540 research outputs found
The Dynamical Origin of the Multi-Planetary System HD45364
The recently discovered planetary system HD45364 which consists of a Jupiter
and Saturn mass planet is very likely in a 3:2 mean motion resonance. The
standard scenario to form planetary commensurabilities is convergent migration
of two planets embedded in a protoplanetary disc. When the planets are
initially separated by a period ratio larger than two, convergent migration
will most likely lead to a very stable 2:1 resonance for moderate migration
rates. To avoid this fate, formation of the planets close enough to prevent
this resonance may be proposed. However, such a simultaneous formation of the
planets within a small annulus, seems to be very unlikely.
Rapid type III migration of the outer planet crossing the 2:1 resonance is
one possible way around this problem. In this paper, we investigate this idea
in detail. We present an estimate for the required convergent migration rate
and confirm this with N-body and hydrodynamical simulations. If the dynamical
history of the planetary system had a phase of rapid inward migration that
forms a resonant configuration, we predict that the orbital parameters of the
two planets are always very similar and hence should show evidence of that.
We use the orbital parameters from our simulation to calculate a radial
velocity curve and compare it to observations. Our model can explain the
observational data as good as the previously reported fit. The eccentricities
of both planets are considerably smaller and the libration pattern is
different. Within a few years, it will be possible to observe the planet-planet
interaction directly and thus distinguish between these different dynamical
states.Comment: 9 pages, 9 figures - accepted for publication in Astronomy and
Astrophysic
Disk Planet Interactions and Early Evolution in Young Planetary Systems
We study and review disk protoplanet interactions using local shearing box
simulations. These suffer the disadvantage of having potential artefacts
arising from periodic boundary conditions but the advantage, when compared to
global simulations, of being able to capture much of the dynamics close to the
protoplanet at high resolution for low computational cost. Cases with and
without self sustained MHD turbulence are considered. The conditions for gap
formation and the transition from type I migration are investigated and found
to depend on whether the single parameter M_p R^3/(M_* H^3), with M_p, M_*, R
and H being the protoplanet mass, the central mass, the orbital radius and the
disk semi-thickness respectively exceeds a number of order unity. We also
investigate the coorbital torques experienced by a moving protoplanet in an
inviscid disk. This is done by demonstrating the equivalence of the problem for
a moving protoplanet to one where the protoplanet is in a fixed orbit which the
disk material flows through radially as a result of the action of an
appropriate external torque. For sustainable coorbital torques to be realized a
quasi steady state must be realized in which the planet migrates through the
disk without accreting significant mass. In that case although there is
sensitivity to computational parameters, in agreement with earlier work by
Masset & Papaloizou (2003) based on global simulations, the coorbital torques
are proportional to the migration speed and result in a positive feedback on
the migration, enhancing it and potentially leading to a runaway. This could
lead to a fast migration for protoplanets in the Saturn mass range in massive
disks and may be relevant to the mass period correlation for extrasolar planets
which gives a preponderance of sub Jovian masses at short orbital period.Comment: To appear in Celestial Mechanics and Dynamical Astronomy (with higher
resolution figures
Models of Giant Planet formation with migration and disc evolution
We present a new model of giant planet formation that extends the
core-accretion model of Pollack etal (1996) to include migration, disc
evolution and gap formation. We show that taking into account these effects can
lead to a much more rapid formation of giant planets, making it compatible with
the typical disc lifetimes inferred from observations of young circumstellar
discs. This speed up is due to the fact that migration prevents the severe
depletion of the feeding zone as observed in in situ calculations. Hence, the
growing planet is never isolated and it can reach cross-over mass on a much
shorter timescale. To illustrate the range of planets that can form in our
model, we describe a set of simulations in which we have varied some of the
initial parameters and compare the final masses and semi-major axes with those
inferred from observed extra-solar planets.Comment: Accepted in Astronomy & Astrophysic
Models of Accreting Gas Giant Protoplanets in Protostellar Disks
(Abridged) We consider models of gas giant planets forming in protoplanetary
disks consisting of solid cores with gaseous envelopes in contact with their
critical Hill spheres while accreting gas from the surrounding disk.We suppose
the luminosity derives from gas accretion alone.We label such models as type A
and follow their evolution which may occur on a time scale similar to the
protostellar disk lifetime until rapid gas accretion. We consider another set
of models, we label type B, with a free surface, powered by gravitational
contraction, while accreting through a disk.We find these models rapidly attain
a radius <~ 2x10^(10)cm without subsequent expansion.We speculate that giant
planet formation is initially described by models of type A, until at the onset
of rapid gas accretion, there is a transition to models of type B. Protoplanet
migration in standard models tends to be most effective near this transition
where it also changes from type I to type II.If a mechanism prevents type I
migration of low mass protoplanets, a rapid inward migration might occur near
the transitional mass regime. Such protoplanets would end up in the inner disk
regions undergoing type II migration and further accretion potentially becoming
sub Jovian close orbiting planets. Noting that dustier more massive cores spend
longer at a larger transitional mass where faster migration is expected, these
may be more prone to end in close orbiters.We find the luminosity of the
protoplanets during the later stages is dominated by the circumplanetary disk
and protoplanet disk boundary layer.For one Jupiter mass the luminosity range
is 10^-(1.5-4) L_sun$ depending on the evolutionary stage and external
conditions.Comment: Accepted for publication in Astronomy and Astrophysic
Planetary Migration and Extrasolar Planets in the 2/1 Mean-Motion Resonance
We analyze the possible relationship between the current orbital elements
fits of known exoplanets in the 2/1 mean-motion resonance and the expected
orbital configuration due to migration. It is found that, as long as the
orbital decay was sufficiently slow to be approximated by an adiabatic process,
all captured planets should be in apsidal corotations. In other words, they
should show a simultaneous libration of both the resonant angle and the
difference in longitudes of pericenter.
