27 research outputs found
On relativistic discs and rings
Sequences of infinitesimally thin, uniformly rotating, self-gravitating
relativistic discs with internal two-dimensional pressure have been
constructed. It is shown that in weaker relativistic configurations the
sequences undergo a continuous bifurcation from a disc to a ring structure,
while in stronger relativistic cases the sequences terminate at the mass-shed
limit where gravitational forces are exactly balanced by centrifugal forces.Comment: 9 pages, requires mn.sty and epsf.sty, 12 figures included, accepted
by Monthly Notices of the Royal Astronomical Societ
Mass Flow and Accretion through gaps in Accretion Discs
We study the structure and dynamics of the gap created by a protoplanet in an
accretion disc. The hydrodynamic equations for a flat, two-dimensional,
non-selfgravitating protostellar accretion disc with an embedded, Jupiter sized
protoplanet on a circular orbit are solved. To simulate possible accretion of
mass onto the protoplanet we continually remove mass from the interior of the
planet's Roche lobe which is monitored. Firstly, it is shown that consistent
results independent on numerical issues (such as boundary or initial
conditions, artificial viscosity or resolution) can be obtained. Then, a
detailed parameter study delineates the influence of the disc viscosity and
pressure on the magnitude of the accretion rate.
We find that, even after the formation of a gap in the disc, the planet is
still able to accrete more mass from the disc. This accretion occurs from
regions of the disc which are radially exterior and interior to the planet's
orbital radius. The rate depends on the magnitude of the viscosity and vertical
thickness of the disc. For a disc viscosity alpha=10^{-3} and vertical
thickness H/r=0.05 we estimate the time scale for the accumulation of one
Jupiter mass to be of order hundred thousand years. For a larger(smaller)
viscosity and disc thickness this accretion rate is increasing(decreasing).
For a very small viscosity (alpha < 5 10^{-4}) the mass accretion rate
through the gap onto the planet is markedly reduced, and the corresponding
accretion time scale becomes larger than the viscous evolution time of the
disc.Comment: 15 pages, Latex, uses MN Latex style v1.4, accepted by MN. Paper,
figures and mpeg simulation available at
http://www.tpi.uni-jena.de/~wak/research/gap/gap.htm
On the evolution of the resonant planetary system HD128311
A significant number of the known multiple exoplanetary systems are
containing a pair of giant planets engaged in a low order mean motion
resonance. Such a resonant condition protects the dynamics of these planets
resulting in very stable orbits. According to recent studies the capture into a
resonance is the result of a planetary migration process induced by the
interaction of the planets with a protoplanetary disk. If the migration is slow
enough (adiabatic) next to a mean motion resonance, the two planets will also
be in apsidal corotation.
The recently refined orbital parameters of the system HD 128311 suggest that
the two giant planets are in a 2:1 mean motion resonance, however without
exhibiting apsidal corotation. Thus the evolution of this system can not be
described by an adiabatic migration process alone.
We present possible evolution scenarios of this system combining migration
processes and sudden perturbations. We model migration scenarios through
numerical integration of the gravitational N-body problem with additional
non-conservative forces. Planet-planet scattering has been investigated by
N-body simulations.
We show that the present dynamical state of the system HD128311 may be
explained by such evolutionary processes.Comment: 4 Pages, 7 Figures, accepted for AA Letter
Dynamical Evolution of Planets in Disks
We study the evolution of a system consisting of two protoplanets still
embedded in a protoplanetary disk. Results of two different numerical
approaches are presented. In the first kind of model the motion of the disk
material is followed by fully viscous hydrodynamical simulations, and the
planetary motion is determined by N-body calculations including exactly the
gravitational potential from the disk material. In the second kind we only
solve the N-body part and add additional analytically given forces which model
the effect of the torques of the disk. This type of modeling is of course
orders of magnitudes faster than the full hydro-model. Another advantage of
this two-fold approach is the possibility of adjusting the otherwise unknown
parameters of the simplified model.
