422 research outputs found
Constraints on resonant-trapping for two planets embedded in a protoplanetary disc
We investigate the evolution of two-planet systems embedded in a
protoplanetary disc, which are composed of a Jupiter-mass planet plus another
body located further out in the disc. We consider outermost planets with masses
ranging from 10 earth masses to 1 M_J. We also examine the case of outermost
bodies with masses < 10 earth masses (M_E). Differential migration of the
planets due to disc torques leads to different evolution outcomes depending on
the mass of the outer protoplanet. For planets with mass < 3.5 M_E the type II
migration rate of the giant exceeds the type I migration rate of the outer
body, resulting in divergent migration. Outer bodies with masses in the range
3.5 < m_o < 20 M_E become trapped at the edge of the gap formed by the giant
planet, because of corotation torques. Higher mass planets are captured into
resonance with the inner planet. If 30 < m_o < 40 M_E or m_o=1 M_J, then the
2:1 resonance is established. If 80 < m_o < 100 M_E, the 3:2 resonance is
favoured. Simulations of gas-accreting protoplanets of mass m_o > 20 M_E,
trapped initially at the edge of the gap, or in the 2:1 resonance, also result
in eventual capture in the 3:2 resonance as the planet mass grows to become
close to the mass of Saturn. Our results suggest that there is a theoretical
lower limit to the mass of an outer planet that can be captured into resonance
with an inner Jovian planet, which is relevant to observations of extrasolar
multiplanet systems. Furthermore, capture of a Saturn-like planet into the 3:2
resonance with a Jupiter-like planet is a very robust outcome of simulations.
This result is relevant to recent scenarios of early Solar System evolution
which require Saturn to have existed interior to the 2:1 resonance with Jupiter
prior to the onset of the Late Heavy Bombardment.Comment: 10 pages, 9 figures, Accepted for publication in A&
On the growth and orbital evolution of giant planets in layered protoplanetary disks
We present the results of hydrodynamic simulations of the growth and orbital
evolution of giant planets embedded in a protoplanetary disk with a dead-zone.
The aim is to examine to what extent the presence of a dead-zone affects the
rates of mass accretion and migration for giant planets. We performed 3D
numerical simulations using a grid-based hydrodynamics code. In these
simulations of non-magnetised disks, the dead-zone is treated as a region where
the vertical profile of the viscosity depends on the distance from the
equatorial plane. We consider dead-zones with vertical sizes, H_dz, ranging
from 0 to H_dz=2.3H, where H is the disk scale-height. For all models, the
vertically integrated viscous stress, and the related mass flux through the
disk, have the same value, such that the simulations test the dependence of
planetary mass accretion and migration on the vertical distribution of the
viscous stress. For each model, an embedded 30 earth-masses planet on a fixed
circular orbit is allowed to accrete gas from the disk. Once the planet mass
becomes equal to that of Saturn or Jupiter, we allow the planet orbit to evolve
due to gravitational interaction with the disk. We find that the time scale
over which a protoplanet grows to become a giant planet is essentially
independent of the dead-zone size, and depends only on the total rate at which
the disk viscously supplies material to the planet. For Saturn-mass planets,
the migration rate depends only weakly on the size of the dead-zone for H_dz<
1.5H, but becomes slower when H_dz=2.3H. This effect is due to the desaturation
of corotation torques which originate from residual material in the partial-gap
region. For Jupiter-mass planets, there is a clear tendency for the migration
to proceed more slowly as the size of the dead-zone increases.Comment: Accepted for publication in A&A. 10 pages, 12 figure
The Migration and Growth of Protoplanets in Protostellar Discs
We investigate the gravitational interaction of a Jovian mass protoplanet
with a gaseous disc with aspect ratio and kinematic viscosity expected for the
protoplanetary disc from which it formed. Different disc surface density
distributions have been investigated. We focus on the tidal interaction with
the disc with the consequent gap formation and orbital migration of the
protoplanet. Nonlinear hydrodynamic simulations are employed using three
independent numerical codes.
A principal result is that the direction of the orbital migration is always
inwards and such that the protoplanet reaches the central star in a near
circular orbit after a characteristic viscous time scale of approximately
10,000 initial orbital periods. This was found to be independent of whether the
protoplanet was allowed to accrete mass or not. Inward migration is helped
through the disappearance of the inner disc, and therefore the positive torque
it would exert, because of accretion onto the central star.Our results indicate
that a realistic upper limit for the masses of closely orbiting giant planets
is approximately 5 Jupiter masses, because of the reduced accretion rates
obtained for planets of increasing mass.
