838 research outputs found
Stability of the viscously spreading ring
We study analytically and numerically the stability of the pressure-less,
viscously spreading accretion ring. We show that the ring is unstable to small
non-axisymmetric perturbations. To perform the perturbation analysis of the
ring we use a stretching transformation of the time coordinate. We find that to
1st order, one-armed spiral structures, and to 2nd order additionally two-armed
spiral features may appear. Furthermore, we identify a dispersion relation
determining the instability of the ring. The theoretical results are confirmed
in several simulations, using two different numerical methods. These
computations prove independently the existence of a secular spiral instability
driven by viscosity, which evolves into persisting leading and trailing spiral
waves. Our results settle the question whether the spiral structures found in
earlier simulations of the spreading ring are numerical artifacts or genuine
instabilities.Comment: 13 pages, 12 figures; A&A accepte
Formation of massive planets in binary star systems
As of today over 40 planetary systems have been discovered in binary star
systems. In all cases the configuration appears to be circumstellar, where the
planets orbit around one of the stars, the secondary acting as a perturber. The
formation of planets in binary star systems is more difficult than around
single stars due to the gravitational action of the companion on the dynamics
of the protoplanetary disk. In this contribution we first briefly present the
relevant observational evidence for planets in binary systems. Then the
dynamical influence that a secondary companion has on a circumstellar disk will
be analyzed through fully hydrodynamical simulations. We demonstrate that the
disk becomes eccentric and shows a coherent precession around the primary star.
Finally, fully hydrodynamical simulations of evolving protoplanets embedded in
disks in binary star systems are presented. We investigate how the orbital
evolution of protoplanetary embryos and their mass growth from cores to massive
planets might be affected in this very dynamical environment. We consider, in
particular, the planet orbiting the primary in the system Gamma Cephei.Comment: To appear in Proceedings: Extrasolar Planets in Multi-body Systems:
Theory and Observations Eds. K. Gozdziewski, A. Niedzielski and J. Schneide
Migration and Accretion of Protoplanets in 2D and 3D Global Hydrodynamical Simulations
Planet evolution is tightly connected to the dynamics of both distant and
close disk material. Hence, an appropriate description of disk-planet
interaction requires global and high resolution computations, which we
accomplish by applying a Nested-Grid method. Through simulations in two and
three dimensions, we investigate how migration and accretion are affected by
long and short range interactions. For small mass objects, 3D models provide
longer growth and migration time scales than 2D ones do, whereas time lengths
are comparable for large mass planets.Comment: 4 pages, 4 figures; to appear in the Conference Proceedings of
"Scientific Frontiers in Research on Extrasolar Planets
Modelling the evolution of planets in disks
To explain important properties of extrasolar planetary systems (eg. close-in
hot Jupiters, resonant planets) an evolutionary scenario which allows for
radial migration of planets in disks is required. During their formation
protoplanets undergo a phase in which they are embedded in the disk and
interact gravitationally with it. This planet-disk interaction results in
torques (through gravitational forces) acting on the planet that will change
its angular momentum and result in a radial migration of the planet through the
disk. To determine the outcome of this very important process for planet
formation, dedicated high resolution numerical modeling is required. This
contribution focusses on some important aspects of the numerical approach that
we found essential for obtaining successful results. We specifically mention
the treatment of Coriolis forces, Cartesian grids, and the FARGO method.Comment: Talk given at JENAM meeting, Vienna 200
Modelling Accretion in Transitional Disks
Transitional disks are protoplanetary disk around young stars that display
inner holes in the dust distribution within a few AU, which is accompanied
nevertheless by some gas accretion onto the central star. These cavities could
possibly be created by the presence of one or more massive planets. If the gap
is created by planets and gas is still present in it, then there should be a
flow of gas past the planet into the inner region. It is our goal to study the
mass accretion rate into the gap and in particular the dependency on the
planet's mass and the thermodynamic properties of the disk. We performed 2D
hydro simulations for disks with embedded planets. We added radiative cooling
from the disk surfaces, radiative diffusion in the disk midplane, and stellar
irradiation to the energy equation to have more realistic models. The mass flow
rate into the gap region depends, for given disk thermodynamics,
non-monotonically on the mass of the planet. Generally, more massive planets
open wider and deeper gaps which would tend to reduce the mass accretion into
the inner cavity. However, for larger mass planets the outer disk becomes
eccentric and the mass flow rate is enhanced over the low mass cases. As a
result, for the isothermal disks the mass flow is always comparable to the
expected mass flow of unperturbed disks M_d, while for more realistic radiative
disks the mass flow is very small for low mass planets (<= 4 M_jup) and about
50% for larger planet masses. For the radiative disks that critical planet mass
for the disk to become eccentric is much larger that in the isothermal case.
