Self-Similar Accretion Flows with Convection

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 rho ~ R^{-3/2}. When convection moves angular momentum inward, the result depends on the viscosity coefficient alpha. If alpha>alpha_{crit1} ~ 0.05, we once again find the standard ADAF solution. For alpha<alpha_{crit}, however, we find a non-accreting solution in which rho ~ R^{-1/2}. We refer to this as a "convective envelope" solution or a "convection-dominated accretion flow". Two-dimensional numerical simulations of ADAFs with values of alpha<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 rho ~ R^{-1/2}, in good agreement with the convective envelope solution. The R^{-1/2} density profile is not a consequence of mass outflow.Comment: 22 pages, 4 figures, final version accepted for publication in ApJ, a new appendix was added and 3 figs were modifie

Magnetically Arrested Disk: An Energetically Efficient Accretion Flow

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.Comment: 4 pages, 2 figure, new refs added, in print in PAS

The Magnetohydrodynamics of Convection-Dominated Accretion Flows

Radiatively inefficient accretion flows onto black holes are unstable due to both an outwardly decreasing entropy (`convection') and an outwardly decreasing rotation rate (the `magnetorotational instability'; MRI). Using a linear magnetohydrodynamic stability analysis, we show that long-wavelength modes are primarily destabilized by the entropy gradient and that such `convective' modes transport angular momentum inwards. Moreover, the stability criteria for the convective modes are the standard Hoiland criteria of hydrodynamics. By contrast, shorter wavelength modes are primarily destabilized by magnetic tension and differential rotation. These `MRI' modes transport angular momentum outwards. The convection-dominated accretion flow (CDAF) model, which has been proposed for radiatively inefficient accretion onto a black hole, posits that inward angular momentum transport and outward energy transport by long-wavelength convective fluctuations are crucial for determining the structure of the accretion flow. Our analysis suggests that the CDAF model is applicable to a magnetohydrodynamic accretion flow provided the magnetic field saturates at a sufficiently sub-equipartition value (plasma beta >> 1), so that long-wavelength convective fluctuations can fit inside the accretion disk. Numerical magnetohydrodynamic simulations are required to determine whether such a sub-equipartition field is in fact obtained.Comment: 17 pages including 3 figures. Accepted for publication in ApJ. New appendix and figure were added; some changes of the text were made in response to the referee

Accretion Disks Phase Transitions: 2-D or not 2-D?

We argue that the proper way to treat thin-thick accretion-disk transitions should take into account the 2-D nature of the problem. We illustrate the physical inconsistency of the 1-D vertically integrated approach by discussing a particular example of the convective transport of energy.Comment: 4 pages, 2 figure

Slim accretion discs: a model for ADAF-SLE transitions

We numerically construct slim, global, vertically integrated models of optically thin, transonic accretion discs around black holes, assuming a regularity condition at the sonic radius and boundary conditions at the outer radius of the disc and near the black hole. In agreement with several previous studies, we find two branches of shock-free solutions, in which the cooling is dominated either by advection, or by local radiation. We also confirm that the part of the accretion flow where advection dominates is in some circumstances limited in size: it does not extend beyond a certain outer limiting radius. New results found in our paper concern the location of the limiting radius and properties of the flow near to it. In particular, we find that beyond the limiting radius, the advective dominated solutions match on to Shapiro, Lightman & Eardley (SLE) discs through a smooth transition region. Therefore, the full global solutions are shock-free and unlimited in size. There is no need for postulating an extra physical effect (e.g. evaporation) for triggering the ADAF-SLE transition. It occurs due to standard accretion processes described by the classic slim disc equations.Comment: 12 pages, 7 figures, MNRAS accepte