Electron temperatures in the inner region of accretion disks around black holes are set by the balance of advection, viscous heating, and radiative interactions. At the lowest accretion rates, radiative processes may be safely ignored, and electrons are nearly virial. Advection carries the lion's share of this internal energy through the event horizon. At near-Eddington accretion rates, advection may be safely ignored, as energy generated from viscous heating is quickly radiated away. What, then, of intermediate accretion rates for which advection, heating, and radiative cooling timescales are all comparable? After all, a large fraction of all known black hole candidates (low-luminosity active galactic nuclei and quiescent black hole X-ray binaries) live in this region of parameter space. In this work we specialize to low accretion rate supermassive black holes subject to synchrotron and Compton losses.The dynamics of accretion are set by angular momentum transport. A leading picture for this process has an instability of magnetic fields threading a differentially rotating fluid, the magnetorotational instability (MRI), driving turbulence that leads to diffusive angular momentum transport. The need to capture this process self-consistently in the near-horizon regime motivated the development of numerical methods for general relativistic magnetohydrodynamics (GRMHD). However, even the local details of MRI-driven turbulence simulations are still not completely understood. Along the way, this work considers a central issue with modeling the MRI: whether the resulting stress is independent of the numerics when resistivity and viscosity are neglected (as they almost always are in GRMHD simulations). GRMHD simulations are now a standard tool for modeling black hole accretion flows, but do not include radiative processes, limiting their application to very low accretion rates. To address this problem we developed the bhlight scheme, which couples proven methods for flux-conservative general relativistic magnetohydrodynamics to covariant Monte Carlo radiation transport to produce a frequency-dependent, full transport general relativistic radiation magnetohydrodynamics (GRRMHD) scheme. This code is robust and accurate across a range of test problems, and computationally efficient on our problem of interest: very sub-Eddington black hole accretion flows for which radiative cooling is still crucial.The turbulent heating rate of the electrons in these (at least somewhat) Coulomb-collisionless flows is crucial to accurately capturating radiative interactions. We subsequently extended bhlight to incorporate the electron heating model of Ressler et al. 2015; the resulting method we term ebhlight. We first apply ebhlight to a study of accretion onto a 10 billion solar mass, a = 0.5 black hole for a range of accretion rates. We find that by an accretion rate of 1e-5 Eddington, radiative cooling significantly reduces the radiative efficiency relative to a non-cooling accretion flow. Coulomb heating far from the black hole leads to a significant enhancement in luminosity due to inverse Compton scattering. With increasing accretion rate in Eddington units, the high energy spectrum evolves from a steep series of Compton bumps to a smooth power law over many decades in frequency. These are the first self-consistent models of radiatively cooled LLAGN using frequency-depedent full transport, and extend from the fully radiatively inefficient regime to near (~ 1%) thin disk efficiencies. We then use ebhlight to study M87, a classic LLAGN source. M87 is one of the two principal targets for the Event Horizon Telescope's campaign to image black hole event horizons. Previous GRMHD studies of M87 have had difficulty achieving self-consistency; radiative cooling appears to be required. Here we include this radiative cooling over a suite of models with different black hole masses and spins (matching the 230 GHz flux of Doeleman et al. 2012), and find that it (together with Coulomb heating) is indeed critical to the thermodynamics of the flow. We also find a Compton y parameter of order unity in all cases. We produce synthetic images from these models in support of upcoming EHT measurements.
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General relativistic radiation magnetohydrodynamics, with applications to black hole accretion disks