Recurrent Outbursts and Jet Ejections Expected in Swift J1644+57: Limit-Cycle Activities in a Supermassive Black Hole

The tidal disruption event by a supermassive black hole in Swift J1644+57 can trigger limit-cycle oscillations between a supercritically accreting X-ray bright state and a subcritically accreting X-ray dim state. Time evolution of the debris gas around a black hole with mass $M=10^{6} {MO}$ is studied by performing axisymmetric, two-dimensional radiation hydrodynamic simulations. We assumed the $alpha$-prescription of viscosity, in which the viscous stress is proportional to the total pressure. The mass supply rate from the outer boundary is assumed to be ${dot M}_{rm supply}=100L_{rm Edd}/c^2$, where $L_{rm Edd}$ is the Eddington luminosity, and $c$ is the light speed. Since the mass accretion rate decreases inward by outflows driven by radiation pressure, the state transition from a supercritically accreting slim disk state to a subcritically accreting Shakura-Sunyaev disk starts from the inner disk and propagates outward in a timescale of a day. The sudden drop of the X-ray flux observed in Swift J1644+57 in August 2012 can be explained by this transition. As long as ${dot M}_{rm supply}$ exceeds the threshold for the existence of a radiation pressure dominant disk, accumulation of the accreting gas in the subcritically accreting region triggers the transition from a gas pressure dominant Shakura-Sunyaev disk to a slim disk. This transition takes place at $t {sim}~50/({alpha}/0.1)$ days after the X-ray darkening. We expect that if $alpha > 0.01$, X-ray emission with luminosity $gtrsim 10^{44}$ ${rm erg}{cdot}{rm s}^{-1}$ and jet ejection will revive in Swift J1644+57 in 2013--2014.