571 research outputs found
Simulating planet migration in globally evolving disks
Numerical simulations of planet-disk interactions are usually performed with
hydro-codes that -- because they consider only an annulus of the disk, over a
2D grid -- can not take into account the global evolution of the disk. However,
the latter governs planetary migration of type II, so that the accuracy of the
planetary evolution can be questioned.
To develop an algorithm that models the local planet-disk interactions
together with the global viscous evolution of the disk, we surround the usual
2D grid with a 1D grid ranging over the real extension of the disk. The 1D and
2D grids are coupled at their common boundaries via ghost rings, paying
particular attention to the fluxes at the interface, especially the flux of
angular momentum carried by waves. The computation is done in the frame
centered on the center of mass to ensure angular momentum conservation.
The global evolution of the disk and the local planet-disk interactions are
both well described and the feedback of one on the other can be studied with
this algorithm, for a negligible additional computing cost with respect to
usual algorithms.Comment: 12 pages, 11 figures, accepted for publication in A&
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
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&
Effects of Turbulence, Eccentricity Damping, and Migration Rate on the Capture of Planets into Mean Motion Resonance
Pairs of migrating extrasolar planets often lock into mean motion resonance
as they drift inward. This paper studies the convergent migration of giant
planets (driven by a circumstellar disk) and determines the probability that
they are captured into mean motion resonance. The probability that such planets
enter resonance depends on the type of resonance, the migration rate, the
eccentricity damping rate, and the amplitude of the turbulent fluctuations.
This problem is studied both through direct integrations of the full 3-body
problem, and via semi-analytic model equations. In general, the probability of
resonance decreases with increasing migration rate, and with increasing levels
of turbulence, but increases with eccentricity damping. Previous work has shown
that the distributions of orbital elements (eccentricity and semimajor axis)
for observed extrasolar planets can be reproduced by migration models with
multiple planets. However, these results depend on resonance locking, and this
study shows that entry into -- and maintenance of -- mean motion resonance
depends sensitively on migration rate, eccentricity damping, and turbulence.Comment: 43 pages including 14 figures; accepted for publication in The
Astrophysical Journa
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
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