We present two-dimensional hydrodynamical simulations of slowly rotating gas that is under the influence of the gravity of a super massive black hole and is irradiated by a thin UV accretion disc and a spherical X-ray corona .
We calculate the accretion luminosity of a system based on the accretion-rate which is assumed to be equal to the mass-supply rate at the radius of \sim 10 ^ { -2 } pc .
For the models with high temperature gas at large radii ( \sim 10 pc ) and high luminosities , we find a strong correlation between the mass-outflow rate ( \dot { M } _ { \mathrm { out } } ) and the luminosity ( L ) .
The power law index ( q ) describing the \dot { M } _ { \mathrm { out } } – L relation is q = 2.0 \left ( \pm 0.1 \right ) , which is very similar to that for radiation-driven stellar and disc wind models .
More surprisingly , for high density at large radii , we find steady state solutions with the accretion luminosity exceeding the Eddington limit .
The super-Eddington accretion proceeds in the equatorial region and is possible because the radiation flux from the disc is significantly reduced in the equatorial direction due to the geometrical foreshortening effect .
In all models , an outflow is driven from an inflow with sub-Keplerian rotation .
For high temperature at large radii , the inflow occurs over a wide range of the polar angles , and the outflow occurs in a relatively narrow polar cone .
However , for the super-Eddington cases with low temperature at large radii , the inflow persists only very close to the equatorial plane , resembling a thin accretion disc , while the outflow arises in a wide range of radii and polar angles .
The geometry of this extreme inflow-outflow solution is very similar to a radiation-driven wind from a luminous Keplerian accretion disc .
For the cold super-Eddington solutions , \dot { M } _ { \mathrm { out } } is only very weakly correlated with L , i.e . 0 \mathrel { \hbox { \raise 2.15 pt \hbox { $ < $ } \hbox to 0.0 pt { \lower 2.15 pt \hbox { $ \sim% $ } } } } q \mathrel { \hbox { \raise 2.15 pt \hbox { $ < $ } \hbox to 0.0 pt { \lower 2.15 pt \hbox { % $ \sim$ } } } } 0.2 .
This weaker correlation is mainly caused by a mismatch between the direction of escaping photons and the inflowing gas : the radiation is emitted mostly in the polar directions whereas the inflowing gas occurs mainly in the equatorial region .