Assuming some process such as termination of the inner disc through a
magnetospheric cavity stops the migration, the range of masses estimated for a
number of close orbiting giant planets (Marcy, Cochran, & Mayor 1999; Marcy &
Butler 1998) as well as their inward orbital migration can be accounted for by
consideration of disc--protoplanet interactions during the late stages of giant
planet formation. Maximally accreting protoplanets reached about four Jovian
masses on reaching the neighbourhood of the central star.Comment: 19 pages, 16 figures, submitted to MNRAS. A version of this paper
that includes high resolution figures may be obtained from
http://www.maths.qmw.ac.uk/~rpn/preprint.htm
Evolution of the eccentricity and inclination of low-mass planets subjected to thermal forces: a numerical study
By means of three dimensional, high resolution hydrodynamical simulations we
study the orbital evolution of weakly eccentric or inclined low-mass
protoplanets embedded in gaseous discs subject to thermal diffusion. We
consider both non-luminous planets, and planets that also experience the
radiative feedback from their own luminosity. We compare our results to
previous analytical work, and find that thermal forces (the contribution to the
disc's force arising from thermal effects) match those predicted by linear
theory within %. When the planet's luminosity exceeds a threshold
found to be within % of that predicted by linear theory, its eccentricity
and inclination grow exponentially, whereas these quantities undergo a strong
damping below this threshold. In this regime of low luminosity indeed, thermal
diffusion cools the surroundings of the planet and allows gas to accumulate in
its vicinity. It is the dynamics of this gas excess that contributes to damp
eccentricity and inclination. The damping rates obtained can be up to
times larger than those due to the resonant interaction with the disc, where
is the disc's aspect ratio. This suggests that models that incorporate
planet-disc interactions using well-known formulae based on resonant
wave-launching to describe the evolution of eccentricity and inclination
underestimate the damping action of the disc on the eccentricity and
inclination of low-mass planets by an order of magnitude.Comment: Accepted for publication in MNRA
Radial Dependence of the Pattern Speed of M51
The grand-design spiral galaxy M51 has long been a crucial target for
theories of spiral structure. Studies of this iconic spiral can address the
question of whether strong spiral structure is transient (e.g.
interaction-driven) or long-lasting. As a clue to the origin of the structure
in M51, we investigate evidence for radial variation in the spiral pattern
speed using the radial Tremaine-Weinberg (TWR) method. We implement the method
on CO observations tracing the ISM-dominant molecular component. Results from
the method's numerical implementation--combined with regularization, which
smooths intrinsically noisy solutions--indicate two distinct patterns speeds
inside 4 kpc at our derived major axis PA=170 deg., both ending at corotation
and both significantly higher than the conventionally adopted global value.
Inspection of the rotation curve suggests that the pattern speed interior to 2
kpc lacks an ILR, consistent with the leading structure seen in HST near-IR
observations. We also find tentative evidence for a lower pattern speed between
4 and 5.3 kpc measured by extending the regularized zone. As with the original
TW method, uncertainty in major axis position angle (PA) is the largest source
of error in the calculation; in this study, where \delta PA=+/-5 deg. a ~20%
error is introduced to the parameters of the speeds at PA=170 deg. Accessory to
this standard uncertainty, solutions with PA=175 deg. (also admitted by the
data) exhibit only one pattern speed inside 4 kpc, and we consider this
circumstance under the semblance of a radially varying PA.Comment: 14 pages in emulateapj format, 12 figures, accepted for publication
in Ap
The Parker Instability in 3-D: Corrugations and Superclouds Along the Carina-Sagittarius Arm
Here we present three-dimensional MHD models for the Parker instability in a
thick magnetized disk, including the presence of a spiral arm. The -field is
assumed parallel to the arm, and the model results are applied to the optical
segment of the Carina-Sagittarius arm. The characteristic features of the
undular and interchange modes are clearly apparent in the simulations. The
undular mode creates large gas concentrations distributed along the arm. This
results in a clear arm/inter-arm difference: the instability triggers the
formation of large interstellar clouds inside the arms, but generates only
small structures with slight density enhancements in the inter-arm regions. The
resulting clouds are distributed in an antisymmetric way with respect to the
midplane, creating an azimuthal corrugation along the arm. For conditions
