Observational Characteristics of Radiation-mediated Shocks in Photospheric Gamma-Ray Burst Emission

Abstract

Emission from the photosphere in gamma-ray burst jets can be substantially affected by subphotospheric energy dissipation, which is typically caused by radiation-mediated shocks. We study the observational characteristics of such emission, in particular the spectral signatures. Relevant shock initial conditions are estimated using a simple internal collision framework, which then serve as inputs for a radiation-mediated shock model that generates synthetic photospheric spectra. Within this framework, we find that if the free fireball acceleration starts at r _0 ∼ 10 ^10 cm, in agreement with hydrodynamical simulations, then the typical spectrum consists of a broad, soft power-law segment with a cutoff at high energies and a hardening in X-rays. The synthetic spectra are generally well fitted with a standard cutoff power-law (CPL) function, as the hardening in X-rays is commonly outside the observable energy range of current detectors. The CPL-fits yield values for the low-energy index, α , and the peak energy, E _peak , that are centered around ∼ −0.8 and ∼220 keV, respectively, similar to typical observed values. We also identify a nonnegligible parameter region for what we call optically shallow shocks : shocks that do not accumulate enough scatterings to reach a steady-state spectrum before decoupling and thereby produce more complex spectra. These occur for optical depths $\tau \lesssim 55\,{u}_{u}^{-2}$ , where u _u = γ _u β _u is the dimensionless specific momentum of the upstream as measured in the shock rest frame.

Keywords

• Gamma-ray bursts
• Shocks