493 research outputs found
Dynamics of the giant planets of the solar system in the gaseous proto-planetary disk and relationship to the current orbital architecture
We study the orbital evolution of the 4 giant planets of our solar system in
a gas disk. Our investigation extends the previous works by Masset and
Snellgrove (2001) and Morbidelli and Crida (2007, MC07), which focussed on the
dynamics of the Jupiter-Saturn system. The only systems that we found to reach
a steady state are those in which the planets are locked in a quadruple mean
motion resonance (i.e. each planet is in resonance with its neighbor). In total
we found 6 such configurations. For the gas disk parameters found in MC07,
these configurations are characterized by a negligible migration rate. After
the disappearance of the gas, and in absence of planetesimals, only two of
these six configurations (the least compact ones) are stable for a time of
hundreds of millions of years or more. The others become unstable on a
timescale of a few My. Our preliminary simulations show that, when a
planetesimal disk is added beyond the orbit of the outermost planet, the
planets can evolve from the most stable of these configurations to their
current orbits in a fashion qualitatively similar to that described in Tsiganis
et al. (2005).Comment: The Astronomical Journal (17/07/2007) in pres
Massive planet migration: Theoretical predictions and comparison with observations
We quantify the utility of large radial velocity surveys for constraining
theoretical models of Type II migration and protoplanetary disk physics. We
describe a theoretical model for the expected radial distribution of extrasolar
planets that combines an analytic description of migration with an empirically
calibrated disk model. The disk model includes viscous evolution and mass loss
via photoevaporation. Comparing the predicted distribution to a uniformly
selected subsample of planets from the Lick / Keck / AAT planet search
programs, we find that a simple model in which planets form in the outer disk
at a uniform rate, migrate inward according to a standard Type II prescription,
and become stranded when the gas disk is dispersed, is consistent with the
radial distribution of planets for orbital radii 0.1 AU < a < 2.5 AU and planet
masses greater than 1.65 Jupiter masses. Some variant models are disfavored by
existing data, but the significance is limited (~95%) due to the small sample
of planets suitable for statistical analysis. We show that the favored model
predicts that the planetary mass function should be almost independent of
orbital radius at distances where migration dominates the massive planet
population. We also study how the radial distribution of planets depends upon
the adopted disk model. We find that the distribution can constrain not only
changes in the power-law index of the disk viscosity, but also sharp jumps in
the efficiency of angular momentum transport that might occur at small radii.Comment: ApJ, in press. References updated to match published versio
Kepler-16b: safe in a resonance cell
The planet Kepler-16b is known to follow a circumbinary orbit around a system
of two main-sequence stars. We construct stability diagrams in the "pericentric
distance - eccentricity" plane, which show that Kepler-16b is in a hazardous
vicinity to the chaos domain - just between the instability "teeth" in the
space of orbital parameters. Kepler-16b survives, because it is close to the
stable half-integer 11/2 orbital resonance with the central binary, safe inside
a resonance cell bounded by the unstable 5/1 and 6/1 resonances. The
neighboring resonance cells are vacant, because they are "purged" by
Kepler-16b, due to overlap of first-order resonances with the planet. The newly
discovered planets Kepler-34b and Kepler-35b are also safe inside resonance
cells at the chaos border.Comment: 17 pages, including 5 figure
Accretion and destruction of planetesimals in turbulent disks
We study the conditions for collisions between planetesimals to be
accretional or disruptive in turbulent disks, through analytical arguments
based on fluid dynamical simulations and orbital integrations. In turbulent
disks, the velocity dispersion of planetesimals is pumped up by random
gravitational perturbations from density fluctuations of the disk gas. When the
velocity dispersion is larger than the planetesimals' surface escape velocity,
collisions between planetesimals do not result in accretion, and may even lead
to their destruction. In disks with a surface density equal to that of the
``minimum mass solar nebula'' and with nominal MRI turbulence, we find that
accretion proceeds only for planetesimals with sizes above km at 1AU
and km at 5AU. We find that accretion is facilitated in disks with
smaller masses. However, at 5AU and for nominal turbulence strength, km-sized
planetesimals are in a highly erosive regime even for a disk mass as small as a
fraction of the mass of Jupiter. The existence of giant planets implies that
either turbulence was weaker than calculated by standard MRI models or some
mechanism was capable of producing Ceres-mass planetesimals in very short
timescales. In any case, our results show that in the presence of turbulence
planetesimal accretion is most difficult in massive disks and at large orbital
distances.Comment: 15 pages, 5 figures, accepted for publication in Ap
Neptune Trojans as a Testbed for Planet Formation