similar to those of the optical segment of the Carina-Sagittarius arm, it has a
wavelength of about 2.4 kpc. This structuring can explain the origin of both HI
superclouds and the azimuthal corrugations in spiral arms. The wavelength
matches the corrugation length derived with the young stellar groups located in
the optical segment of the Carina-Sagittarius arm. Keywords: Galaxy: kinematics
and dynamics -- Galaxy: structure -- Instabilities -- ISM: clouds -- ISM:
magnetic fields -- ISM: structure -- MHDComment: 29 pages, 12 figures, Latex, Accepted by the Astrophysical Journa
On the evolution of eccentric and inclined protoplanets embedded in protoplanetary disks
Young planets embedded in their protoplanetary disk interact gravitationally
with it leading to energy and angular momentum exchange. This interaction
determines the evolution of the planet through changes to the orbital
parameters. We investigate changes in the orbital elements of a 20 Earth--mass
planet due to the torques from the disk. We focus on the non-linear evolution
of initially non-vanishing eccentricity and/or inclination . We treat
the disk as a two- or three-dimensional viscous fluid and perform
hydrodynamical simulations with an embedded planet. We find rapid exponential
decay of the planet orbital eccentricity and inclination for small initial
values of and , in agreement with linear theory. For larger values of the decay time increases and the decay rate scales as , consistent with existing theoretical models. For large inclinations
( > 6 deg) the inclination decay rate shows an identical scaling . We find an interesting dependence of the migration on the
eccentricity. In a disk with aspect ratio the migration rate is
enhanced for small non-zero eccentricities (), while for larger values
we see a significant reduction by a factor of . We find no indication
for a reversal of the migration for large , although the torque experienced
by the planet becomes positive when . This inward migration is
caused by the persisting energy loss of the planet.
For non gap forming planets, eccentricity and inclination damping occurs on a
time scale that is very much shorter than the migration time scale. The results
of non linear hydrodynamic simulations are in very good agreement with linear
theory for small and .Comment: accepted for Astronomy & Astrophysics, 16 pages, 16 figures,
animations under:
http://www.tat.physik.uni-tuebingen.de/~kley/publ/paper/eccp.htm
Recent developments in planet migration theory
Planetary migration is the process by which a forming planet undergoes a
drift of its semi-major axis caused by the tidal interaction with its parent
protoplanetary disc. One of the key quantities to assess the migration of
embedded planets is the tidal torque between the disc and planet, which has two
components: the Lindblad torque and the corotation torque. We review the latest
results on both torque components for planets on circular orbits, with a
special emphasis on the various processes that give rise to additional, large
components of the corotation torque, and those contributing to the saturation
of this torque. These additional components of the corotation torque could help
address the shortcomings that have recently been exposed by models of planet
population syntheses. We also review recent results concerning the migration of
giant planets that carve gaps in the disc (type II migration) and the migration
of sub-giant planets that open partial gaps in massive discs (type III
migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal
effects in Astronomy and Astrophysics", Lecture Notes in Physic
On disc driven inward migration of resonantly coupled planets with application to the system around GJ876
We consider two protoplanets gravitationally interacting with each other and
a protoplanetary disc. The two planets orbit interior to a tidally maintained
disc cavity while the disc interaction indices inward migration. When the
migration is slow enough, the more rapidly migrating outer protoplanet
approaches and becomes locked in a 2:1 commensurability with the inner one.
This is maintained in subsequent evolution. We study this evolution using a
simple anaytic model, full hydrodynamic 2D simulations of the disc planet
system and longer time N body integrations incorporating simple prescriptions
for the effect of the disc on the planet orbits. The eccentricity of the
protoplanets are found to be determined by the migration rate induced in the
outer planet orbit by the external disc. We apply our results to the recently
discovered resonant planets around GJ876. Simulation shows that a disc with
parameters expected for protoplanetary discs causes trapping in the 2:1
commensurability when the planets orbit in an inner cavity and that
eccentricities in the observed range may be obtained.Comment: 8 pages, 5 figures, submitted to A&A on 30/03/200
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