Bifurcation, Efficiency, and the Role of Injection in Shock Acceleration with the Bohm Diffusion

Abstract

The efficiency and uniqueness of the diffusive shock acceleration is studied on the basis of the novel kinetic solutions. These solutions obtained earlier (paper I, astro-ph/9707152) selfconsistently describe a strong coupling of cosmic rays with the gas flow. They show that the dependence of the acceleration efficiency upon physical parameters is critical in nature. In this paper we investigate a steady acceleration in the parameter space formed by the injection rate (u ), the upper cut-off momentum p_1 and the Mach number M while the flow compression R serves as an order parameter. We determine a manifold of all possible solutions in this parameter space.