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 ∼ 1010 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 τ ≲ 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.

Ending the prompt phase in photospheric models of gamma-ray bursts

“…with γ = 0.1−0.5. The efficiency can be large if dissipation takes place close to the photospheric radius (Beloborodov 2010;Gottlieb et al 2019;Samuelsson & Ryde 2023). Although the efficiency could very well vary during the ESD, here we kept it constant for simplicity.…”

“…which is very short unless Γ is small or ĖK or f is huge (see e.g. Dereli-Bégué et al 2022;Samuelsson & Ryde 2023).…”

Radiation-mediated shocks in GRB prompt emission

“…We model the RMS using the Kompaneets RMS Approximation [KRA, 9,10]. The numerical code that implements the KRA is called Komrad.…”

Subphotospheric Emission from Short Gamma-Ray Bursts: Protons Mold the Multimessenger Signals

“…In order to obtain gamma-ray spectra compatible with observations, dissipative effects below the photosphere are required. Among the typically invoked processes are synchrotron and inverse Compton radiation from a nonthermal lepton population (Pe'er et al 2006;Giannios 2008;Vurm et al 2013;Vurm & Beloborodov 2016;Bhattacharya & Kumar 2020), radiation-mediated shocks (Bromberg et al 2011;Lundman & Beloborodov 2021;Samuelsson & Ryde 2022), and protonneutron (pn) collisions induced as neutrons drift with respect to the proton flow in the jet (Beloborodov 2010;Vurm et al 2011). While much work on these scenarios has been carried out relying on analytical outflow models, the effects of dissipative processes on the photon spectra remain to be demonstrated in consistent numerical simulations (e.g., as performed with a Monte Carlo approach in Ito et al 2015;Parsotan et al 2018;Ito et al 2021Ito et al , 2023.…”