We show that the low‐frequency quasi‐periodic oscillations (QPOs) seen in the power‐density spectra of black hole binaries (and neutron stars) can be explained by the Lense–Thirring precession. This has been proposed many times in the past, and simple, single‐radius models can qualitatively match the observed increase in QPO frequency by decreasing a characteristic radius, as predicted by the truncated disc models. However, this also predicts that the frequency is strongly dependent on spin, and gives a maximum frequency at the last stable orbit which is generally much higher than the remarkably constant maximum frequency at ∼10 Hz observed in all black hole binaries. The key aspect of our model, which makes it match these observations, is the precession of a radially extended region of the hot inner flow. The outer radius is set by the truncation radius of the disc as above, but the inner radius lies well outside of the last stable orbit at the point where numerical simulations show that the density drops off sharply for a misaligned flow. Physically motivated analytic estimates for this inner radius show that it increases with a*, decreasing the expected frequency in a way which almost completely cancels the expected increase with spin, and ties the maximum predicted frequency to around 10 Hz for all a*. This is the first QPO model which explains both frequencies and spectrum in the context of a well‐established geometry for the accretion flow.

This paper presents a continuation of our efforts to numerically study accretion disks that are misaligned (tilted) with respect to the rotation axis of a Kerr black hole. Here we present results of a global numerical simulation which fully incorporates the effects of the black hole spacetime as well as magnetorotational turbulence that is the primary source of angular momentum transport in the flow. This simulation shows dramatic differences from comparable simulations of untilted disks. Accretion onto the hole occurs predominantly through two opposing plunging streams that start from high latitudes with respect to both the black-hole and disk midplanes. This is due to the aspherical nature of the gravitational spacetime around the rotating black hole. These plunging streams start from a larger radius than would be expected for an untilted disk. In this regard the tilted black hole effectively acts like an untilted black hole of lesser spin. Throughout the duration of the simulation, the main body of the disk remains tilted with respect to the symmetry plane of the black hole; thus there is no indication of a Bardeen-Petterson effect in the disk at large. The torque of the black hole instead principally causes a global precession of the main disk body. In this simulation the precession has a frequency of 3(M ⊙ /M ) Hz, a value consistent with many observed low-frequency quasi-periodic oscillations. However, this value is strongly dependent on the size of the disk, so this frequency may be expected to vary over a large range.

This review covers the main aspects of black hole accretion disk theory. We begin with the view that one of the main goals of the theory is to better understand the nature of black holes themselves. In this light we discuss how accretion disks might reveal some of the unique signatures of strong gravity: the event horizon, the innermost stable circular orbit, and the ergosphere. We then review, from a first-principles perspective, the physical processes at play in accretion disks. This leads us to the four primary accretion disk models that we review: Polish doughnuts (thick disks), Shakura-Sunyaev (thin) disks, slim disks, and advection-dominated accretion flows (ADAFs). After presenting the models we discuss issues of stability, oscillations, and jets. Following our review of the analytic work, we take a parallel approach in reviewing numerical studies of black hole accretion disks. We finish with a few select applications that highlight particular astrophysical applications: measurements of black hole mass and spin, black hole vs. neutron star accretion disks, black hole accretion disk spectral states, and quasi-periodic oscillations (QPOs).

We present the first systematic analysis of the X-ray variability of Sgr A * during the Chandra Xray Observatory's 2012 Sgr A * X-ray Visionary Project (XVP). With 38 High Energy Transmission Grating Spectrometer (HETGS) observations spaced an average of 7 days apart, this unprecedented campaign enables detailed study of the X-ray emission from this supermassive black hole at high spatial, spectral and timing resolution. In 3 Ms of observations, we detect 39 X-ray flares from Sgr A * , lasting from a few hundred seconds to approximately 8 ks, and ranging in 2 − 10 keV luminosity from ∼ 10 34 erg s −1 to 2 × 10 35 erg s −1 . Despite tentative evidence for a gap in the distribution of flare peak count rates, there is no evidence for X-ray color differences between faint and bright flares. Our preliminary X-ray flare luminosity distribution dN/dL is consistent with a power law with index −1.9 +0.3 −0.4 ; this is similar to some estimates of Sgr A * 's NIR flux distribution. The observed flares contribute one-third of the total X-ray output of Sgr A * during the campaign, and as much as 10% of the quiescent X-ray emission could be comprised of weak, undetected flares, which may also contribute high-frequency variability. We argue that flares may be the only source of X-ray emission from the inner accretion flow.

