Fluid simulations of cosmic ray-modified shocks

ABSTRACT Cosmic ray (CR)-modified shocks are a demanding test of numerical codes. We use them to and validate the two-moment method for CR hydrodynamics, as well characterize realism shock acceleration in two-fluid simulations which inevitably arises. Previously, codes were unable incorporate streaming this regime, have never been compared against analytic solutions. First, we find new solution highly discrepant efficiency from standard solution. It arises bi-directional CRs away subshock, similar Zeldovich spike radiative shocks. Since fewer diffuse back upstream, favours much lower efficiency, typically ${\lesssim}10{{\ \rm per\ cent}}$ (even Mach number > 10) opposed ${\gtrsim}50{{\ found previous work. At ≳10, bifurcates into three branches, with efficient, intermediate, inefficient acceleration. Our code accurately recovers these solutions across entire parameter space probed, no ad hoc closure relations. For generic initial conditions, branch is robustly chosen by code; intermediate unstable. The preferred very weakly modified CRs. high numbers (≳10), gas jump conditions approach that purely hydrodynamic shock, sub-grid prescription thermal injection required reasonable efficiencies ${\sim}10{{\ cent}}$. CR-modified long equilibration times (∼1000 diffusion time) develop precursor, must be resolved ≳10 cells convergence. Non-equilibrium effects, poor resolution, obliquity magnetic field all reduce efficiency. Shocks galaxy-scale will generally contribute little without modification.