DIFFUSIVE PARTICLE ACCELERATION IN SHOCKED, VISCOUS ACCRETION DISKS: GREEN'S FUNCTION ENERGY DISTRIBUTION

The acceleration of relativistic particles in a viscous accretion disk containing a standing shock is investigated as a possible explanation for the energetic outflows observed around radio-loud black holes. The energy/space distribution of the accelerated particles is computed by solving a transport equation that includes the effects of first-order Fermi acceleration, bulk advection, spatial diffusion, and particle escape. The velocity profile of the accreting gas is described using a model for shocked viscous disks recently developed by the authors, and the corresponding Green's function distribution for the accelerated particles in the disk and the outflow is obtained using a classical method based on eigenfunction analysis. The accretion-driven, diffusive shock acceleration scenario explored here is conceptually similar to the standard model for the acceleration of cosmic rays at supernova-driven shocks. However, in the disk application, the distribution of the accelerated particles is much harder than would be expected for a plane-parallel shock with the same compression ratio. Hence the disk environment plays a key role in enhancing the efficiency of the shock acceleration process. The presence of the shock helps to stabilize the disk by reducing the Bernoulli parameter, while channeling the excess binding energy into the escaping relativistic particles. In applications to M87 and Sgr A*, we find that the kinetic power in the jet is , and the outflowing relativistic particles have a mean energy ∼300 times larger than that of the thermal gas in the disk at the shock radius. Our results suggest that a standing shock may be an essential ingredient in accretion onto underfed black holes, helping to resolve the long-standing problem of the stability of advection-dominated accretion disks.