Observational characteristics of radiation-mediated shocks in photospheric gamma-ray burst emission

Abstract

Emission from the photosphere in gamma-ray burst (GRB) jets can be substantially affected by subphotospheric energy dissipation, which is typically caused by radiation-mediated shocks (RMSs). We study the observational characteristics of such emission, in particular the spectral signatures. Invoking an internal collision framework to estimate relevant shock initial conditions, we use an RMS model to generate synthetic photospheric spectra. The spectra are then fitted with a standard cutoff power-law (CPL) function to compare with corresponding GRB catalogues. We find mean values and standard deviations for the low-energy index and the peak energy as α cpl = −0.76 ± 0.227 and log(E peak /keV) = 2.42 ± 0.408, respectively. The range of α cpl values obtained cover a substantial fraction of the catalogued values, α cat cpl = −0.80 ± 0.311. This requires that the free fireball acceleration starts at r 0 ∼ 10 10 cm, which is in agreement with hydrodynamical simulations. The CPL function generally provides a good fit, even though the synthetic spectra typically exhibit an additional break at lower energies. We also identify a non-negligible parameter region for what we call "optically shallow shocks": shocks that do not accumulate enough scatterings to reach a steady-state spectrum before decoupling. These occur for optical depths τ 55 u −2 u , where u u = γ u β u ∼ 2 is the dimensionless specific momentum of the upstream as measured in the shock rest frame. We conclude that photospheric emission, which has passed through an RMS, is spectrally consistent with the dominant fraction of observed bursts.