We show that most of hot, optically thin accretion disk models which ignore advective cooling are not self-consistent. We have found new types of optically thin disk solutions where cooling is dominated by radial advection of heat. These new solutions are thermally and viscously stable.

We consider an accretion flow model originally proposed by Bisnovatyi-Kogan & Ruzmaikin (1974), which has been confirmed in recent 3D MHD simulations. In the model, the accreting gas drags in a strong poloidal magnetic field to the center such that the accumulated field disrupts the axisymmetric accretion flow at a relatively large radius. Inside the disruption radius, the gas accretes as discrete blobs or streams with a velocity much less than the free-fall velocity. Almost the entire rest mass energy of the gas is released as heat, radiation and mechanical/magnetic energy. Even for a non-rotating black hole, the efficiency of converting mass to energy is of order 50% or higher. The model is thus a practical analog of an idealized engine proposed by Geroch and Bekenstein.

Abstract. We note that the recently discovered 450 Hz frequency in the X-ray flux of the black hole candidate GRO J1655-40 is in a 3:2 ratio to the previously known 300 Hz frequency of quasi-periodic oscillations (QPO) in the same source. If the origin of high frequency QPOs in black hole systems is a resonance between orbital and epicyclic motion of accreting matter, as suggested previously, the angular momentum of the black hole can be accurately determined, given its mass. We find that the dimensionless angular momentum is in the range 0.2 < j < 0.67 if the mass is in the (corresponding) range of 5.5 to 7.9 solar masses. Key words. equation of state -relativity -stars: black holes -X-raysWe have previously suggested that "twin" kHz QPOs in accreting neutron stars arise as a result of non-linear 1:2 or 1:3 resonance between the radial epicyclic motion and the orbital motion of matter in a nearly Keplerian accretion disk. As a corollary, we have noted (Kluźniak & Abramowicz 2001) that the same phenomenon should also arise in accreting black holes, where only a single high frequency had been observed. Strohmayer (2001) now reports the discovery of a second QPO in GRO J1655-40, a well known black hole candidate in a low-mass X-ray binary, with the mass of the compact X-ray source determined from optical studies to be in the range 5.9 < M/M < 7.9 (Shabhaz et al. 1999). There are time intervals, when both QPOs are present at the same time.The two QPOs now known in the source occur at frequencies 300 Hz and 450 Hz, i.e., in a 2:3 ratio, strongly supporting the notion of a resonance in the system. (The effects of orbital resonances are commonly observed in the solar system -the rotation of the Moon and gaps in the rings of Saturn are well known examples.) Of all rational ratios only 2:3, 1:2 and 1:3 resonances are capable of giving a 2:3 ratio of frequencies. Specifically, if the lower frequency in the resonance is ω, and the higher frequency Ω, the only possibilities are that Ω = 300 Hz and Ω + ω = 450 Hz for the 1:2 resonance, or that Ω = 450 Hz and Ω − ω = 300 Hz for the 1:3 resonance.Send offprint requests to: W. Kluźniak, e-mail: wlodek@camk.edu.plIn the spirit of Kluźniak & Abramowicz (2001), we consider resonances between orbital and epicyclic motion in the Kerr metric. The fluid in a geometrically thin and axially symmetric accretion disk follows circular orbits, and any departures (caused by gradients of pressure) from circular geodesic motion are second order in the small parameter of characteristic thickness divided by the radius of the disk. We assume that an n:m resonance can be excited at or near that radius where the ratio of the epicyclic frequency to the orbital frequency is n:m. The formulae for the frequencies can be found, e.g., in the review by Kato (2001) and references therein. We find, for instance, that for j = 0.2 (see below) the radial epicyclic frequency is in a 1:2 resonance with orbital frequency at r = 7.22 M , i.e., at 3.6 Schwarzschild radii. For j = 0.67, the same frequencies are in ...

