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

TL;DR

This paper derives time-dependent analytical solutions for quasi-steady shocks with cooling, compares them with simulations, and highlights the importance of cooling history in shock evolution.

Contribution

It introduces analytical solutions for quasi-steady shocks with cooling and evaluates their accuracy against hydrodynamical simulations.

Findings

Quasi-steady shock solutions differ significantly from adiabatic and steady-state models.

Cooling history critically influences shock trajectory.

Analytical solutions effectively approximate time-dependent shock behavior.

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.