A Self-Consistent Model for the Formation of Relativistic Outflows in Advection-Dominated Accretion Disks with Shocks

In this Letter, we suggest that the relativistic protons powering the outflows emanating from radio-loud systems containing black holes are accelerated at standing, centrifugally-supported shocks in hot, advection-dominated accretion disks. Such disks are ideal sites for first-order Fermi acceleration at shocks because the gas is tenuous, and consequently the mean free path for particle-particle collisions generally exceeds the thickness of the disk. The accelerated particles are therefore able to avoid thermalization, and as a result a small fraction of them achieve very high energies and escape from the disk. In our approach the hydrodynamics and the particle acceleration are coupled and the solutions are obtained self-consistently based on a rigorous mathematical treatment. The theoretical analysis of the particle transport parallels the early studies of cosmic-ray acceleration in supernova shock waves. We find that particle acceleration in the vicinity of the shock can extract enough energy to power a relativistic jet. Using physical parameters appropriate for M87 and Sgr A*, we confirm that the jet kinetic luminosities predicted by the theory agree with the observational estimates.