Three-dimensional simulations of super-critical black hole accretion disks --- luminosities, photon trapping and variability

We present a set of four three-dimensional, general relativistic, radiation MHD simulations of black hole accretion at super-critical mass accretion rates, $\dot{M} > \dot{M}_{\rm Edd}$. We use these simulations to study how disk properties are modified when we vary the black hole mass, the black hole spin, or the mass accretion rate. In the case of a non-rotating black hole, we find that the total efficiency is of order $3\%\dot M c^2$, approximately a factor of two less than the efficiency of a standard thin accretion disk. The radiation flux in the funnel along the axis is highly super-Eddington, but only a small fraction of the energy released by accretion escapes in this region. The bulk of the $3\%\dot M c^2$ of energy emerges farther out in the disk, either in the form of photospheric emission or as a wind. In the case of a black hole with a spin parameter of 0.7, we find a larger efficiency of about $8\%\dot M c^2$. By comparing the relative importance of advective and diffusive radiation transport, we show that photon trapping is effective near the equatorial plane. However, near the disk surface, vertical transport of radiation by diffusion dominates. We compare the properties of our fiducial three-dimensional run with those of an equivalent two-dimensional axisymmetric model with a mean-field dynamo. The latter simulation runs nearly 100 times faster than the three-dimensional simulation, and gives very similar results for time-averaged properties of the accretion flow.