Observational signatures of sub-photospheric radiation-mediated shocks in the prompt phase of gamma-ray bursts

A shock that forms below the photosphere of a gamma-ray burst (GRB) outflow is mediated by Compton scattering of radiation advected into the shock by the upstream fluid. The characteristic scale of such a shock, a few Thomson depths, is larger than any kinetic scale involved by several orders of magnitude. Hence, unlike collisionless shocks, radiation-mediated shocks cannot accelerate particles to nonthermal energies. The spectrum emitted by a shock that emerges from the photosphere of a GRB jet reflects the temperature profile downstream of the shock, with a possible contribution at the highest energies from the shock transition layer itself. We study the properties of radiation-mediated shocks that form during the prompt phase of GRBs and compute the time-integrated spectrum emitted by the shocked fluid following shock breakout. We show that the time-integrated emission from a single shock exhibits a prominent thermal peak, with the location of the peak depending on the shock velocity profile. We also point out that multiple shock emission can produce a spectrum that mimics a Band spectrum.