Radiation-mediated shocks in gamma-ray bursts: spectral evolution

Radiation-mediated shocks (RMSs) occurring below the photosphere in a gamma-ray burst (GRB) jet could play a crucial role in shaping the prompt emission. In this paper, we study the time-resolved signal expected from such early shocks. We model an internal collision using a 1D special relativistic hydrodynamical simulation, and we follow the photon distributions in the resulting forward and reverse shocks as well as in the common downstream region to well above the photosphere using a designated RMS simulation code. We compute the light curve and time-resolved spectrum of the resulting single pulse taking into account the emission at different optical depths and angles to the line of sight. For the specific case considered, we find a light curve consisting of a short pulse lasting $\sim 0.1~$s for an assumed redshift of $z = 1$, which could constitute a whole short GRB or be a building block within a highly variable longer GRB light curve. The efficiency is large, with $\approx 23$% of the total burst energy being radiated. The spectrum has a complex shape at very early times, after which it settles into a more generic shape with a smooth curvature below the peak energy, $E_p$, and a clear high-energy power law that cuts off at $\sim 5~$MeV in the observer frame. The spectrum becomes narrower and softer at late times with $E_p$ steadily decreasing during the pulse decay from $E_p \approx 250~$keV to $E_p \approx 100~$keV. The low-energy index, $\alpha$, decreases during the bright part of the pulse from $\alpha \approx -0.5$ to $\alpha \approx -1$, although the low-energy part is better fit with a broken power law when the signal-to-noise ratio is high. The high-energy power law is generated by the reverse shock at low optical depths ($\tau < 30$) and has an index that decreases from $\beta \approx -2$ to $\beta \approx -2.4$.