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We discuss the issues of stability of accretion disks that may undergo the limit-cycle oscillations due to the two main types of thermal-viscous instabilities. These are induced either by the domination of radiation pressure in the innermost regions close to the central black hole, or by the partial ionization of hydrogen in the zone of appropriate temperatures. These physical processes may lead to the intermittent activity in AGN on timescales between hundreds and millions of years. We list a number of observational facts that support the idea of the cyclic activity in high accretion rate sources. We conclude however that the observed features of quasars may provide only indirect signatures of the underlying instabilities. Also, the support from the sources with stellar mass black holes, whose variability timescales are observationally feasible, is limited to a few cases of the microquasars. Therefore we consider a number of plausible mechanisms of stabilization of the limit cycle oscillations in high accretion rate accretion disks. The newly found is the stabilizing effect of the stochastic viscosity fluctuations.
Several active galactic nuclei and microquasars are observed to eject plasmoids that move at relativistic speeds. We envisage the plasmoids as pre-existing current carrying magnetic flux ropes that were initially anchored in the accretion disk-corona
The exact time-dependent solution is obtained for a magnetic field growth during a spherically symmetric accretion into a black hole (BH) with a Schwarzschild metric. Magnetic field is increasing with time, changing from the initially uniform into a
We present new thermal equilibrium solutions for optically thin and thick disks incorporating magnetic fields. The purpose of this paper is to explain the bright hard state and the bright/slow transition observed in the rising phases of outbursts in
The episodic dynamics of the magnetic eruption of a spinning black hole (BH) accretion disks and its associated intense shapeup of their jets is studied via three-dimensional general-relativistic magnetohydrodynamics (GRMHD). The embedded magnetic fi
We calculate the observable signature of a black hole accretion disk with a gap or hole created by a secondary black hole embedded in the disk. We find that for an interesting range of parameters of black hole masses (~10^6 to 10^9 solar masses), orb