Time-dependent analytic solutions of quasi-steady shocks with cooling

Abstract

I present time-dependent analytical solutions of quasi-steady shocks with cooling, where quasi-steady shocks are objects composed of truncated steady-state models of shocks at any intermediate time. I compare these solutions to simulations with a hydrodynamical code and finally discuss quasi-steady shocks as approximations to time-dependent shocks. Large departure of both the adiabatic and steady-state approximations from the quasi-steady solution emphasise the importance of the cooling history in determining the trajectory of a shock.