General Relativistic Magnetohydrodynamic Simulations of the Hard State as a Magnetically-Dominated Accretion Flow

(Abridged) We present one of the first physically-motivated two-dimensional general relativistic magnetohydrodynamic (GRMHD) numerical simulations of a radiatively-cooled black-hole accretion disk. The fiducial simulation combines a total-energy-conserving formulation with a radiative cooling function, which includes bremsstrahlung, synchrotron, and Compton effects. By comparison with other simulations we show that in optically thin advection-dominated accretion flows, radiative cooling can significantly affect the structure, without necessarily leading to an optically thick, geometrically thin accretion disk. We further compare the results of our radiatively-cooled simulation to the predictions of a previously developed analytic model for such flows. For the very low stress parameter and accretion rate found in our simulated disk, we closely match a state called the "transition" solution between an outer advection-dominated accretion flow and what would be a magnetically-dominated accretion flow (MDAF) in the interior. The qualitative and quantitative agreement between the numerical and analytic models is quite good, with only a few well-understood exceptions. According to the analytic model then, at significantly higher stress or accretion, we would expect a full MDAF to form. The collection of simulations in this work also provide important data for interpreting other numerical results in the literature, as they span the most common treatments of thermodynamics, including simulations evolving: 1) the internal energy only; 2) the internal energy plus an explicit cooling function; 3) the total energy without cooling; and 4) total energy including cooling. We find that the total energy formulation is a necessary prerequisite for proper treatment of radiative cooling in MRI accretion flows.