385 research outputs found
The effect of planetary migration on the corotation resonance
The migration of a planet through a gaseous disc causes the locations of
their resonant interactions to drift and can alter the torques exerted between
the planet and the disc. We analyse the time-dependent dynamics of a
non-coorbital corotation resonance under these circumstances. The ratio of the
resonant torque in a steady state to the value given by Goldreich & Tremaine
(1979) depends essentially on two dimensionless quantities: a dimensionless
turbulent diffusion time-scale and a dimensionless radial drift speed. When the
drift speed is comparable to the libration speed and the viscosity is small,
the torque can become much larger than the unsaturated value in the absence of
migration, but is still proportional to the large-scale vortensity gradient in
the disc. Fluid that is trapped in the resonance and drifts with it acquires a
vortensity anomaly relative to its surroundings. If the anomaly is limited by
viscous diffusion in a steady state, the resulting torque is inversely
proportional to the viscosity, although a long time may be required to achieve
this state. A further, viscosity-independent, contribution to the torque comes
from fluid that streams through the resonant region. In other cases, torque
oscillations occur before the steady value is achieved. We discuss the
significance of these results for the evolution of eccentricity in
protoplanetary systems. We also describe the possible application of these
findings to the coorbital region and the concept of runaway (or type III)
migration. [Abridged]Comment: 15 pages, 6 figures, to be published in MNRA
Large Scale B-Field in Stationary Accretion Disks
We reconsider the problem of the formation of a large-scale magnetic field in
the accretion disks around black holes. In contrast with previous work we take
into account the nonuniform vertical structure of the disk. The high electrical
conductivity of the outer layers of the disk prevents the outward diffusion of
the magnetic field. This implies a stationary state with a strong magnetic
field in the inner parts of the accretion disk close to the black hole.Comment: 5 pages, 2 figure
The effect of an isothermal atmosphere on the propagation of three-dimensional waves in a thermally stratified accretion disk
We extend our analysis of the three-dimensional response of a vertically
polytropic disk to tidal forcing at Lindblad resonances by including the
effects of a disk atmosphere. The atmosphere is modeled as an isothermal layer
that joins smoothly on to an underlying polytropic layer. The launched wave
progressively enters the atmosphere as it propagates away from the resonance.
The wave never propagates vertically, however, and the wave energy rises to a
(finite) characteristic height in the atmosphere. The increase of wave
amplitude associated with this process of wave channeling is reduced by the
effect of the atmosphere. For waves of large azimuthal mode number m generated
by giant planets embedded in a disk, the increase in wave amplitude is still
substantial enough to be likely to dissipate the wave energy by shocks for even
modest optical depths (tau greater than about 10) over a radial distance of a
few times the disk thickness. For low-m waves generated in circumstellar disks
in binary stars, the effects of wave channeling are less important and the
level of wave nonlinearity increases by less than a factor of 10 in going from
the disk edge to the disk center. For circumbinary disks, the effects of wave
channeling remain important, even for modest values of optical depth.Comment: 11 pages, 4 figures, submitted to the Astrophysical Journa
Saturation of the corotation resonance in a gaseous disk
We determine the torque exerted in a steady state by an external potential on
a three-dimensional gaseous disk at a non-coorbital corotation resonance. Our
model accounts for the feedback of the torque on the surface density and
vorticity in the corotation region, and assumes that the disk has a barotropic
equation of state and a nonzero effective viscosity. The ratio of the torque to
the value given by the formula of Goldreich & Tremaine depends essentially on a
single dimensionless parameter, which quantifies the extent to which the
resonance is saturated. We discuss the implications for the eccentricity
evolution of young planets.Comment: 23 pages, 1 figure, revised version, to be published in the
Astrophysical Journa
The evolution of a warped disc around a Kerr black hole
We consider the evolution of a warped disc around a Kerr black hole, under
conditions such that the warp propagates in a wavelike manner. This occurs when
