Long-term evolution of supercritical black hole accretion with outflows:
  a subgrid feedback model for cosmological simulations
  We study the long-term evolution of the global structure of axisymmetric
accretion flows onto a black hole (BH) at rates substantially higher than the
Eddington value ($\dot{M}_{\rm Edd}$), performing two-dimensional
hydrodynamical simulations with and without radiative diffusion. In the
high-accretion optically-thick limit, where the radiation energy is efficiently
trapped within the inflow, the accretion flow becomes adiabatic and comprises
of turbulent gas in the equatorial region and strong bipolar outflows. As a
result, the mass inflow rate decreases toward the center as $\dot{M}_{\rm
in}\propto r^{p}$ with $p\sim 0.5-0.7$ and a small fraction of the inflowing
gas feeds the nuclear BH. Thus, super-Eddington accretion is sustained only
when a larger amount of gas is supplied from larger radii at $>
100-1000~\dot{M}_{\rm Edd}$. The global structure of the flow settles down to a
quasi-steady state in millions of the orbital timescale at the BH event
horizon, which is $> 10-100$ times longer than that addressed in previous
(magneto-)RHD simulation studies. Energy transport via radiative diffusion
accelerates the outflow near the poles in the inner region but does not change
the overall properties of the accretion flow compared to the cases without
diffusion. Based on our simulation results, we provide a mechanical feedback
model for super-Eddington accreting BHs. This can be applied as a sub-grid
model in large-scale cosmological simulations that do not sufficiently resolve
galactic nuclei, and to the formation of the heaviest gravitational-wave
sources via accretion in dense environments.
