The long-term evolution of a black hole accretion torus: a comparison between GRMHD simulations and relativistic thin disk theory

In this paper we analyse the long-term evolution of a black hole accretion torus using novel GRMHD simulations which, for the first time, have been run out to extremely large evolutionary times $t_{\rm max} = 10^7 GM_\bullet/c^3$. This allows for detailed comparisons between the gross evolution of this GRMHD simulation and existing "spreading disk" analytical theories. We show that the long-term features of this evolution are well described by General Relativistic Thin Disk Theory (GRTDT), which reproduces various aspects of the GRMHD evolution to within a factor $\sim 2$, despite the disk in our simulation not being remotely thin, showing dynamically dominant (MAD) magnetic fields, and launching a powerful wind. Thin disk theory functions as an accurate and cheap effective theory for the evolution in radius and time of the bulk of the disk material, and for the time dependence of the horizon accretion rate. We argue that this effectiveness originates from the global conservation laws of mass and angular momentum, together with a turbulent stress which we find to be local and independent of density, lending support to the ad-hoc local-stress-tensor phenomenology employed in analytical models. We also find that the turbulent accretion rate variability in the inner disk is log-normally distributed, consistent with a key assumption in the modeling of observed variability.