509 research outputs found
On the corotation torque in a radiatively inefficient disk
We consider the angular momentum exchange at the corotation resonance between
a two-dimensional gaseous disk and a uniformly rotating external potential,
assuming that the disk flow is adiabatic. We first consider the linear case for
an isolated resonance, for which we give an expression of the corotation torque
that involves the pressure perturbation, and which reduces to the usual
dependence on the vortensity gradient in the limit of a cold disk. Although
this expression requires the solution of the hydrodynamic equations, it
provides some insight into the dynamics of the corotation region. In the
general case, we find an additional dependence on the entropy gradient at
corotation. This dependence is associated to the advection of entropy
perturbations. These are not associated to pressure perturbations. They remain
confined to the corotation region, where they yield a singular contribution to
the corotation torque. In a second part, we check our torque expression by
means of customized two-dimensional hydrodynamical simulations. In a third
part, we contemplate the case of a planet embedded in a Keplerian disk, assumed
to be adiabatic. We find an excess of corotation torque that scales with the
entropy gradient, and we check that the contribution of the entropy
perturbation to the torque is in agreement with the expression obtained from
the linear analysis. We finally discuss some implications of the corotation
torque expression for the migration of low mass planets in the regions of
protoplanetary disks where the flow is radiatively inefficient on the timescale
of the horseshoe U-turns.Comment: 36 pages, 19 figures, accepted for publication in Ap
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
A torque formula for non-isothermal Type I planetary migration - II. Effects of diffusion
We study the effects of diffusion on the non-linear corotation torque, or
horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for
which the width of the horseshoe region is much smaller than the scale height
of the disc. In the absence of diffusion, the non-linear corotation torque
saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can
act to sustain the corotation torque. In the limit of very strong diffusion,
the linear corotation torque is recovered. For the case of thermal diffusion,
this limit corresponds to having a locally isothermal equation of state. We
present some simple models that are able to capture the dependence of the
torque on diffusive processes to within 20% of the numerical simulations.Comment: 12 pages, 8 figures, accepted for publication in MNRA
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
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
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&
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
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
The dynamical role of the circumplanetary disc in planetary migration
Numerical simulations of planets embedded in protoplanetary gaseous discs are
a precious tool for studying the planetary migration ; however, some
approximations have to be made. Most often, the selfgravity of the gas is
neglected. In that case, it is not clear in the literature how the material
inside the Roche lobe of the planet should be taken into account. Here, we want
to address this issue by studying the influence of various methods so far used
by different authors on the migration rate.
We performed high-resolution numerical simulations of giant planets embedded
in discs. We compared the migration rates with and without gas selfgravity,
testing various ways of taking the circum-planetary disc (CPD) into account.
Different methods lead to significantly different migration rates. Adding the
mass of the CPD to the perturbing mass of the planet accelerates the migration.
Excluding a part of the Hill sphere is a very touchy parameter that may lead to
an artificial suppression of the type III, runaway migration. In fact, the CPD
is smaller than the Hill sphere. We recommend excluding no more than a 0.6 Hill
radius and using a smooth filter. Alternatively, the CPD can be given the
acceleration felt by the planet from the rest of the protoplanetary disc.
The gas inside the Roche lobe of the planet should be very carefully taken
into account in numerical simulations without any selfgravity of the gas. The
entire Hill sphere should not be excluded. The method used should be explicitly
given. However, no method is equivalent to computing the full selfgravity of
the gas.Comment: 15 pages, 19 figures (most in color), in press in Astronomy and
Astrophysic
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