686 research outputs found
Magnetothermal and magnetorotational instabilities in hot accretion flows
In a hot, dilute, magnetized accretion flow, the electron mean-free path can
be much greater than the Larmor radius, thus thermal conduction is anisotropic
and along magnetic field lines. In this case, if the temperature decreases
outward, the flow may be subject to a buoyancy instability (the magnetothermal
instability, or MTI). The MTI amplifies the magnetic field, and aligns field
lines with the radial direction. If the accretion flow is differentially
rotating, the magnetorotational instability (MRI) may also be present. Using
two-dimensional, time-dependent magnetohydrodynamic simulations, we investigate
the interaction between these two instabilities. We use global simulations that
span over two orders of magnitude in radius, centered on the region around the
Bondi radius where the infall time of gas is longer than the growth time of
both the MTI and MRI. Significant amplification of the magnetic field is
produced by both instabilities, although we find that the MTI primarily
amplifies the radial component, and the MRI primarily the toroidal component,
of the field, respectively. Most importantly, we find that if the MTI can
amplify the magnetic energy by a factor , and the MRI by a factor ,
then when the MTI and MRI are both present, the magnetic energy can be
amplified by a factor of . We therefore conclude that
amplification of the magnetic energy by the MTI and MRI operates independently.
We also find that the MTI contributes to the transport of angular momentum,
because radial motions induced by the MTI increase the Maxwell (by amplifying
the magnetic field) and Reynolds stresses. Finally, we find that thermal
conduction decreases the slope of the radial temperature profile. The increased
temperature near the Bondi radius decreases the mass accretion rate.Comment: 8 pages, 9 figures, accepted by MNRA
On the Fate of Gas Accreting at a Low Rate onto a Black Hole
Gas supplied conservatively to a black hole at rates well below the Eddington
rate may not be able to radiate effectively and the net energy flux, including
the energy transported by the viscous torque, is likely to be close to zero at
all radii. This has the consequence that the gas accretes with positive energy
so that it may escape. Accordingly, we propose that only a small fraction of
the gas supplied actually falls onto the black hole and that the binding energy
it releases is transported radially outward by the torque so as to drive away
the remainder in the form of a wind. This is a generalization of and an
alternative to an "ADAF" solution. Some observational implications and possible
ways to distinguish these two types of flow are briefly discussed.Comment: 5 pages, 2 figures, submitted to Monthly Notices of the Royal
Astronomical Society Letter
Angular momentum transport in protostellar discs
Angular momentum transport in protostellar discs can take place either
radially, through turbulence induced by the magnetorotational instability
(MRI), or vertically, through the torque exerted by a large-scale magnetic
field that threads the disc. Using semi-analytic and numerical results, we
construct a model of steady-state discs that includes vertical transport by a
centrifugally driven wind as well as MRI-induced turbulence. We present
approximate criteria for the occurrence of either one of these mechanisms in an
ambipolar diffusion-dominated disc. We derive ``strong field'' solutions in
which the angular momentum transport is purely vertical and ``weak field''
solutions that are the stratified-disc analogues of the previously studied MRI
channel modes; the latter are transformed into accretion solutions with
predominantly radial angular-momentum transport when we implement a
turbulent-stress prescription based on published results of numerical
simulations. We also analyze ``intermediate field strength'' solutions in which
both modes of transport operate at the same radial location; we conclude,
however, that significant spatial overlap of these two mechanisms is unlikely
to occur in practice. To further advance this study, we have developed a
general scheme that incorporates also the Hall and Ohm conductivity regimes in
discs with a realistic ionization structure.Comment: 8 pages, 4 figures, 1 table; accepted for publication in MNRA
Oscillation modes of relativistic slender tori
Accretion flows with pressure gradients permit the existence of standing
waves which may be responsible for observed quasi-periodic oscillations (QPO's)
in X-ray binaries. We present a comprehensive treatment of the linear modes of
a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary
specific angular momentum distribution, orbiting in an arbitrary axisymmetric
spacetime with reflection symmetry. We discuss the physical nature of the
modes, present general analytic expressions and illustrations for those which
are low order, and show that they can be excited in numerical simulations of
relativistic tori. The mode oscillation spectrum simplifies dramatically for
near Keplerian angular momentum distributions, which appear to be generic in
global simulations of the magnetorotational instability. We discuss our results
in light of observations of high frequency QPO's, and point out the existence
of a new pair of modes which can be in an approximate 3:2 ratio for arbitrary
black hole spins and angular momentum distributions, provided the torus is
radiation pressure dominated. This mode pair consists of the axisymmetric
vertical epicyclic mode and the lowest order axisymmetric breathing mode.Comment: submitted to MNRA
The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
The magnetorotational instability is thought to be responsible for the
generation of magnetohydrodynamic turbulence that leads to enhanced outward
angular momentum transport in accretion discs. Here, we present the first
formal analytical proof showing that, during the exponential growth of the
instability, the mean (averaged over the disc scale-height) Reynolds stress is
always positive, the mean Maxwell stress is always negative, and hence the mean
total stress is positive and leads to a net outward flux of angular momentum.