We present a complete set of corotational solutions for the 2/1
commensurability, including previously known solutions and new results.
Comparisons with observed exoplanets show that current orbital fits of three
known planetary systems in this resonance are either consistent with apsidal
corotations (GJ876 and HD82943) or correspond to bodies with uncertain orbits
(HD160691).
Finally, we discuss the applicability of these results as a test for the
planetary migration hypothesis itself. If all future systems in this
commensurability are found to be consistent with corotational solutions, then
resonance capture of these bodies through planetary migration is a working
hypothesis. Conversely, If any planetary pair is found in a different
configuration, then either migration did not occur for those bodies, or it took
a different form than currently believed.Comment: Submitted to MNRA
The interaction of planets with a disc with MHD turbulence III: Flow morphology and conditions for gap formation in local and global simulations
We present the results of both global cylindrical disc simulations and local
shearing box simulations of protoplanets interacting with a disc undergoing MHD
turbulence with zero net flux magnetic fields. We investigate the nature of the
disc response and conditions for gap formation. This issue is an important one
for determining the type and nature of the migration of the protoplanet, with
the presence of a deep gap being believed to enable slower migration. For both
types of simulation we find a common pattern of behaviour for which the main
parameter determining the nature of the response is , with
, , , and being the protoplanet mass, the central mass, the
orbital radius and the disc semi-thickness respectively. We find that as this
parameter is increased towards 0.1, the presence of the protoplanet is first
indicated by the appearance of the well known trailing wake which, although it
may appear erratic on account of the turbulence, appears to be well defined.
Once the above parameter exceeds a number around unity a gap starts to develop
inside which the magnetic energy density tends to be concentrated in the high
density wakes. This gap formation condition can be understood from simple
dimensional considerations of the conditions for nonlinearity, and the balance
of angular momentum transport due to Maxwell and Reynolds' stresses with that
due to tidal torques. An important result is that the basic flow morphology in
the vicinity of the protoplanet is very similar in both the local and global
simulations. This indicates that local shearing box simulations, which are
computationally less demanding, capture much of the physics of disc-planet
interaction. Thus they may provide a useful tool for studying the local
interaction between forming protoplanets and turbulent, protostellar discs.Comment: 20 pages, 28 figures (some colour), accepted for publication in
M.N.R.A.S. with minor modification. A pdf version containing high resolution
colour figures is available from
http://www.maths.qmul.ac.uk/~rpn/projects/mhd along with additional images
and movies. A companion paper accepted without change by M.N.R.A.S. is also
availabl
The interaction of planets with a disc with MHD turbulence IV: Migration rates of embedded protoplanets
(Abridged) We present global disc and local shearing box simulations of
planets interacting with a MHD turbulent disc. We examine the torque exerted by
the disc on the embedded planets as a function of planet mass, and thus make a
first study of orbital migration of planets due to interaction with turbulent
discs. Global simulations were performed for a disc with H/R=0.07 and planet
masses M_p=3,10,30 Earth masses, and 3 Jupiter masses. Shearing box runs were
performed for values of (M_p/M_*)/(H/R)^3=0.1,0.3,1.0 and 2.0, M_* being the
central mass. These allow embedded and gap forming planets to be examined. In
all cases the instantaneous torque exerted on a planet showed strong
fluctuations. In the embedded cases it oscillated between negative and positive
values, and migration occurs as a random walk, unlike the usual type I
migration. Running time averages for embedded planets over 20-25 orbital
periods show that large fluctuations occur on longer time scales, preventing
convergence of the average torque to well defined values, or even to a well
defined sign. Fluctuations become relatively smaller for larger masses, giving
better convergence, due to the planet's perturbation of the disc becoming
larger than the turbulence in its vicinity. Eventually gap formation occurs,
with a transition to type II migration. The existence of significant
fluctuations occurring in turbulent discs on long time scales is important for
