1,052 research outputs found
Disc-planet interactions in sub-keplerian discs
One class of protoplanetary disc models, the X-wind model, predicts strongly
subkeplerian orbital gas velocities, a configuration that can be sustained by
magnetic tension. We investigate disc-planet interactions in these subkeplerian
discs, focusing on orbital migration for low-mass planets and gap formation for
high-mass planets. We use linear calculations and nonlinear hydrodynamical
simulations to measure the torque and look at gap formation. In both cases, the
subkeplerian nature of the disc is treated as a fixed external constraint. We
show that, depending on the degree to which the disc is subkeplerian, the
torque on low-mass planets varies between the usual Type I torque and the
one-sided outer Lindblad torque, which is also negative but an order of
magnitude stronger. In strongly subkeplerian discs, corotation effects can be
ignored, making migration fast and inward. Gap formation near the planet's
orbit is more difficult in such discs, since there are no resonances close to
the planet accommodating angular momentum transport. In stead, the location of
the gap is shifted inwards with respect to the planet, leaving the planet on
the outside of a surface density depression. Depending on the degree to which a
protoplanetary disc is subkeplerian, disc-planet interactions can be very
different from the usual Keplerian picture, making these discs in general more
hazardous for young planets.Comment: 4 pages, 4 figures, accepted in Astronomy and Astrophysics Letters,
minor language change
A torque formula for non-isothermal Type I planetary migration - II. Effects of diffusion
We study the effects of diffusion on the non-linear corotation torque, or
horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for
which the width of the horseshoe region is much smaller than the scale height
of the disc. In the absence of diffusion, the non-linear corotation torque
saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can
act to sustain the corotation torque. In the limit of very strong diffusion,
the linear corotation torque is recovered. For the case of thermal diffusion,
this limit corresponds to having a locally isothermal equation of state. We
present some simple models that are able to capture the dependence of the
torque on diffusive processes to within 20% of the numerical simulations.Comment: 12 pages, 8 figures, accepted for publication in MNRA
On the width and shape of the corotation region for low-mass planets
We study the coorbital flow for embedded, low mass planets. We provide a
simple semi-analytic model for the corotation region, which is subsequently
compared to high resolution numerical simulations. The model is used to derive
an expression for the half-width of the horseshoe region, x_s, which in the
limit of zero softening is given by x_s/r_p = 1.68(q/h)^(1/2), where q is the
planet to central star mass ratio, h is the disc aspect ratio and r_p the
orbital radius. This is in very good agreement with the same quantity measured
from simulations. This result is used to show that horseshoe drag is about an
order of magnitude larger than the linear corotation torque in the zero
softening limit. Thus the horseshoe drag, the sign of which depends on the
gradient of specific vorticity, is important for estimates of the total torque
acting on the planet. We further show that phenomena, such as the Lindblad
wakes, with a radial separation from corotation of ~ a pressure scale height H
can affect x_s, even though for low-mass planets x_s << H. The effect is to
distort streamlines and to reduce x_s through the action of a back pressure.
This effect is reduced for smaller gravitational softening parameters and
planets of higher mass, for which x_s becomes comparable to H.Comment: 15 pages, 11 figures, accepted for publication in MNRA
Type I migration in optically thick accretion discs
We study the torque acting on a planet embedded in an optically thick
accretion disc, using global two-dimensional hydrodynamic simulations. The
temperature of an optically thick accretion disc is determined by the energy
balance between the viscous heating and the radiative cooling. The radiative
cooling rate depends on the opacity of the disc. The opacity is expressed as a
function of the temperature. We find the disc is divided into three regions
that have different temperature distributions. The slope of the entropy
distribution becomes steep in the inner region of the disc with the high
temperature and the outer region of the disc with the low temperature, while it
becomes shallow in the middle region with the intermediate temperature. Planets
in the inner and outer regions move outward owing to the large positive
corotation torque exerted on the planet by an adiabatic disc, on the other
hand, a planet in the middle region moves inward toward the central star.
Planets are expected to accumulate at the boundary between the inner and middle
regions of the adiabatic disc. The positive corotation torque decreases with an
increase in the viscosity of the disc. We find that the positive corotation
torque acting on the planet in the inner region becomes too small to cancel the
negative Lindblad torque when we include the large viscosity, which destroys
the enhancement of the density in the horseshoe orbit of the planet. This leads
to the inward migration of the planet in the inner region of the disc. A planet
with 5 Earth masses in the inner region can move outward in a disc with the
surface density of 100 g/cm^2 at 1 AU when the accretion rate of a disc is
smaller than 2x10^{-8} solar mass/yr.Comment: 17 pages, 15 figure
Parallel normreducing transformations for the algebraic eigenvalue problem
Eigenvalues;mathematics
Type I Migration in Radiatively Efficient Discs
We study Type I migration of a planet in a radiatively efficient disk using
global two dimensional hydrodynamic simulations. The large positive corotation
torque is exerted on a planet by an adiabatic disk at early times when the disk
has the steep negative entropy gradient. The gas on the horseshoe orbit of the
planet is compressed adiabatically during the change of the orbit from the slow
orbit to the fast orbit, increasing its density and exerting the positive
torque on the planet. The planet would migrate outward in the adiabatic disk
before saturation sets in. We further study the effect of energy dissipation by
radiation on Type I migration of the planet. The corotation torque decreases
when the energy dissipates effectively because the density of the gas on the
horseshoe orbit does not increase by the compression compared with the gas of
the adiabatic disk. The total torque is mainly determined by the negative
Lindblad torque and becomes negative. The planet migrates inward toward the
central star in the radiatively efficient disk. The migration velocity is
dependent on the radiative efficiency and greatly reduced if the radiative
cooling works inefficiently.Comment: 12 pages, 10 figures, 1 table, Accepted for publication in MNRA
Dynamical corotation torques on low-mass planets
We study torques on migrating low-mass planets in locally isothermal discs.
Previous work on low-mass planets generally kept the planet on a fixed orbit,
after which the torque on the planet was measured. In addition to these static
torques, when the planet is allowed to migrate it experiences dynamical
torques, which are proportional to the migration rate and whose sign depends on
the background vortensity gradient. We show that in discs a few times more
massive than the Minimum Mass Solar Nebula, these dynamical torques can have a
profound impact on planet migration. Inward migration can be slowed down
significantly, and if static torques lead to outward migration, dynamical
torques can take over, taking the planet beyond zero-torque lines set by
saturation of the corotation torque in a runaway fashion. This means the region
in non-isothermal discs where outward migration is possible can be larger than
what would be concluded from static torques alone.Comment: 14 pages, 13 figures, accepted for publication in MNRA
A quadratically convergent parallel Jacobi-process for diagonal dominant matrices with nondistinct eigenvalues
Matrices;Eigenvalues;mathematics
Jacobi-type algorithms for eigenvalues on vector- and parallel computers
Algebra;Numerical Computation
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