Cosmic ray moderation of the thermal instability

We apply the Hermite-Bieler theorem in the analysis of the effect of cosmic rays on the thermal stability of an initially uniform, static background. The cosmic rays were treated in a fluid approximation and the diffusion coefficient was assumed to be constant in time and space. The inclusion of cosmic rays does not alter the criterion for the thermal stability of a medium subjected to isobaric perturbations. It does alter the criteria for the stability of a medium perturbed by small amplitude sound waves. In the limit of a high background cosmic ray pressure to thermal pressure ratio, the instability in response to high frequency sound waves is suppressed.