461 research outputs found
Low-mass planets in nearly inviscid disks: Numerical treatment
Embedded planets disturb the density structure of the ambient disk and
gravitational back-reaction will induce possibly a change in the planet's
orbital elements. The accurate determination of the forces acting on the planet
requires careful numerical analysis. Recently, the validity of the often used
fast orbital advection algorithm (FARGO) has been put into question, and
special numerical resolution and stability requirements have been suggested. In
this paper we study the process of planet-disk interaction for small mass
planets of a few Earth masses, and reanalyze the numerical requirements to
obtain converged and stable results. One focus lies on the applicability of the
FARGO-algorithm. Additionally, we study the difference of two and
three-dimensional simulations, compare global with local setups, as well as
isothermal and adiabatic conditions. We study the influence of the planet on
the disk through two- and three-dimensional hydrodynamical simulations. To
strengthen our conclusions we perform a detailed numerical comparison where
several upwind and Riemann-solver based codes are used with and without the
FARGO-algorithm.
With respect to the wake structure and the torque density acting on the
planet we demonstrate that the FARGO-algorithm yields correct results, and that
at a fraction of the regular cpu-time. We find that the resolution requirements
for achieving convergent results in unshocked regions are rather modest and
depend on the pressure scale height of the disk. By comparing the torque
densities of 2D and 3D simulations we show that a suitable vertical averaging
procedure for the force gives an excellent agreement between the two. We show
that isothermal and adiabatic runs can differ considerably, even for adiabatic
indices very close to unity.Comment: accepted by Astronomy & Astrophysic
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
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&
The mass-period distribution of close-in exoplanets
The lower limit to the distribution of orbital periods P for the current
population of close-in exoplanets shows a distinctive discontinuity located at
approximately one Jovian mass. Most smaller planets have orbital periods longer
than P~2.5 days, while higher masses are found down to P~1 day.
We analyze whether this observed mass-period distribution could be explained
in terms of the combined effects of stellar tides and the interactions of
planets with an inner cavity in the gaseous disk.
We performed a series of hydrodynamical simulations of the evolution of
single-planet systems in a gaseous disk with an inner cavity mimicking the
inner boundary of the disk. The subsequent tidal evolution is analyzed assuming
that orbital eccentricities are small and stellar tides are dominant.
We find that most of the close-in exoplanet population is consistent with an
inner edge of the protoplanetary disk being located at approximately P>2 days
for solar-type stars, in addition to orbital decay having been caused by
stellar tides with a specific tidal parameter on the order of Q'*=10^7. The
data is broadly consistent with planets more massive than one Jupiter mass
undergoing type II migration, crossing the gap, and finally halting at the
interior 2/1 mean-motion resonance with the disk edge. Smaller planets do not
open a gap in the disk and remain trapped in the cavity edge. CoRoT-7b appears
detached from the remaining exoplanet population, apparently requiring
additional evolutionary effects to explain its current mass and semimajor axis.Comment: 8 Pages, 8 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
High-resolution spectroscopic view of planet formation sites
Theories of planet formation predict the birth of giant planets in the inner,
dense, and gas-rich regions of the circumstellar disks around young stars.
These are the regions from which strong CO emission is expected. Observations
have so far been unable to confirm the presence of planets caught in formation.
We have developed a novel method to detect a giant planet still embedded in a
circumstellar disk by the distortions of the CO molecular line profiles
emerging from the protoplanetary disk's surface. The method is based on the
fact that a giant planet significantly perturbs the gas velocity flow in
addition to distorting the disk surface density. We have calculated the
emerging molecular line profiles by combining hydrodynamical models with
semianalytic radiative transfer calculations. Our results have shown that a
giant Jupiter-like planet can be detected using contemporary or future
high-resolution near-IR spectrographs such as VLT/CRIRES or ELT/METIS. We have
also studied the effects of binarity on disk perturbations. The most
interesting results have been found for eccentric circumprimary disks in
mid-separation binaries, for which the disk eccentricity - detectable from the
asymmetric line profiles - arises from the gravitational effects of the
companion star. Our detailed simulations shed new light on how to constrain the
disk kinematical state as well as its eccentricity profile. Recent findings by
independent groups have shown that core-accretion is severely affected by disk
eccentricity, hence detection of an eccentric protoplanetary disk in a young
binary system would further constrain planet formation theories.Comment: IAU Symposium 276 (contributed talk
Origin and Detectability of coorbital planets from radial velocity data
We analyze the possibilities of detection of hypothetical exoplanets in
coorbital motion from synthetic radial velocity (RV) signals, taking into
account different types of stable planar configurations, orbital eccentricities
and mass ratios. For each nominal solution corresponding to small-amplitude
oscillations around the periodic solution, we generate a series of synthetic RV
curves mimicking the stellar motion around the barycenter of the system. We
then fit the data sets obtained assuming three possible different orbital
architectures: (a) two planets in coorbital motion, (b) two planets in a 2/1
mean-motion resonance, and (c) a single planet. We compare the resulting
residuals and the estimated orbital parameters.
For synthetic data sets covering only a few orbital periods, we find that the
discrete radial velocity signal generated by a coorbital configuration could be
easily confused with other configurations/systems, and in many cases the best
orbital fit corresponds to either a single planet or two bodies in a 2/1
resonance. However, most of the incorrect identifications are associated to
dynamically unstable solutions.
We also compare the orbital parameters obtained with two different fitting
strategies: a simultaneous fit of two planets and a nested multi-Keplerian
model. We find that the nested models can yield incorrect orbital
configurations (sometimes close to fictitious mean-motion resonances) that are
nevertheless dynamically stable and with orbital eccentricities lower than the
correct nominal solutions.
Finally, we discuss plausible mechanisms for the formation of coorbital
configurations, by the interaction between two giant planets and an inner
cavity in the gas disk. For equal mass planets, both Lagrangian and
anti-Lagrangian configurations can be obtained from same initial condition
depending on final time of integration.Comment: 14 pages, 16 figures.2012. MNRAS, 421, 35
Numerical simulations of the type III migration:I. Disc model and convergence tests
We investigate the fast (type III) migration regime of high-mass protoplanets
orbiting in protoplanetary disks. This type of migration is dominated by
corotational torques. We study the details of flow structure in the planet's
vicinity, the dependence of migration rate on the adopted disc model, and the
numerical convergence of models (independence of certain numerical parameters
such as gravitational softening). We use two-dimensional hydrodynamical
simulations with adaptive mesh refinement,based on the FLASH code with improved
time-stepping scheme. We perform global disk simulations with sufficient
resolution close to the planet, which is allowed to freely move throughout the
grid. We employ a new type of equation of state in which the gas temperature
depends on both the distance to the star and planet, and a simplified
correction for self-gravity of the circumplanetary gas. We find that the
migration rate in the type III migration regime depends strongly on the gas
dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is
sensitive to the aspect ratio of the circumplanetary disc. Furthermore,
corrections due to the gas self-gravity are necessary to reduce numerical
artifacts that act against rapid planet migration. Reliable numerical studies
of Type III migration thus require consideration of both the thermal andthe
self-gravity corrections, as well as a sufficient spatial resolution and the
calculation of disk-planet attraction both inside and outside the Hill sphere.
With this proviso, we find Type III migration to be a robust mode of migration,
astrophysically promising because of a speed much faster than in the previously
studied modes of migration.Comment: 17 pages, 15 figures, submitted to MNRAS. Comments welcom
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
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