A stability analysis of radiative shocks in the presence of a transverse   magnetic field
  Radiative shock waves may be subject to a global thermal instability in which the cooling layer and shock front undergo growing resonant oscillations. For strong hydrodynamic shocks, the presence of the overstability depends on the temperature and density indices of power-law cooling functions and the specific heat ratio, $\alpha$, $\beta$ and $\gamma$, respectively. Here, we investigate the stabilising influence of a transverse magnetic field by introducing the shock Alfv\'en number, $M_a$ as a fourth parameter. We thus investigate the stability criteria for both molecular and atomic shocks under a wide range of conditions. In particular, we find that all molecular shocks in which the cooling increases with the temperature ($\alpha > 0$) are stabilised to the first four modes if $M_a < 20$ ($\beta = 2$). For $\alpha = -0.5$, the first overtone remains stable only for $M_a < 8$. We conclude that molecular shocks in the interstellar medium are probably stabilised by a transverse magnetic field unless exceptional circumstances arise in which the cooling strongly increases as the gas cools. 
Babulakshmanan Ramachandran and Michael D. Smith