Instability of the Density Spike in the Evolution of Cosmic-Ray modified Shocks

Details Instability of the Density Spike in the Evolution of Cosmic-Ray modified Shocks Instability of the Density Spike in the Evolution of Cosmic-Ray modified Shocks

May 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aas...188.0715j&link_type=abstract

American Astronomical Society, 188th AAS Meeting, #07.15; Bulletin of the American Astronomical Society, Vol. 28, p.834

Astronomy and Astrophysics

Astronomy

Scientific paper

We study the formation mechanism and evolution of the density enhancement (density spike) that appears downstream during the evolution of cosmic-ray modified shocks. The density spike results from double compression of the flow by the cosmic-ray precursor and the gas subshock as the cosmic-ray pressure modifies the gas shock. Density in this over-compressed region increases as Mach number increases. Theoretically, the spike's maximum density can be as high as 16 for gamma_g = gamma_c = 5/3, and 28 for gamma_g = 5/3 and gamma_c = 4/3, where gamma_g and gamma_c are the adiabatic index for gas and cosmic-rays, respectively. As the shock structure reaches a steady state, the density spike lags behind and is further compressed. Consequently, the density can be higher than 16 for gamma_c = 5/3. We found that this density spike is unstable under the modified Rayleigh-Taylor instability criterion. Our linear analysis shows that the flow is unstable when the gradients of total pressure (gas pressure + cosmic-ray pressure) and gas density have opposite signs. The growth of the instability is followed by two-dimensional numerical simulations by solving the two-fluid equations. It grows impulsively at early stage and decays afterward. This region can become turbulent. The appearance of the density spike is common whenever the shock becomes cosmic-ray modified, and whenever a cosmic-ray modified shock undergoes a period of enhanced particle acceleration. That can happen, for example, if the shock encounters a dense interstellar cloud. Therefore, observational discovery of this unstable density spike, possibly through strong radio emission (due to amplified magnetic field by the instability), will provide evidence for the diffusive shock acceleration of cosmic-ray particles and the existence of cosmic-ray modified shock structures. This work is supported by the NSF, by NASA and by the Univesity of Minnesota Supercomputer Institute.

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