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The Gravo-Magneto Limit Cycle in Accretion Disks

Previous theoretical studies have found that repeating outbursts can occur in certain regions of an accretion disk, due to sudden transitions in time from gravitationally produced turbulence to magnetically produced turbulence. We analyze the disk evolution in a state diagram that plots the mass accretion rate versus disk surface density. We determine steady state accretion branches that involve gravitational and magnetic sources of turbulence. Using time-dependent numerical disk simulations, we show that cases having outbursts track along a nonsteady 'dead zone' branch and some steady state accretion branches. The outburst is the result of a rapid inter-branch transition. The gravo-magneto outbursts are then explained on this diagram as a limit cycle that is analogous to the well-known S-curve that has been applied to dwarf nova outbursts. The diagram and limit cycle provide a conceptual framework for understanding the nature of the outbursts that may occur in accretion disks of all scales, from circumplanetary to protoplanetary to AGN accretion disks.