We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing length formalism. We seek self-similar solutions in which the rotational velocity and sound speed scale as R −1/2 , where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one limit, the transport occurs down the angular velocity gradient, so convection moves angular momentum outward. In the other, the transport is down the specific angular momentum gradient, so convection moves angular momentum inward. We also consider general prescriptions which lie in between the two limits.When convection moves angular momentum outward, we recover the usual self-similar solution for ADAFs in which the mass density scales as ρ ∝ R −3/2 . When convection moves angular momentum inward, the result depends on the viscosity coefficient α. If α > α crit1 ∼ 0.05, we once again find the standard ADAF solution. For α < α crit , however, we find a non-accreting solution in which ρ ∝ R −1/2 . We refer to this as a "convective envelope" solution or a "convectiondominated accretion flow." Two-dimensional numerical simulations of ADAFs with values of α < ∼ 0.03 have been reported by several authors. The simulated ADAFs exhibit convection. By virtue of their axisymmetry, convection in these simulations moves angular momentum inward, as we confirm by computing the Reynolds stress. The simulations give ρ ∝ R −1/2 , in good agreement with the convective envelope solution. The R −1/2 density profile is not a consequence of mass outflow. The relevance of these axisymmetric low-α simulations to real accretion flows is uncertain.

We present three-dimensional MHD simulations of rotating radiatively inefficient accretion flows onto black holes. We continuously inject magnetized matter into the computational domain near the outer boundary and run the calculations long enough for the resulting accretion flow to reach a quasi-steady state. We have studied two limiting cases for the geometry of the injected magnetic field: pure toroidal field and pure poloidal field. In the case of toroidal field injection, the accreting matter forms a nearly axisymmetric, geometrically-thick, turbulent accretion disk. The disk resembles in many respects the convection-dominated accretion flows found in previous numerical and analytical investigations of viscous hydrodynamic flows. Models with poloidal field injection evolve through two distinct phases. In an initial transient phase, the flow forms a relatively flattened, quasi-Keplerian disk with a hot corona and a bipolar outflow. However, when the flow later achieves steady state, it changes in character completely. The magnetized accreting gas becomes two-phase, with most of the volume being dominated by a strong dipolar magnetic field from which a thermal low-density wind flows out. Accretion occurs mainly via narrow slowly-rotating radial streams which 'diffuse' through the magnetic field with the help of magnetic reconnection events.

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).

The mass of the central black hole in the active galaxy NGC 4258 (M106) has been measured to be M = 3:6 10 7 M (Miyoshi et al. 1995). The Eddington luminosity corresponding to this mass is L E = 4:5 10 45 erg s 1 . By contrast the X-ray luminosity of the nucleus of NGC 4258 between 2 10 keV is (4 1) 10 40 erg s 1 while the optical/UV luminosity is less than 1:5 10 42 erg s 1 . The luminosity of NGC 4258 is therefore extremely sub-Eddington, L 10 5 L E in X-rays and L 3 10 4 L E even if we take the maximum optical/UV luminosity. Assuming the usual accretion e ciency of 0.1 would imply accretion rates orders of magnitude lower than in Seyfert galaxies and quasars. We show that the properties of the AGN in NGC 4258 can be explained by an accretion ow in the form of a very hot, optically-thin plasma which advects most of the viscously generated thermal energy into the central black hole and radiates only a small fraction of the energy. In this case the accretion rate in Eddington units could be as high as 0:16 , where is the standard viscosity parameter; and the size of the hot disk should be larger than 10 times the Schwarzschild radius. We compare the predictions of this model with observations and discuss its application to other low luminosity AGN.

Abstract. In all microquasars with double peak high frequency QPOs, the ratio of the frequencies is 3:2, which supports the suggestion that a non-linear resonance between two modes of oscillation in the accretion disk plays a role in exciting the observed modulations of the X-ray flux. We discuss evidence in favor of this interpretation and relate the black hole spin to the frequencies expected for various types of resonances that may occur in nearly Keplerian disks in strong gravity. For those microquasars where the mass of the central X-ray source is known, the black hole spin can be deduced from a comparison of the observed and expected frequencies.