On the linear analysis of unstable radiative shocks

We study the stability properties of strong hydrodynamic shocks and their associated radiative cooling layers. We explore a range of conditions which covers both molecular and atomic gas impacting against a rigid wall. Through a linear analysis employing a cooling function of the form ? ? ? ?T ? and a specific heat ratio of ?, we determine the overstability regime in the parameter space consisting of ?, ? and ?. In general, if ? is sufficiently low, the fundamental mode leads to long-wavelength growing oscillations. For the fundamental mode, we find that values of ? corresponding to molecular hydrodynamics lead to a significantly restricted instability range for ? in comparison with the shocks in a monatomic medium. The conditions for the growth of higher-order modes, however, are relatively unchanged. This predicts that certain molecular shocks are prone to displaying signatures of small-scale rapid variability. Dissociative shocks, however, can be subject to a large-scale overstability if subsequent molecule formation in the cooling layer abruptly increases the cooling rate. In contrast to the dynamical rippling overstability, the cooling overstability is suppressed for a sufficiently low specific heat ratio.