37 research outputs found
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
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
Convection in radiatively inefficient black hole accretion flows
Recent numerical simulations of radiatively inefficient accretion flows onto
compact objects have shown that convection is a general feature in such flows.
Dissipation of rotational and gravitational energies in the accretion flows
results in inward increase of entropy and development of efficient convective
motions. Convection-dominated accretion flows (CDAFs) have a structure that is
modified significantly in comparison with the canonical advection-dominated and
Bondi-like accretion flows. The flows are characterized by the flattened radial
density profiles, ~R^{-1/2}, and have reduced mass accretion rates. Convection
transports outward a significant amount of the released binding energy of the
accretion flow. We discuss basic dynamical and observational properties of
ADAFs using numerical models and self-similar analytical solutions.Comment: 12 pages, 4 figures, invited plenary review at the 20th Texas
Symposium on Relativistic Astrophysics, Austin, Texas, 2000, eds J. C.
Wheeler and H. Marte
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