  We study super-Eddington accretion flows onto black holes using a global
three dimensional radiation magneto-hydrodynamical simulation. We solve the
time dependent radiative transfer equation for the specific intensities to
accurately calculate the angular distribution of the emitted radiation.
Turbulence generated by the magneto-rotational instability provides
self-consistent angular momentum transfer. The simulation reaches inflow
equilibrium with an accretion rate ~220L_edd/c^2 and forms a radiation driven
outflow along the rotation axis. The mechanical energy flux carried by the
outflow is ~20% of the radiative energy flux. The total mass flux lost in the
outflow is about 29% of the net accretion rate. The radiative luminosity of
this flow is ~10L_edd. This yields a radiative efficiency ~4.5%, which is
comparable to the value in a standard thin disk model. In our simulation,
vertical advection of radiation caused by magnetic buoyancy transports energy
faster than photon diffusion, allowing a significant fraction of the photons to
escape from the surface of the disk before being advected into the black hole.
We contrast our results with the lower radiative efficiencies inferred in most
models, such as the slim disk model, which neglect vertical advection. Our
inferred radiative efficiencies also exceed published results from previous
global numerical simulations, which did not attribute a significant role to
vertical advection. We briefly discuss the implications for the growth of
supermassive black holes in the early universe and describe how these results
provided a basis for explaining the spectrum and population statistics of
ultraluminous X-ray sources.
