Sub-photospheric, radiation-mediated shocks in gamma-ray bursts: Multiple shock emission and the band spectrum

We compute the time-integrated, thermal emission produced by a series of radiation-mediated shocks that emerge from the photosphere of a gamma-ray burst outflow. We show that for a sufficiently broad distribution of shock strengths, the overall shape of the time-integrated spectral energy distribution below the peak is a power law, νE _ναν^α, with a slope of 1 < α < 2. A substructure in the spectral energy distribution (SED) can also be produced in this model for certain choices of the shock train distribution. In particular, we demonstrate that our model can reproduce the double-peak SED observed in some bursts, in events where a strong shock is followed by a sequence of sufficiently weaker ones.