More importantly, we show that the ratio of the Maxwell to the Reynolds
stresses during the late times of the exponential growth of the instability is
determined only by the local shear and does not depend on the initial spectrum
of perturbations or the strength of the seed magnetic. Even though we derived
these properties of the stress tensors for the exponential growth of the
instability in incompressible flows, numerical simulations of shearing boxes
show that this characteristic is qualitatively preserved under more general
conditions, even during the saturated turbulent state generated by the
instability.Comment: 9 pages, 4 figures. Minor revisions. Accepted for publication in
MNRA
A Magnetohydrodynamic Nonradiative Accretion Flow in Three Dimensions
We present a global magnetohydrodynamic (MHD) three dimensional simulation of
a nonradiative accretion flow originating in a pressure supported torus. The
evolution is controlled by the magnetorotational instability which produces
turbulence. The flow forms a nearly Keplerian disk. The total pressure scale
height in this disk is comparable to the vertical size of the initial torus.
Gas pressure dominates only near the equator; magnetic pressure is more
important in the surrounding atmosphere. A magnetically dominated bound outflow
is driven from the disk. The accretion rate through the disk exceeds the final
rate into the hole, and a hot torus forms inside 10 r_g. Hot gas, pushed up
against the centrifugal barrier and confined by magnetic pressure, is ejected
in a narrow, unbound, conical outflow. The dynamics are controlled by magnetic
turbulence, not thermal convection, and a hydrodynamic alpha model is
inadequate to describe the flow. The limitations of two dimensional MHD
simulations are also discussed.Comment: 5 pages, 2 figures, submitted to ApJ Letters. For web version and
mpeg animations see http://www.astro.virginia.edu/~jh8h/nraf
On Nonshearing Magnetic Configurations in Differentially Rotating Disks
A new class of disk MHD equilibrium solutions is described, which is valid within the standard local (``shearing sheet'') approximation scheme. These solutions have the following remarkable property: velocity streamlines and magnetic lines of force rotate rigidly, even in the presence of differential rotation. This situation comes about because the Lorentz forces acting upon modified epicycles compel fluid elements to follow magnetic lines of force. Field line (and streamline) configurations may be elliptical or hyperbolic, prograde or retrograde. These structures have previously known hydrodynamical analogs: the ``planet'' solutions described by Goodman, Narayan, & Goldreich. The primary focus of this investigation is configurations in the disk plane. A related family of solutions lying in a vertical plane is briefly discussed; other families of solutions may exist. Whether these MHD structures are stable is not yet known, but could readily be determined by three-dimensional simulations. If stable or quasi-stable, these simple structures may find important applications in both accretion and galactic disks
Vortex generation in protoplanetary disks with an embedded giant planet
Vortices in protoplanetary disks can capture solid particles and form
planetary cores within shorter timescales than those involved in the standard
core-accretion model. We investigate vortex generation in thin unmagnetized
protoplanetary disks with an embedded giant planet with planet to star mass
ratio and . Two-dimensional hydrodynamical simulations of a
protoplanetary disk with a planet are performed using two different numerical
methods. The results of the non-linear simulations are compared with a
time-resolved modal analysis of the azimuthally averaged surface density
profiles using linear perturbation theory. Finite-difference methods
implemented in polar coordinates generate vortices moving along the gap created
by Neptune-mass to Jupiter-mass planets. The modal analysis shows that unstable
modes are generated with growth rate of order for azimuthal
numbers m=4,5,6, where is the local Keplerian frequency.
Shock-capturing Cartesian-grid codes do not generate very much vorticity around
a giant planet in a standard protoplanetary disk. Modal calculations confirm
that the obtained radial profiles of density are less susceptible to the growth
of linear modes on timescales of several hundreds of orbital periods.
Navier-Stokes viscosity of the order (in units of )
is found to have a stabilizing effect and prevents the formation of vortices.
This result holds at high resolution runs and using different types of boundary
conditions. Giant protoplanets of Neptune-mass to Jupiter-mass can excite the
Rossby wave instability and generate vortices in thin disks. The presence of
vortices in protoplanetary disks has implications for planet formation, orbital
migration, and angular momentum transport in disks.Comment: 14 pages, 15 figures, accepted for publication in A&
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