Linear analysis of an oscillatory instability of radiative shock waves

A linear stability analysis of a planar radiative shock structure is presented that is applicable both to accretion onto compact objects and to radiative shock waves in the interstellar medium. The cooling function of the shock is directly proportional to temperature raised to the power alpha. An oscillatory instability similar to that found in numerical calculations of accretion onto degenerate dwarfs is investigated, and it is shown that multiple modes of oscillation are possible. Oscillation frequencies are determined, along with the values of alpha for which the various modes are unstable. It is concluded that the instability may explain why steady-state shock-wave models cannot reproduce certain observations of old supernova remnants and Herbig-Haro objects.