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

A 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. The time evolution of debris gas around a black hole with mass $M = 10^{6} M_\odot$ is studied by performing axisymmetric, two-dimensional radiation hydrodynamic simulations. We assume the $\alpha$ -prescription of viscosity, in which the viscous stress is proportional to the total pressure. The mass supply rate from the outer boundary was assumed to be ${\dot M}_{\rm supply} = 100 L_{\rm Edd}/c^2$ , 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 on a timescale of one day. The sudden drop of the X-ray flux observed in Swift J1644 $+$ 57 in 2012 August 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, the accumulation of 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) d after the X-ray darkening. We expect that if $\alpha \gt $ 0.01, X-ray emission with luminosity $\gtrsim 10^{44}$ erg s $^{-1}$ and jet ejection will revive in Swift J1644 $+$ 57 in 2013–2014.