303 research outputs found
Stability, Instability, and "Backwards'' Transport in Accretion Disks"
The stratification of entropy and the stratification of angular momentum are
closely analogous. Of particular interest is the behavior of disks in which
angular momentum transport is controlled by convection, and heat transport by
dynamical turbulence. In both instances we argue that the transport must
proceed ``backwards'' relative to the sense one would expect from a simple
enhanced diffusion approach. Reversed angular momentum transport has already
been seen in numerical simulations; contra-gradient thermal diffusion should be
amenable to numerical verification as well. These arguments also bear on the
observed nonlinear local stability of isolated Keplerian disks. We also
describe a diffusive instability that is the entropy analogue to the
magnetorotational instability. It affects thermally stratified layers when
Coulomb conduction and a weak magnetic field are present. The criterion for
convective instability goes from one of upwardly decreasing entropy to one of
upwardly decreasing temperature. The maximum growth rate is of order the
inverse sound crossing time, independent of the thermal conductivity. The
indifference of the growth rate to the conduction coefficient, its simple
dynamical scaling, and the replacement in the stability criterion of a
conserved quantity (entropy) gradient by a free energy (temperature) gradient
are properties similar to those exhibited by the magnetorotational instability.Comment: 21 pages, 5 figs., AAS LaTEX macros v4.0. Accepted to ApJ, final
versio
Localized magnetorotational instability and its role in the accretion disc dynamo
(Abriged) The magnetorotational instability (MRI) is believed to be an
efficient way to transport angular momentum in accretion discs. It has also
been suggested as a way to amplify magnetic fields in discs, the instability
acting as a nonlinear dynamo. Recent numerical work has shown that a
large-scale magnetic field, which is predominantly azimuthal, can be sustained
by motions driven by the MRI of this same field. Following this idea, we
present an analytical calculation of the MRI in the presence of an azimuthal
field with a non-trivial vertical structure. We find that the mean radial EMF
associated to MRI modes tends to reduce the magnetic energy, acting like a
turbulent resistivity by mixing the non-uniform azimuthal field. Meanwhile, the
azimuthal EMF generates a radial field that, in combination with the Keplerian
shear, tends to amplify the azimuthal field and can therefore assist in the
dynamo process. This effect, however, is reversed for sufficiently strong
azimuthal fields, naturally leading to a saturation of the dynamo and possibly
to a cyclic behaviour of the magnetic field, as found in previous numerical
works.Comment: 15 pages, 5 figure
Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs
We consider the stability of warping modes in Keplerian discs. We find them
to be parametrically unstable using two lines of attack, one based on
three-mode couplings and the other on Floquet theory. We confirm the existence
of the instability, and investigate its nonlinear development in three
dimensions, via numerical experiment. The most rapidly growing non-axisymmetric
disturbances are the most nearly axisymmetric (low m) ones. Finally, we offer a
simple, somewhat speculative model for the interaction of the parametric
instability with the warp. We apply this model to the masing disc in NGC 4258
and show that, provided the warp is not forced too strongly, parametric
instability can fix the amplitude of the warp.Comment: 14 pages, 6 figures, revised version with appendix added, to be
published in MNRA
New composite models of partially ionized protoplanetary disks
We study an accretion disk in which three different regions may coexist: MHD
turbulent regions, dead zones and gravitationally unstable regions. Although
the dead zones are stable, there is some transport due to the Reynolds stress
associated with waves emitted from the turbulent layers. We model the transport
in each of the different regions by its own parameter, this being 10
to times smaller in dead zones than in active layers. In
gravitationally unstable regions, is determined by the fact that the
disk self-adjusts to a state of marginal stability. We construct steady-state
models of such disks. We find that for uniform mass flow, the disk has to be
more massive, hotter and thicker at the radii where there is a dead zone. In
disks in which the dead zone is very massive, gravitational instabilities are
present. Whether such models are realistic or not depends on whether
hydrodynamical fluctuations driven by the turbulent layers can penetrate all
the way inside the dead zone. This may be more easily achieved when the ratio
of the mass of the active layer to that of the dead zone is relatively large,
which in our models corresponds to in the dead zone being about 10% of
in the active layers. If the disk is at some stage of its evolution
not in steady-state, then the surface density will evolve toward the
steady-state solution. However, if in the dead zone is much smaller
than in the active zone, the timescale for the parts of the disk beyond a few
AU to reach steady-state may become longer than the disk lifetime. Steady-state
disks with dead zones are a more favorable environment for planet formation
than standard disks, since the dead zone is typically 10 times more massive
than a corresponding turbulent zone at the same location.Comment: 13 pages, 5 figures, accepted for publication in Ap
Precessing warped accretion discs in X-ray binaries
We study the radiation-driven warping of accretion discs in the context of
X-ray binaries. The latest evolutionary equations are adopted, which extend the
classical alpha theory to time-dependent thin discs with non-linear warps. We
also develop accurate, analytical expressions for the tidal torque and the
radiation torque, including self-shadowing.