lower mass embedded protoplanets. If significant fluctuations occur on the
longest disc evolutionary time scales, convergence of torque running averages
for practical purposes will not occur, and the migration behaviour of low mass
protoplanets considered as an ensemble would be very different from predictions
of type I theory for laminar discs.Comment: 19 pages, 24 figures (some colour), submitted to M.N.R.A.S. A gzipped
postscript version containing high resolution colour figures is available
from http://www.maths.qmul.ac.uk/~rp
The interaction of a giant planet with a disc with MHD turbulence II: The interaction of the planet with the disc
We present a global MHD simulation of a turbulent accretion disc interacting
with a protoplanet of 5 Jupiter masses. The disc model had H/r=0.1,and a value
of the Shakura & Sunyaev alpha ~ 0.005. The protoplanet opened a gap in the
disc, with the interaction leading to inward migration on the expected time
scale. Spiral waves were launched by the protoplanet and although they were
diffused and dissipated through interaction with the turbulence, they produced
an outward angular momentum flow which compensated for a reduced flux
associated with the turbulence, so maintaining the gap. When compared with
laminar disc models with the same estimated alpha, the gap was found to be
deeper and wider indicating that the turbulent disc behaved as if it possessed
a smaller alpha. This may arise for two reasons. First, the turbulence does not
provide a source of constantly acting friction in the near vicinity of the
planet that leads to steady mass flow into the gap region. Instead the
turbulence is characterised by large fluctuations in the radial velocity, and
time averaging over significant time scales is required to recover the
underlying mass flow through the disc. Near the planet the disc material
experiences high amplitude perturbations on time scales that are short relative
to the time scale required for averaging. The disc response is thus likely to
be altered relative to a Navier--Stokes model. Second, the simulation indicates
that an ordered magnetic connection between the inner and outer disc can occur
enabling angular momentum to flow out across the gap, helping to maintain it
independently of the protoplanet's tide. This type of effect may assist gap
formation for smaller mass protoplanets which otherwise would not be able to
maintain them.Comment: 14 pages, 17 figures, accepted for publication in MNRAS. A gzipped
postscript version including high resolution figures is available at
http://www.maths.qmw.ac.uk/~rp
Vortex Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-T_c Superconductors
The distribution of thermally excited vortex loops near a superfluid phase
transition is calculated from a renormalized theory. The number density of
loops with a given perimeter is found to change from exponential decay with
increasing perimeter to algebraic decay as T_c is approached, in agreement with
recent simulations of both cosmic strings and high-T_c superconductors.
Predictions of the value of the exponent of the algebraic decay at T_c and of
critical behavior in the vortex density are confirmed by the simulations,
giving strong support to the vortex-folding model proposed by Shenoy.Comment: Version to appear in Phys. Rev. Lett, with a number of corrections
and addition
Simulations of planet-disc interactions using Smoothed Particle Hydrodynamics
We have performed Smoothed Particle Hydrodynamics (SPH) simulations to study
the time evolution of one and two protoplanets embedded in a protoplanetary
accretion disc. We investigate accretion and migration rates of a single
protoplanet depending on several parameters of the protoplanetary disc, mainly
viscosity and scale height. Additionally, we consider the influence of a second
protoplanet in a long time simulation and examine the migration of the two
planets in the disc, especially the growth of eccentricity and chaotic
behaviour. One aim of this work is to establish the feasibility of SPH for such
calculations considering that usually only grid-based methods are adopted. To
resolve shocks and to prevent particle penetration, we introduce a new approach
for an artificial viscosity, which consists of an additional artificial bulk
viscosity term in the SPH-representation of the Navier-Stokes equation. This
allows for an accurate treatment of the physical kinematic viscosity to
describe the shear, without the use of an artificial shear viscosity.Comment: 11 pages, 14 figures, uses natbib.sty and aa.cls; accepted for
publication by A&A. Please contact the author for a version with
high-resolution figure
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