Inverse Compton Cooling in the Coronae of Simulated Black Hole Accretion Flows

We present a formulation for a local cooling function to be employed in the diffuse, hot corona region of 3D GRMHD simulations of accreting black holes. This new cooling function calculates the cooling rate due to inverse Compton scattering by considering the relevant microphysics in each cell in the corona and approximating the radiation energy density and Compton temperature there by integrating over the thermal seed photon flux from the disk surface. The method either assumes ion and electron temperatures are equal (1T), or calculates them separately (2T) using an instantaneous equilibrium approach predicated on the actual relevant rate equations (Coulomb and Compton). The method is shown to be consistent with a more detailed ray-tracing calculation where the bulk of the cooling occurs, but is substantially less costly to perform. As an example, we apply these methods to a \textsc{harm3d} simulation of a $10 M_\odot$, non-spinning black hole, accreting at nominally 1\% the Eddington value. Both 1T and 2T approaches lead to increased radiative efficiency and a larger fraction of total cooling in the corona as compared to the original target-temperature cooling function used by \textsc{harm3d}, especially in the 1T case. Time-averaged post-processing reveals that the continuum spectral observations predicted from these simulations are qualitatively similar to actual X-ray binary data, especially so for the 1T approach which yields a harder power-law component ($\Gamma = 2.25$) compared to the 2T version ($\Gamma = 2.53$)