New paper: Radiation mediated shocks in gamma-ray bursts: Pair creation

Sub-photospheric shock dissipation is one of the main proposed mechanisms for producing the prompt gamma-ray burst (GRB) emission. Such shocks are mediated by scattering of radiation. We introduce a time dependent, special relativistic code which dynamically couples Monte Carlo radiative transfer to the flow hydrodynamics. The code also self-consistently implements electron-positron pair production and annihilation. We simulate shocks with properties relevant for GRBs and study the steady-state solutions, which are accurate deep below the jet photosphere. The shock generates a power-law photon spectrum through the first-order Fermi mechanism, extending upwards from the typical upstream photon energy. Strong shocks (for which the downstream pressure is much larger than the upstream pressure) have rising \(\nu F_\nu\) shock spectra. The spectrum extends up to \(\epsilon_\mathrm{max}\equiv E_\mathrm{max}/m_ec^2\sim v^2\) for non-relativistic shocks, where \(m_e\) is the electron rest mass and \(v\) is the relative speed between the upstream and downstream in units of the speed of light \(c\). For mildly relativistic shocks the power law softens at \(\epsilon\geq10^{-1}\) due to Klein-Nishina effects, and shocks with \(v\gamma\ge1\), where \(\gamma\equiv(1-v^2)^{-1/2}\), produce electron-positron pairs. As an example, a strong shock with \(v\gamma=3\) and a photon-to-proton ratio of \(n_\gamma/n_p=2\times10^5\) has a peak pair-to-proton ratio of \(Z_\pm\approx225\). The main effect of pairs in a steady-state shock is to decrease its spatial width by a factor of \(\sim Z_\pm\). The post-shock spectrum thermalizes in the downstream. In absence of emission and absorption processes, kinetic equilibrium at temperature \(\theta_d\equiv kT_d/m_ec^2\approx \epsilon_d/3\) is reached at an optical depth of \(\tau\gg\theta_d^{-1}\) behind the shock, where \(\epsilon_d\) is the average downstream photon energy. The paper on arXiv.