249 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
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
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
On type-I migration near opacity transitions. A generalized Lindblad torque formula for planetary population synthesis
We give an expression for the Lindblad torque acting on a low-mass planet
embedded in a protoplanetary disk that is valid even at locations where the
surface density or temperature profile cannot be approximated by a power law,
such as an opacity transition. At such locations, the Lindblad torque is known
to suffer strong deviation from its standard value, with potentially important
implications for type I migration, but the full treatment of the tidal
interaction is cumbersome and not well suited to models of planetary population
synthesis. The expression that we propose retains the simplicity of the
standard Lindblad torque formula and gives results that accurately reproduce
those of numerical simulations, even at locations where the disk temperature
undergoes abrupt changes. Our study is conducted by means of customized
numerical simulations in the low-mass regime, in locally isothermal disks, and
compared to linear torque estimates obtained by summing fully analytic torque
estimates at each Lindblad resonance. The functional dependence of our modified
Lindblad torque expression is suggested by an estimate of the shift of the
Lindblad resonances that mostly contribute to the torque, in a disk with sharp
gradients of temperature or surface density, while the numerical coefficients
of the new terms are adjusted to seek agreement with numerics. As side results,
we find that the vortensity related corotation torque undergoes a boost at an
opacity transition that can counteract migration, and we find evidence from
numerical simulations that the linear corotation torque has a non-negligible
dependency upon the temperature gradient, in a locally isothermal disk.Comment: Appeared in special issue of "Celestial Mechanics and Dynamical
Astronomy" on Extrasolar Planetary System
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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