We present results from two long-duration general relativistic magneto-hydrodynamic (GRMHD) simulations of advection-dominated accretion around a non-spinning black hole. The first simulation was designed to avoid significant accumulation of magnetic flux around the black hole. This simulation was run for a time of 200 000 GM/c 3 and achieved inflow equilibrium out to a radius ∼90 GM/c 2 . Even at this relatively large radius, the mass outflow rateṀ out is found to be only 60 per cent of the net mass inflow rateṀ BH into the black hole. The second simulation was designed to achieve substantial magnetic flux accumulation around the black hole in a magnetically arrested disc. This simulation was run for a shorter time of 100 000 GM/c 3 . Nevertheless, because the mean radial velocity was several times larger than in the first simulation, it reached inflow equilibrium out to a radius ∼170 GM/c 2 . Here,Ṁ out becomes equal toṀ BH at r ∼ 160 GM/c 2 . Since the mass outflow rates in the two simulations do not show robust convergence with time, it is likely that the true outflow rates are lower than our estimates. The effect of black hole spin on mass outflow remains to be explored. Neither simulation shows strong evidence for convection, though a complete analysis including the effect of magnetic fields is left for the future.

The standard general relativistic model of a razor-thin accretion disc around a black hole, developed by Novikov & Thorne (NT) in 1973, assumes the shear stress vanishes at the radius of the innermost stable circular orbit (ISCO) and that, outside the ISCO, the shear stress is produced by an effective turbulent viscosity. However, astrophysical accretion discs

A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the X-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit (ISCO), whose radius depends only on the mass and spin of the black hole. In the Fe Kα method, which applies to both classes of black holes, one models the profile of the relativistically-broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuumfitting method, which has so far only been applied to stellar-mass black holes, one models the thermal X-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the continuum-fitting method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.

Using long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficient accretion discs, the energy, momentum and mass outflow rates from such systems are estimated. Outflows occur via two fairly distinct modes: a relativistic jet and a subrelativistic wind. The jet power depends strongly on the black hole spin and on the magnetic flux at the horizon. Unless these are very small, the energy output in the jet dominates over that in the wind. For a rapidly spinning black hole accreting in the magnetically arrested limit, it is confirmed that jet power exceeds the total rate of accretion of rest mass energy. However, because of strong collimation, the jet probably does not have a significant feedback effect on its immediate surroundings. The power in the wind is more modest and shows a weaker dependence on black hole spin and magnetic flux. Nevertheless, because the wind subtends a large solid angle, it is expected to provide efficient feedback on a wide range of scales inside the host galaxy. Empirical formulae are obtained for the energy and momentum outflow rates in the jet and the wind.

We obtain estimates of Sgr A* accretion flow and black hole parameters by fitting polarized sub-mm observations with spectra computed using three-dimensional (3D) general relativistic (GR) magnetohydrodynamical (MHD) (GRMHD) simulations. Observations are compiled from averages over many epochs from reports in 29 papers for estimating the mean fluxes F ν , linear polarization (LP) fractions, circular polarization (CP) fractions, and electric vector position angles (EVPAs). GRMHD simulations are computed with dimensionless spins a * = 0, 0.5, 0.7, 0.9, 0.98 over a 20, 000M time interval. We perform fully self-consistent GR polarized radiative transfer using our new code to explore the effects of spin a * , inclination angle θ, position angle (PA), accretion rateṀ , and electron temperature T e (T e is reported for radius 6M ). By fitting the mean sub-mm fluxes and LP/CP fractions, we obtain estimates for these model parameters and determine the physical effects that could produce polarization signatures. Our best bet model has a * = 0.5, θ = 75 • , PA = 115 • ,Ṁ = 4.6×10 −8 M ⊙ year −1 , and T e = 3.1 × 10 10 K at 6M . The sub-mm CP is mainly produced by Faraday conversion as modified by Faraday rotation, and the emission region size at 230 GHz is consistent with the VLBI size of 37µas. Across all spins, model parameters are in the ranges θ = 42 • − 75 • ,Ṁ = (1.4 − 7.0) × 10 −8 M ⊙ year −1 , and T e = (3 − 4) × 10 10 K. Polarization is found both to help differentiate models and to introduce new observational constraints on the effects of the magnetic field that might not be fit by accretion models so-far considered.