay Phase (SDP) that is observed in most Swift GRBs is the tail of the prompt emission. The most popular model to explain the SDP is Hight Latitude Emission (HLE). Knowing if the SDP is consistent with HLE would help distinguish between prompt emission models giving rise to HLE and those who do not. We describe the realistic self-consistent model we developped for the prompt emission and its HLE tail, here in the case of internal shocks (IS) only. The prompt emission is modeled as the sum of independent pulses. A single pulse is modeled as emission from an ultra-relativistic thin spherical expanding shell. We obtain analytic expressions for the flux. We find that the observed spectrum is also a Band function, naturally softening with time. The decay of the SDP is initially dominated by the tail of the last pulse, but other pulses can dominate later.