THE DENSITY SPIKE IN COSMIC-RAY-MODIFIED SHOCKS - FORMATION, EVOLUTION, AND INSTABILITY

We examine the formation and evolution of the density enhancement (den sity spike) that appears downstream of strong, cosmic-ray-modified sho cks. This feature results from temporary overcompression of the flow b y the combined cosmic-ray shock precursor and gas subshock. Formation of the density spike is expected whenever shock modification by cosmic -ray pressure increases strongly. That occurrence may be anticipated f or newly generated strong shocks, or for strong shocks or cosmic-ray-m odified shocks encountering a region of higher external density, for e xample. The predicted mass density within the spike increases with the shock Mach number and with shocks more dominated by cosmic-ray pressu re. For very strong shocks, the total compression compared to the upst ream gas may approach D(gamma(g) + 1)/(gamma(g) - 1) during the format ion period, where gamma(g) is the gas adiabatic index and D is the com pression ratio through the precursor. As the full shock reaches equili brium, the spike detaches, lags behind the modified shock transition, and is further compressed, so that the density can exceed the limit qu oted above. We find this spike to be linearly unstable under a modifie d Rayleigh-Taylor instability criterion at the early stage of its form ation. Our linear analysis shows that the flow is unstable when the gr adients of total pressure (gas pressure + cosmic-ray pressure) and gas density have opposite signs. We confirm this numerically using two in dependent codes based on the two-fluid model for cosmic-ray transport. These two-dimensional simulations show that the instability grows imp ulsively at early stages and then slows down as the gradients of total pressure and gas density decrease. Flow within the density spike beco mes disordered through the instability. It seems likely that this can significantly increase the local magnetic field beyond compressional e ffects. Observational discovery of this unstable density spike behind shocks, possibly through radio emission enhanced by the amplified magn etic fields, would provide evidence for the existence of strongly cosm ic-ray-modified shock structures.