We investigate the possible non-linear dynamics of the system within the
framework of bifurcation theory. First, we re-examine the stability of an
initially flat disc to the Pringle instability. Then we compute directly the
branches of non-linear solutions representing steadily precessing discs.
Finally, we determine the stability of the non-linear solutions. Each problem
involves only ordinary differential equations, allowing a rapid, accurate and
well resolved solution.
We find that radiation-driven warping is probably not a common occurrence in
low-mass X-ray binaries. We also find that stable, steadily precessing discs
exist for a narrow range of parameters close to the stability limit. This could
explain why so few systems show clear, repeatable `super-orbital' variations.
The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close
to the stability limit for a reasonable choice of parameters. Systems far from
the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably
experience quasi-periodic or chaotic variability as first noticed by Wijers &
Pringle. We show that radiation-driven warping provides a coherent and
persuasive framework but that it does not provide a generic explanation for the
long-term variabilities in all X-ray binaries.Comment: 20 pages, 10 figures, to be published in MNRA
Magnetothermal instabilities in magnetized anisotropic plasmas
Using the transport equations for an ideal anisotropic collisionless plasma
derived from the Vlasov equation by the 16-moment method, we analyse the
influence of pressure anisotropy exhibited by collisionless magnetized plasmas
on the magnetothermal (MTI) and heat-flux-driven buoyancy (HBI) instabilities.
We calculate the dispersion relation and the growth rates for these
instabilities in the presence of a background heat flux and for configurations
with static pressure anisotropy, finding that when the frequency at which heat
conduction acts is much larger than any other frequency in the system (i.e.
weak magnetic field) the pressure anisotropy has no effect on the MTI/HBI,
provided the degree of anisotropy is small. In contrast, when this ordering of
timescales does not apply the instability criteria depend on pressure
anisotropy. Specifically, the growth time of the instabilities in the
anisotropic case can be almost one order of magnitude smaller than its
isotropic counterpart. We conclude that in plasmas where pressure anisotropy is
present the MTI/HBI are modified. However, in environments with low magnetic
fields and small anisotropy such as the ICM the results obtained from the
16-moment equations under the approximations considered are similar to those
obtained from ideal MHD.Comment: v3: 16 pages, 2 figures, fixed typos, added references and a final
note on related wor
On the angular momentum transport due to vertical convection in accretion discs
The mechanism of angular momentum transport in accretion discs has long been
debated. Although the magnetorotational instability appears to be a promising
process, poorly ionized regions of accretion discs may not undergo this
instability. In this letter, we revisit the possibility of transporting angular
momentum by turbulent thermal convection. Using high-resolution spectral
methods, we show that strongly turbulent convection can drive outward angular
momentum transport at a rate that is, under certain conditions, compatible with
observations of discs. We find however that the angular momentum transport is
always much weaker than the vertical heat transport. These results indicate
that convection might be another way to explain global disc evolution, provided
that a sufficiently unstable vertical temperature profile can be maintained.Comment: 6 pages, 5 figures, accepted in MNRA
The response of a turbulent accretion disc to an imposed epicyclic shearing motion
We excite an epicyclic motion, whose amplitude depends on the vertical
position, , in a simulation of a turbulent accretion disc. An epicyclic
motion of this kind may be caused by a warping of the disc. By studying how the
epicyclic motion decays we can obtain information about the interaction between
the warp and the disc turbulence. A high amplitude epicyclic motion decays
