Plasma kinetic effects in relativistic radiation-mediated shocks

Fast shocks that form in optically thick media are mediated by Compton scattering and, if relativistic, pair creation. Since the radiation force acts primarily on electrons and positrons, the question arises of how the force is mediated to the ions which are the dominant carriers of the shock energy. It has been widely thought that a small charge separation induced by the radiation force generates an electric field inside the shock that decelerates the ions. In this paper we argue that, while this is true in subrelativistic shocks which are devoid of positrons, in relativistic radiation mediated shocks (RRMS), which are dominated by newly created $e^{+}{e}^{-}$ pairs, additional coupling is needed, owing to the opposite electric force acting on electrons and positrons. Specifically, we show that dissipation of the ions energy must involve collective plasma interactions. By constructing a multifluid model for RRMS that incorporates friction forces, we estimate that momentum transfer between electrons and positrons (and/or ions) via collective interactions on scales of tens to thousands of proton skin depths, depending on whether friction is effective only between $e^{+}{e}^{-}$ pairs or also between pairs and ions, is sufficient to couple all particles and radiation inside the shock into a single fluid. This leaves open the question of whether in relativistic RMS particles can effectively accelerate to high energies by scattering off plasma turbulence. Such acceleration might have important consequences for relativistic shock breakout signals.

Figure 1

Solutions of the shock equations for frictionless fluids, ${\chi }_{pe}={\chi }_{ee}=0$. Shown are the profiles of the Lorentz factors of protons ($p$), electrons ($e^{-}$) and positrons ($e^{+}$), plotted as functions of the pair-loaded optical depth ${\tau }^{*}$ (a), and the dimensionless electric field $\tilde{E}$ (black line) and positron density ${\tilde{n}}_{+}^{\prime }$ (red dashed line) (b). The inset shows a zoom of the electric field solution.

Figure 2

Solutions obtained for ${\tilde{\chi }}_{pe}={\tilde{\chi }}_{ee}={10}^3$ (upper panels), and ${10}^5$ (lower panels). Panels (a) and (c) display the Lorentz factor profiles of the proton, electron, and positron fluids, and panels (b) and (d) the positron density (red line) and the density of total quanta, ${\tilde{n}}_l^{\prime }=1+{\tilde{n}}_{+}^{\prime }+{\tilde{n}}_{-}^{\prime }$ (black line). The insets in (a) and (c) exhibit the electric field $\tilde{E}$.

Figure 3

Lorentz factors profiles of the proton (black lines), electron (blue lines) and positrons (red lines), obtained for ${\tilde{\chi }}_{pe}=0$ and two values of ${\tilde{\chi }}_{ee}, {10}^6$ (dashed lines) and ${10}^8$ (solid lines). The different curves in the latter case are indistinguishable (all seen as the red solid line between the dashed black and red/blue lines.