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In this Letter, we suggest that the relativistic protons powering theoutflows emanating from radio-loud systems containing black holes areaccelerated at standing, centrifugally-supported shocks in hot,advection-dominated accretion disks. Such disks are ideal sites for first-orderFermi acceleration at shocks because the gas is tenuous, and consequently themean free path for particle-particle collisions generally exceeds the thicknessof the disk. The accelerated particles are therefore able to avoidthermalization, and as a result a small fraction of them achieve very highenergies and escape from the disk. In our approach the hydrodynamics and theparticle acceleration are coupled and the solutions are obtainedself-consistently based on a rigorous mathematical treatment. The theoreticalanalysis of the particle transport parallels the early studies of cosmic-rayacceleration in supernova shock waves. We find that particle acceleration inthe vicinity of the shock can extract enough energy to power a relativisticjet. Using physical parameters appropriate for M87 and Sgr A*, we confirm thatthe jet kinetic luminosities predicted by the theory agree with theobservational estimates.Comment: accepted for publication in Astrophysical Journal Letter

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