the dimensionless effective viscosity, alpha, that damps the warp is less than
the characteristic angular semi-thickness, H/R, of the disc. We adopt
linearized equations that are valid for warps of sufficiently small amplitude
in a Newtonian disc, but also account for the apsidal and nodal precession that
occur in the Kerr metric. Through analytical and time-dependent studies, we
confirm the results of Demianski & Ivanov, and of Ivanov & Illarionov, that
such a disc takes on a characteristic warped shape. The inner part of the disc
is not necessarily aligned with the equator of the hole, even in the presence
of dissipation. We draw attention to the fact that this might have important
implications for the directionality of jets emanating from discs around
rotating black holes.Comment: 8 pages, 6 figures, to be published in MNRA
Type I planet migration in nearly laminar disks - long term behavior
We carry out 2-D high resolution numerical simulations of type I planet
migration with different disk viscosities. We find that the planet migration is
strongly dependent on disk viscosities. Two kinds of density wave damping
mechanisms are discussed. Accordingly, the angular momentum transport can be
either viscosity dominated or shock dominated, depending on the disk
viscosities. The long term migration behavior is different as well. Influences
of the Rossby vortex instability on planet migration are also discussed. In
addition, we investigate very weak shock generation in inviscid disks by small
mass planets and compare the results with prior analytic results.Comment: Accepted for publication in Ap
On the Decelerating Shock Instability of Plane-Parallel Slab with Finite Thickness
Dynamical stability of the shock compressed layer with finite thickness is
investigated. It is characterized by self-gravity, structure, and shock
condition at the surfaces of the compressed layer. At one side of the shocked
layer, its surface condition is determined via the ram pressure, while at the
other side the thermal pressure supports its structure. When the ram pressure
dominates the thermal pressure, we expect deceleration of the shocked layer.
Especially, in this paper, we examine how the stratification of the
decelerating layer has an effect on its dynamical stability. Performing the
linear perturbation analysis, a {\it more general} dispersion relation than the
previous one obtained by one of the authors is derived. It gives us an
interesting information about the stability of the decelerating layer.
Importantly, the DSI (Decelerating Shock Instability) and the gravitational
instability are always incompatible. We also consider the evolution effect of
the shocked layer. In the early stages of its evolution, only DSI occurs. On
the contrary, in the late stages, it is possible for the shocked layer to be
unstable for the DSI (in smaller scale) and the gravitational instability (in
larger scale). Furthermore, we find there is a stable range of wavenumbers
against both the DSI and the gravitational instability between respective
unstable wavenumber ranges. These stable modes suggest the ineffectiveness of
DSI for the fragmentation of the decelerating slab.Comment: 17 pages, 6 figures. The Astrophysical Journal Vol.532 in pres
Secular interactions between inclined planets and a gaseous disk
In a planetary system, a secular particle resonance occurs at a location
where the precession rate of a test particle (e.g. an asteroid) matches the
frequency of one of the precessional modes of the planetary system. We
investigate the secular interactions of a system of mutually inclined planets
with a gaseous protostellar disk that may contain a secular nodal particle
resonance. We determine the normal modes of some mutually inclined planet-disk
systems. The planets and disk interact gravitationally, and the disk is
internally subject to the effects of gas pressure, self-gravity, and turbulent
viscosity. The behavior of the disk at a secular resonance is radically
different from that of a particle, owing mainly to the effects of gas pressure.
The resonance is typically broadened by gas pressure to the extent that global
effects, including large-scale warps, dominate. The standard resonant torque
formula is invalid in this regime. Secular interactions cause a decay of the
inclination at a rate that depends on the disk properties, including its mass,
turbulent viscosity, and sound speed. For a Jupiter-mass planet embedded within
a minimum-mass solar nebula having typical parameters, dissipation within the
disk is sufficient to stabilize the system against tilt growth caused by
mean-motion resonances.Comment: 30 pages, 6 figures, to be published in The Astrophysical Journa
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