Radiation mediated shocks in gamma-ray bursts: Pair creation

Abstract

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 ${\epsilon }_{max}\equiv E_{max}/m_e{c}^2\sim v^2$ 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 $\epsilon \gtrsim 10^{-1}$ due to Klein-Nishina effects, and shocks with $v\gamma \gtrsim 1$, 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 $n_{\gamma }/n_p=2\times 10^5$ has a peak pair-to-proton ratio of $Z_{\pm }\approx 225$. 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 ${\theta }_d\equiv k{T}_d/m_e{c}^2\approx {\epsilon }_d/3$ is reached at an optical depth of $\tau \gg {\theta }_d^{-1}$ behind the shock, where ${\epsilon }_d$ is the average downstream photon energy.

14 pages, 8 figures, submitted to ApJ

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• Relativistic Photon Mediated Shocks
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