first by exciting inertial waves through a parametric instability, but its
subsequent exponential damping may be reproduced by a turbulent viscosity. We
estimate the effective viscosity parameter, , pertaining to
such a vertical shear. We also gain new information on the properties of the
disc turbulence in general, and measure the usual viscosity parameter,
, pertaining to a horizontal (Keplerian) shear. We find that,
as is often assumed in theoretical studies, is approximately
equal to and both are much less than unity, for the field
strengths achieved in our local box calculations of turbulence. In view of the
smallness () of and we conclude
that for the timescale for diffusion
or damping of a warp is much shorter than the usual viscous timescale. Finally,
we review the astrophysical implications.Comment: 12 pages, 18 figures, MNRAS accepte
Jet launching from accretion discs in the local approximation
The acceleration of an outflow along inclined magnetic field lines emanating
from an accretion disc can be studied in the local approximation, as employed
in the computational model known as the shearing box. By including the slow
magnetosonic point within the computational domain, the rate of mass loss in
the outflow can be calculated. The accretion rates of mass and magnetic flux
can also be determined, although some effects of cylindrical geometry are
omitted. We formulate a simple model for the study of this problem and present
the results of one-dimensional numerical simulations and supporting
calculations. Quasi-steady solutions are obtained for relatively strong
poloidal magnetic fields for which the magnetorotational instability is
suppressed. In this regime the rate of mass loss decreases extremely rapidly
with increasing field strength, or with decreasing surface density or
temperature. If the poloidal magnetic field in an accretion disc can locally
achieve an appropriate strength and inclination then a rapid burst of ejection
may occur. For weaker fields it may be possible to study the launching process
in parallel with the magnetorotational instability, but this will require
three-dimensional simulations.Comment: 8 pages, 4 figures, to be published in MNRA
On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks
Subcritical transition to turbulence in Keplerian accretion disks is still a
controversial issue and some theoretical progress is required in order to
determine whether or not this scenario provides a plausible explanation for the
origin of angular momentum transport in non-magnetized accretion disks.
Motivated by the recent discoveries of exact nonlinear steady self-sustaining
solutions in linearly stable non-rotating shear flows, we attempt to compute
similar solutions in Rayleigh-stable rotating plane Couette flows and to
identify transition mechanisms in such flows by combining nonlinear
continuation methods and asymptotic theory. We obtain exact nonlinear solutions
for Rayleigh-stable cyclonic regimes but show that it is not possible to
compute solutions for Rayleigh-stable anticyclonic regimes, including Keplerian
flow, using similar techniques. We also present asymptotic descriptions of
these various problems at large Reynolds numbers that provide some insight into
the differences between the non-rotating and Rayleigh-stable anticyclonic
regimes and derive some necessary conditions for mechanisms analogous to the
non-rotating self-sustaining process to be present in flows on the Rayleigh
line. Our results demonstrate that subcritical transition mechanisms cannot be
identified in wall-bounded Rayleigh-stable anticyclonic shear flows by
transposing directly the phenomenology of subcritical transition in cyclonic
and non-rotating wall-bounded shear flows. Asymptotic developments, however,
leave open the possibility that nonlinear self-sustaining solutions may exist
in unbounded or periodic flows on the Rayleigh line. These could serve as a
starting point to discover solutions in Rayleigh-stable flows, but the
nonlinear stability of Keplerian accretion disks remains to be determined.Comment: 16 pages, 12 figures. Accepted for publication in A&
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