Recent high resolution observations of the Galactic center black hole allow for direct comparison with accretion disk simulations. We compare two-temperature synchrotron emission models from three dimensional, general relativistic magnetohydrodynamic simulations to millimeter observations of Sgr A*. Fits to very long baseline interferometry and spectral index measurements disfavor the monochromatic face-on black hole shadow models from our previous work. Inclination angles ≤ 20 • are ruled out to 3σ. We estimate the inclination and position angles of the black hole, as well as the electron temperature of the accretion flow and the accretion rate, to be i = 50−2 × 10 −9 M ⊙ yr −1 respectively, with 90% confidence. The black hole shadow is unobscured in all best fit models, and may be detected by observations on baselines between Chile and California, Arizona or Mexico at 1.3mm or .87mm either through direct sampling of the visibility amplitude or using closure phase information. Millimeter flaring behavior consistent with the observations is present in all viable models, and is caused by magnetic turbulence in the inner radii of the accretion flow. The variability at optically thin frequencies is strongly correlated with that in the accretion rate. The simulations provide a universal picture of the 1.3mm emission region as a small region near the midplane in the inner radii of the accretion flow, which is roughly isothermal and has ν/ν c ∼ 1 − 20, where ν c is the critical frequency for thermal synchrotron emission.

Recent developments in compact object astrophysics, especially the discovery of merging neutron stars by LIGO, the imaging of the black hole in M87 by the Event Horizon Telescope, and high-precision astrometry of the Galactic Center at close to the event horizon scale by the GRAVITY experiment motivate the development of numerical source models that solve the equations of general relativistic magnetohydrodynamics (GRMHD). Here we compare GRMHD solutions for the evolution of a magnetized accretion flow where turbulence is promoted by the magnetorotational instability from a set of nine GRMHD codes: Athena++, BHAC, Cosmos++, ECHO, H-AMR, iharm3D, HARM-Noble, IllinoisGRMHD, and KORAL. Agreement among the codes improves as resolution increases, as measured by a consistently applied, specially developed set of code performance metrics. We conclude that the community of GRMHD codes is mature, capable, and consistent on these test problems.

Accumulating observational evidence for a number of radio galaxies suggests an association between their jets and regions of active star formation. The standard picture is that shocks generated by the jet propagate through an inhomogeneous medium and trigger the collapse of overdense clouds, which then become active star-forming regions. In this contribution, we report on recent hydrodynamic simulations of radiative shock-cloud interactions using two different cooling models: an equilibrium cooling-curve model assuming solar metallicities and a non-equilibrium chemistry model appropriate for primordial gas clouds. We consider a range of initial cloud densities and shock speeds in order to quantify the role of cooling in the evolution. Our results indicate that for moderate cloud densities ( 1 cm −3 ) and shock Mach numbers ( 20), cooling processes can be highly efficient and result in more than 50% of the initial cloud mass cooling to below 100 K. We also use our results to estimate the final H 2 mass fraction for the simulations that use the non-equilibrium chemistry package. This is an important measurement, since H 2 is the dominant coolant for a primordial gas cloud. We find peak H 2 mass fractions of 10 −2 and total H 2 mass fractions of 10 −5 for the cloud gas, consistent with cosmological simulations of first star formation. Finally, we compare our results with the observations of jet-induced star formation in "Minkowski's Object," a small irregular starburst system associated with a radio jet in the nearby cluster of galaxies Abell 194. We conclude that its morphology, star formation rate (∼ 0.3M ⊙ yr −1 ) and stellar mass (∼ 1.2 × 10 7 M ⊙ ) can be explained by the interaction of a ∼ 9 × 10 4 km s −1 jet with an ensemble of moderately dense (∼ 10 cm −3 ), warm (10 4 K) intergalactic clouds in the vicinity of its associated radio galaxy at the center of the galaxy cluster.

A new code and methodology are introduced for solving the general relativistic magnetohydrodynamic (GRMHD) equations in fixed background spacetimes using time-explicit, finitevolume discretization. The code has options for solving the GRMHD equations using traditional artificial-viscosity (AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV (eAV) scheme using artificial-viscosity together with a dual energy-flux-conserving formulation. The dual energy approach allows for accurate modeling of highly relativistic flows at boost factors well beyond what has been achieved to date by standard artificial viscosity methods. It provides the benefit of Godunov methods in capturing high Lorentz boosted flows but without complicated Riemann solvers, and the advantages of traditional artificial viscosity methods in their speed and flexibility. Additionally, the GRMHD equations are solved on an unstructured grid that supports local adaptive mesh refinement using a fully threaded oct-tree (in three dimensions) network to traverse the grid hierarchy across levels and immediate neighbors. A number of tests are presented to demonstrate robustness of the numerical algorithms and adaptive mesh framework over a wide spectrum of problems, boosts, and astrophysical applications, including relativistic shock tubes, shock collisions, magnetosonic shocks, Alfvén wave propagation, blast waves, magnetized Bondi flow, and the magneto-rotational instability in Kerr black hole spacetimes.