2012ApJ...748...63B

An accreting massive black hole (MBH) in a galactic nucleus is surrounded by a dense stellar cluster. We analyze and simulate numerically the evolution of a thin accretion disk due to its internal viscous torques, due to the frame-dragging torques of a spinning MBH (the Bardeen-Petterson effect), and due to the orbit-averaged gravitational torques by the stars (resonant relaxation). We show that the evolution of the MBH mass accretion rate, the MBH spin growth rate, and the covering fraction of the disk relative to the central ionizing continuum source, are all strongly coupled to the stochastic fluctuations of the stellar potential via the warps that the stellar torques excite in the disk. These lead to fluctuations by factors of up to a few in these quantities over a wide range of timescales, with most of the power on timescales ≳ (M_•/M_d)P(R_d), where M_• and M_d are the masses of the MBH and disk, and P is the orbital period at the disk's mass-weighted mean radius R_d. The response of the disk is stronger the lighter it is and the more centrally concentrated the stellar cusp. As proof of concept, we simulate the evolution of the low-mass maser disk in NGC 4258 and show that its observed O(10°) warp can be driven by the stellar torques. We also show that the frame dragging of a massive active galactic nucleus disk couples the stochastic stellar torques to the MBH spin and can excite a jitter of a few degrees in its direction relative to that of the disk's outer regions.