Acoustic instability in cosmic ray mediated shocks

We have examined the acoustic instability in cosmic ray dominated media that can amplify sound waves shorter than the scale height of the cosmic-ray pressure. The effects of the instability on the particle distribution have been studied using a time-dependent numerical method in which the diffusion-advection transport equation for the particle distribution function is solved self-consistently with the hydrodynamic conservation equations. Incident sound waves can grow into shocks in the precursors of strong cosmic ray mediated shocks, so that the gas entropy is increased significantly before shock passage, and the postshock cosmic ray pressure is slightly decreased. Fresh particles can be injected from the gas at the small-scale shocks, even after the initial large-scale shock becomes smooth due to the development of a strong cosmic ray pressure precursor. However, even though the instability can amplify the sound waves into moderately strong gas shocks, the cosmic ray pressure and the particle distribution are not significantly affected by these shocks. This is because diffusion of the cosmic rays causes the perturbation on the particle distribution to be much smaller than those of gasdynamic variables. We suggest the possibility that the amplified small-scale density structures might produce ESE, a class of flux variation observed in some compact radio sources and thought to be caused by scattering or refraction in the intervening interstellar medium.