Energetic particle acceleration in spherically symmetric accretion flows and shocks

Steady state, spherically symmetric solutions of the cosmic-ray transport equation describing the acceleration of energetic particles in galactic accretion flows onto neutron stars, black holes, white dwarfs, and protostars are studied. The results indicate that astrophysical accretion flows can be partitioned into distinct classes depending upon whether the accretion rate lies above or below a critical value of a few times 10 to the -7th stellar masses/yr. When the particle transport is convection-dominated, both classes of accretion flows exhibit a spectral index appropriate for first-order Fermi acceleration at a plane shock in the absence of losses. As the particle transport becomes diffusion-dominated, both classes show a break and precipitous falloff in the particle spectrum due to the escape of these particles from the accretion flow. The precise nature of the spectrum depends on the relationship between the particle momentum and the spatial diffusion coefficient.