The results give very good agreement between the methods. Using two different
initial setups for the planets and disk, we obtain in the first case a resonant
trapping into the 3:1 resonance, and in the second case a trapping into the 2:1
resonance. Resonant capture leads to a rise in the eccentricity and to an
alignment of the of the spatial orientation of orbits. The characteristics of
the numerical results agree very favorably with those of 3 observed planetary
systems (GJ 876, HD 82943, and 55 Cnc) known to be in mean motion resonances.Comment: 14 Pages, Proc. of IAU Colloquium 189, Astrophysical Tides, Nanjing
Sept. 2002, uses kluwer.st
Planet migration in three-dimensional radiative discs
The migration of growing protoplanets depends on the thermodynamics of the
ambient disc. Standard modelling, using locally isothermal discs, indicate in
the low planet mass regime an inward (type-I) migration. Taking into account
non-isothermal effects, recent studies have shown that the direction of the
type-I migration can change from inward to outward. In this paper we extend
previous two-dimensional studies, and investigate the planet-disc interaction
in viscous, radiative discs using fully three-dimensional radiation
hydrodynamical simulations of protoplanetary accretion discs with embedded
planets, for a range of planetary masses.
We use an explicit three-dimensional (3D) hydrodynamical code NIRVANA that
includes full tensor viscosity. We have added implicit radiation transport in
the flux-limited diffusion approximation, and to speed up the simulations
significantly we have newly adapted and implemented the FARGO-algorithm in a 3D
context.
First, we present results of test simulations that demonstrate the accuracy
of the newly implemented FARGO-method in 3D. For a planet mass of 20 M_earth we
then show that the inclusion of radiative effects yields a torque reversal also
in full 3D. For the same opacity law used the effect is even stronger in 3D
than in the corresponding 2D simulations, due to a slightly thinner disc.
Finally, we demonstrate the extent of the torque reversal by calculating a
sequence of planet masses. Through full 3D simulations of embedded planets in
viscous, radiative discs we confirm that the migration can be directed outwards
up to planet masses of about 33 M_earth. Hence, the effect may help to resolve
the problem of too rapid inward migration of planets during their type-I phase.Comment: 16 pages, Astronomy&Astrophysics, in pres
Stellar irradiated discs and implications on migration of embedded planets I: equilibrium discs
The strength and direction of migration of low mass planets depends on the
disc's thermodynamics. In discs where the viscous heating is balanced by
radiative transport, the migration can be directed outwards, a process which
extends the lifetime of growing planetary embryos. We investigate the influence
of opacity and stellar irradiation on the disc thermodynamics. Utilizing the
resulting disc structure, we determine the regions of outward migration. We
perform two-dimensional numerical simulations of equilibrium discs with viscous
heating, radiative cooling and stellar irradiation. We use the hydrodynamical
code NIRVANA that includes a full tensor viscosity and stellar irradiation, as
well as a two temperature solver that includes radiation transport in the
flux-limited diffusion approximation. The migration is studied by using torque
formulae. In the constant opacity case, we reproduce the analytical results of
a black-body disc: the stellar irradiation dominates in the outer regions --
leading to flaring -- while the viscous heating dominates close to the star. We
find that the inner edge of the disc should not be significantly puffed-up by
the stellar irradiation. If the opacity depends on the local density and
temperature, the structure of the disc is different, and several bumps in the
aspect ratio H/r appear, due to transitions between different opacity regimes.
The bumps in the disc can shield the outer disc from stellar irradiation.
Stellar irradiation is an important factor for determining the disc structure
and has dramatic consequences for the migration of embedded planets. Compared
to discs with only viscous heating, a stellar irradiated disc features a much
smaller region of outward migration for a range of planetary masses. This
suggests that the region where the formation of giant planet cores takes place
is smaller, which in turn might lead to a shorter growth phase