196 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
Multidimensional upwind hydrodynamics on unstructured meshes using graphics processing units - I. Two-dimensional uniform meshes
SJP is supported by a Royal Society University Research Fellowship
Growing and moving low-mass planets in non-isothermal disks
We study the interaction of a low-mass planet with a protoplanetary disk with
a realistic treatment of the energy balance by doing radiation-hydrodynamical
simulations. We look at accretion and migration rates and compare them to
isothermal studies. We used a three-dimensional version of the hydrodynamical
method RODEO, together with radiative transport in the flux-limited diffusion
approach. The accretion rate, as well as the torque on the planet, depend
critically on the ability of the disk to cool efficiently. For densities
appropriate to 5 AU in the solar nebula, the accretion rate drops by more than
an order of magnitude compared to isothermal models, while at the same time the
torque on the planet is positive, indicating outward migration. It is necessary
to lower the density by a factor of 2 to recover inward migration and more than
2 orders of magnitude to recover the usual Type I migration. The torque appears
to be proportional to the radial entropy gradient in the unperturbed disk.
These findings are critical for the survival of protoplanets, and they should
ultimately find their way into population synthesis models.Comment: Accepted for publication in Astronomy and Astrophysic
The evolution of a binary in a retrograde circular orbit embedded in an accretion disk
Supermassive black hole binaries may form as a consequence of galaxy mergers.
Both prograde and retrograde orbits have been proposed. We study a binary of a
small mass ratio, q, in a retrograde orbit immersed in and interacting with a
gaseous accretion disk in order to estimate time scales for inward migration
leading to coalescence and the accretion rate to the secondary component. We
employ both semi-analytic methods and two dimensional numerical simulations,
focusing on the case where the binary mass ratio is small but large enough to
significantly perturb the disk. We develop the theory of type I migration for
this case and determine conditions for gap formation finding that then inward
migration occurs on a time scale equal to the time required for one half of the
secondary mass to be accreted through the unperturbed disk, with accretion onto
the secondary playing only a minor role. The semi-analytic and fully numerical
approaches are in good agreement, the former being applicable over long time
scales. Inward migration induced by interaction with the disk alleviates the
final parsec problem. Accretion onto the secondary does not significantly
affect the orbital evolution, but may have observational consequences for high
accretion efficiency. The binary may then appear as two sources of radiation
rotating around each other. This study should be extended to consider orbits
with significant eccentricity and the effects of gravitational radiation at
small length scales. Note too that torques acting between a circumbinary disk
and a retrograde binary orbit may cause the mutual inclination to increase on a
timescale that can be similar to, or smaller than that for orbital evolution,
depending on detailed parameters. This is also an aspect for future study
(abridged).Comment: 24 pages, 18 figures, accepted for publication in A&A. For movies of
the simulations see
http://astro.qmul.ac.uk/people/sijme-jan-paardekooper/publication
Planetesimal collisions in binary systems
We study the collisional evolution of km-sized planetesimals in tight binary
star systems to investigate whether accretion towards protoplanets can proceed
despite the strong gravitational perturbations from the secondary star. The
orbits of planetesimals are numerically integrated in two dimensions under the
influence of the two stars and gas drag. The masses and orbits of the
planetesimals are allowed to evolve due to collisions with other planetesimals
and accretion of collisional debris. In addition, the mass in debris can evolve
due to planetesimal-planetesimal collisions and the creation of new
planetesimals. We show that it is possible in principle for km-sized
planetesimals to grow by two orders of magnitude in size if the efficiency of
planetesimal formation is relatively low. We discuss the limitations of our
two-dimensional approach.Comment: 5 pages, 5 figures, accepted for publication in MNRA
On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration
We study the torque on low mass protoplanets on fixed circular orbits,
embedded in a protoplanetary disc in the isothermal limit. For low mass
protoplanets and large viscosity the corotation torque behaves as expected from
linear theory. However, when the viscosity becomes small enough to enable
horseshoe turns to occur, the linear corotation torque exists only temporarily
after insertion of a planet into the disc, being replaced by the horseshoe drag
first discussed by Ward. This happens after a time that is equal to the
horseshoe libration period reduced by a factor amounting to about twice the
disc aspect ratio. This torque scales with the radial gradient of specific
vorticity, as does the linear torque, but we find it to be many times larger.
If the viscosity is large enough for viscous diffusion across the coorbital
region to occur within a libration period, we find that the horseshoe drag may
be sustained. If not, the corotation torque saturates leaving only the linear
Lindblad torques. As the magnitude of the non linear coorbital torque
(horseshoe drag) is always found to be larger than the linear torque, we find
that the sign of the total torque may change even for for mildly positive
surface density gradients. In combination with a kinematic viscosity large
enough to keep the torque from saturating, strong sustained deviations from
linear theory and outward or stalled migration may occur in such cases
(abridged).Comment: 15 pages, 15 figures, accepted for publication in MNRA
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