Global simulations of axisymmetric radiative black hole accretion discs in general relativity with a mean-field magnetic dynamo

We present a mean-field model that emulates the magnetic dynamo operating in magnetized accretion discs. We have implemented this model in the general relativisic radiation magnetohydrodynamic (GRRMHD) code KORAL, using results from local shearing sheet simulations of the magnetorotational instability to fix the parameters of the dynamo. With the inclusion of this dynamo, we are able to run 2D axisymmetric GRRMHD simulations of accretion discs for arbitrarily long times. The simulated discs exhibit sustained turbulence, with the poloidal and toroidal magnetic field components driven towards a state similar to that seen in 3D studies. Using this dynamo code, we present a set of long-duration global simulations of super-Eddington, optically thick discs around non-spinning and spinning black holes. Super-Eddington discs around non-rotating black holes exhibit a surprisingly large efficiency, eta approximate to 0.04, independent of the accretion rate, where we measure efficiency in terms of the total energy output, both radiation and mechanical, flowing out to infinity. This value significantly exceeds the efficiency predicted by slim disc models for these accretion rates. Super-Eddington discs around spinning black holes are even more efficient, and appear to extract black hole rotational energy through a process similar to the Blandford-Znajek mechanism. All the simulated models are characterized by highly super-Eddington radiative fluxes collimated along the rotation axis. We also present a set of simulations that were designed to have Eddington or slightly sub-Eddington accretion rates ((M) over dot less than or similar to 2 (M) over dot(Edd)). None of these models reached a steady state. Instead, the discs collapsed as a result of runaway cooling, presumably because of a thermal instability.