Massive embedded planets can reduce the mass flow across the gap considerably,
to values of about an order of magnitude smaller than the standard disk
accretion rate, and can be responsible for opening large cavities. The
remaining mass flow into the central cavity is in good agreement with the
observations.Comment: 10 pages, 29 figures, accepted for publication in Astronomy &
Astrophysic
Influence of viscosity and the adiabatic index on planetary migration
The strength and direction of migration of low mass embedded planets depends
on the disk's thermodynamic state, where the internal dissipation is balanced
by radiative transport, and the migration can be directed outwards, a process
which extends the lifetime of growing embryos. Very important parameters
determining the structure of disks, and hence the direction of migration, are
the viscosity and the adiabatic index. In this paper we investigate the
influence of different viscosity prescriptions (alpha-type and constant) and
adiabatic indices on disk structures and how this affects the migration rate of
planets embedded in such disks. We perform 3D numerical simulations of
accretion disks with embedded planets. We use the explicit/implicit
hydrodynamical code NIRVANA that includes full tensor viscosity and radiation
transport in the flux-limited diffusion approximation, as well as a proper
equation of state for molecular hydrogen. The migration of embedded 20Earthmass
planets is studied. Low-viscosity disks have cooler temperatures and the
migration rates of embedded planets tend toward the isothermal limit. In these
disks, planets migrate inwards even in the fully radiative case. The effect of
outward migration can only be sustained if the viscosity in the disk is large.
Overall, the differences between the treatments for the equation of state seem
to play a more important role in disks with higher viscosity. A change in the
adiabatic index and in the viscosity changes the zero-torque radius that
separates inward from outward migration. For larger viscosities, temperatures
in the disk become higher and the zero-torque radius moves to larger radii,
allowing outward migration of a 20 Earth-mass planet to persist over an
extended radial range. In combination with large disk masses, this may allow
for an extended period of the outward migration of growing protoplanetary
cores
Stability and Formation of the Resonant System HD 73526
Based on radial velocity measurements it has been found recently that the two
giant planets detected around the star HD 73526 are in 2:1 resonance. However,
as our numerical integration shows, the derived orbital data for this system
result in chaotic behavior of the giant planets, which is uncommon among the
resonant extrasolar planetary systems.
We intend to present regular (non-chaotic) orbital solutions for the giant
planets in the system HD 73526 and offer formation scenarios based on combining
planetary migration and sudden perturbative effects such as planet-planet
scattering or rapid dispersal of the protoplanetary disk. A comparison with the
already studied resonant system HD 128311, exhibiting similar behavior, is also
done.
The new sets of orbital solutions have been derived by the Systemic Console
(www.oklo.org). The stability of these solutions has been investigated by the
Relative Lyapunov indicator, while the migration and scattering effects are
studied by gravitational N-body simulations applying non-conservative forces as
well. Additionally, hydrodynamic simulations of embedded planets in
protoplanetary disks are performed to follow the capture into resonance.
For the system HD 73526 we demonstrate that the observational radial velocity
data are consistent with a coplanar planetary system engaged in a stable 2:1
resonance exhibiting apsidal corotation. We have shown that, similarly to the
system HD 128311, the present dynamical state of HD 73526 could be the result
of a mixed evolutionary process melting together planetary migration and a
perturbative event.Comment: 12 pages, 14 figures, accepted in A&A, v2: technical change
Formation of the resonant system HD 60532
Among multi-planet planetary systems there are a large fraction of resonant
systems. Studying the dynamics and formation of these systems can provide
valuable informations on processes taking place in protoplanetary disks where
the planets are thought have been formed. The recently discovered resonant
system HD 60532 is the only confirmed case, in which the central star hosts a
pair of giant planets in 3:1 mean motion resonance. We intend to provide a
physical scenario for the formation of HD 60532, which is consistent with the
orbital solutions derived from the radial velocity measurements. Observations
indicate that the system is in an antisymmetric configuration, while previous
theoretical investigations indicate an asymmetric equilibrium state. The paper
aims at answering this discrepancy as well. We performed two-dimensional
hydrodynamical simulations of thin disks with an embedded pair of massive
planets. Additionally, migration and resonant capture are studied by
gravitational N-body simulations that apply properly parametrized
non-conservative forces. Our simulations suggest that the capture into the 3:1
mean motion resonance takes place only for higher planetary masses, thus
favouring orbital solutions having relatively smaller inclination i=20 degrees.
The system formed by numerical simulations qualitatively show the same
behaviour as HD 60532. We also find that the presence of an inner disk (between
the inner planet and the star) plays a very important role in determining the
final configurations of resonant planetary systems. Its damping effect on the
inner planet's eccentricity is responsible for the observed antisymmetric state
of HD 60532.Comment: 7 pages, 7 figures, Accepted for publication in Astronomy &
Astrophysic
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