Shock Modification by Cosmic-Ray-Excited Turbulences

Toshio Terasawa, Tohru Hada, Shuichi Matsukiyo, Mitsuo Oka, Aya Bamba, Ryo Yamazaki
2007 Progress of Theoretical Physics Supplement  
In cosmic-ray-mediated shocks large amplitude Alfvén waves are believed to be generated by accelerated cosmic ray particles. The enhanced magnetic pressure shared by these waves is non-negligible in the momentum and energy balances across the shock transition region. Accordingly the shock Rankine-Hugoniot condition is further modified, and the compression ratio across the shock departs from the classical values of 4 (nonrelativistic) and 7 (relativistic). We argue that in the 'grand
more » ... 'grand equipartition' limit, namely equipartition among the waves, the background plasma, and the cosmic ray particles, the compression ratio recovers to the value of 4, and the corresponding spectral index of cosmic ray particles also comes back to the canonical value of 2. §1. Physics of cosmic-ray-mediated shocks: an overview In purely hydrodynamic/hydromagnetic shocks, the bulk velocity U and the pressure of the background plasma change abruptly from the upstream values U 1 and P g 1 to the downstream values U 2 and P g 2 ( Fig. 1(a) ). It is widely believed that cosmic ray particles are efficiently accelerated diffusively at shocks in various astrophysical environments, such as supernova remnants (SNRs), etc. In the test particle limit ( Fig. 1(a) ), the cosmic ray pressure P CR increases exponentially toward the shock in the upstream region. Once the nonlinear back reaction of P CR on the shock structure becomes nonnegligible, U and P g change gradually over a spatial scaleD/U 1 of P CR , whereD is the effective diffusion coefficient for cosmic ray particles. 1), 2) Such situation is described in terms of 'cosmic-ray-mediated' shocks (CRMSs). 1)-3) For relatively weak CRMSs ( Fig. 1(b) ), the gradual change from U 1 ends at an intermediate speed U m which is followed by an abrupt jump from U m to U 2 ('subshock'). For stronger CRMSs (Fig. 1(c) ), the two fluid model of CRMSs predicts that the subshock disappears and U smoothly changes from U 1 to U 2 . It is further argued that in these stronger CRMSs the background plasma is adiabatically compressed and that the increase of P g is much less than that of P CR . Since cosmic ray particles behaves as a relativistic gas with a ratio of specific heat γ = 4/3, it is expected that the compression ratio r of strong CRMSs becomes as high as 7 instead of 4 for nonrelativistic gases with γ = 5/3. Since the scattering mean free path λ CR of cosmic ray particles usually becomes longer as their energy increases, the higher energy particles 'feel' the larger velocity
doi:10.1143/ptps.169.146 fatcat:6yn4vc3gqzaalj3quv5hefltxm