GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF THE HARD STATE AS A MAGNETICALLY DOMINATED ACCRETION FLOW

We present one of the first physically motivated two-dimensional general relativistic magnetohydrodynamic 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 (ADAFs), 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 (alpha approximate to 0.003, (M) over dot/(M) over dot(EDD) approximate to 5 x 10-(6)), we closely match a state called the transition solution between an outer ADAF 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 alpha or (M) over dot we would expect a full MDAF to form. The collection of simulations in this work also provides 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) the total energy including cooling. We find that the total energy formulation is a necessary prerequisite for proper treatment of radiative cooling in magneto-rotational instability accretion flows, as the internal energy formulation produces a large unphysical numerical cooling of its own. We also find that the relativistic cooling functions must be handled carefully numerically in order to avoid equally unphysical heating or cooling runaways.