Long timescale numerical simulations of large, super-critical accretion discs

In this paper, we report on three of the largest (in terms of simulation domain size) and longest (in terms of duration) 3D general relativistic radiation magnetohydrodynamic simulations of super-critical accretion onto black holes. The simulations are all set for a rapidly rotating ($a_* = 0.9$), stellar-mass ($M_\mathrm{BH} = 6.62 M_\odot$) black hole. The simulations vary in their initial target mass accretion rates (assumed measured at large radius), with values sampled in the range $\dot{m}=\dot{M}/\dot{M}_\mathrm{Edd} = 1-10$. We find in practice, though, that all of our simulations settle close to a net accretion rate of $\dot{m}_\mathrm{net} = \dot{m}_\mathrm{in}-\dot{m}_\mathrm{out} \approx 1$ (over the radii where our simulations have reached equilibrium), even though the inward mass flux (measured at large radii) $\dot{m}_\mathrm{in}$ can exceed 1,000 in some cases. This is possible because the outflowing mass flux $\dot{m}_\mathrm{out}$ adjusts itself to very nearly cancel out $\dot{m}_\mathrm{in}$, so that at all radii $\dot{M}_\mathrm{net} \approx \dot{M}_\mathrm{Edd}$. In other words, these simulated discs obey the Eddington limit. We compare our results with the predictions of the slim disc (advection-dominated) and critical disc (wind/outflow-dominated) models, finding that they agree quite well with the critical disc model both qualitatively and quantitatively. We also speculate as to why our results appear to contradict most previous numerical studies of super-critical accretion.