The problem of accretion in the Trojan 1:1 resonance is akin to the standard
problem of planet formation, transplanted from a star-centered disk to a disk
centered on the Lagrange point. The newly discovered class of Neptune Trojans
promises to test theories of planet formation by coagulation. Neptune Trojans
resembling the prototype 2001 QR322 (``QR'')--whose radius of ~100 km is
comparable to that of the largest Jupiter Trojan--may outnumber their Jovian
counterparts by a factor of ~10. We discover that seeding the 1:1 resonance
with debris from planetesimal collisions and having the seed particles accrete
in situ naturally reproduces the inferred number of QR-sized Trojans. We
analyze accretion in the Trojan sub-disk by applying the two-groups method,
accounting for kinematics specific to the resonance. We find that a Trojan
sub-disk comprising decimeter-sized seed particles and having a surface density
1e-3 that of the local minimum-mass disk produces ~10 QR-sized objects in ~1
Gyr, in accord with observation. Further growth is halted by collisional
diffusion of seed particles out of resonance. In our picture, the number and
sizes of the largest Neptune Trojans represent the unadulterated outcome of
dispersion-dominated, oligarchic accretion. Large Neptune Trojans, perhaps the
most newly accreted objects in our Solar System, may today have a dispersion in
orbital inclination of less than ~10 degrees, despite the existence of niches
of stability at higher inclinations. Such a vertically thin disk, born of a
dynamically cold environment necessary for accretion, and raised in minimal
contact with external perturbations, contrasts with the thick disks of other
minor body belts.Comment: Accepted to ApJ April 6, 200
Building Terrestrial Planets
This paper reviews our current understanding of terrestrial planets
formation. The focus is on computer simulations of the dynamical aspects of the
accretion process. Throughout the chapter, we combine the results of these
theoretical models with geochemical, cosmochemical and chronological
constraints, in order to outline a comprehensive scenario of the early
evolution of our Solar System. Given that the giant planets formed first in the
protoplanetary disk, we stress the sensitive dependence of the terrestrial
planet accretion process on the orbital architecture of the giant planets and
on their evolution. This suggests a great diversity among the terrestrial
planets populations in extrasolar systems. Issues such as the cause for the
different masses and accretion timescales between Mars and the Earth and the
origin of water (and other volatiles) on our planet are discussed at depth
Migration of Jupiter-family comets and resonant asteroids to near-Earth space
We estimated the rate of comet and asteroid collisions with the terrestrial
planets by calculating the orbits of 13000 Jupiter-crossing objects (JCOs) and
1300 resonant asteroids and computing the probabilities of collisions based on
random-phase approximations and the orbital elements sampled with a 500 yr
step. The Bulirsh-Stoer and a symplectic orbit integrator gave similar results
for orbital evolution, but sometimes give different collision probabilities
with the Sun. A small fraction of former JCOs reached orbits with aphelia
inside Jupiter's orbit, and some reached Apollo orbits with semi-major axes
less than 2 AU, Aten orbits, and inner-Earth orbits (with aphelia less than
0.983 AU) and remained there for millions of years. Though less than 0.1% of
the total, these objects were responsible for most of the collision probability
of former JCOs with Earth and Venus. Some Jupiter-family comets can reach
inclinations i>90 deg. We conclude that a significant fraction of near-Earth
objects could be extinct comets that came from the trans-Neptunian region.Comment: Proc. of the international conference "New trends in astrodynamics
and applications" (20-22 January 2003, University of Maryland, College Park
Generic perturbations of linear integrable Hamiltonian systems
In this paper, we investigate perturbations of linear integrable Hamiltonian
systems, with the aim of establishing results in the spirit of the KAM theorem
(preservation of invariant tori), the Nekhoroshev theorem (stability of the
action variables for a finite but long interval of time) and Arnold diffusion
(instability of the action variables). Whether the frequency of the integrable
system is resonant or not, it is known that the KAM theorem does not hold true
for all perturbations; when the frequency is resonant, it is the Nekhoroshev
theorem which does not hold true for all perturbations. Our first result deals
with the resonant case: we prove a result of instability for a generic
perturbation, which implies that the KAM and the Nekhoroshev theorem do not
hold true even for a generic perturbation. The case where the frequency is
non-resonant is more subtle. Our second result shows that for a generic
perturbation, the KAM theorem holds true. Concerning the Nekhrosohev theorem,
it is known that one has stability over an exponentially long interval of time,
and that this cannot be improved for all perturbations. Our third result shows
that for a generic perturbation, one has stability for a doubly exponentially
long interval of time. The only question left unanswered is whether one has
instability for a generic perturbation (necessarily after this very long
interval of time)
Secondary resonances of co-orbital motions
The size distribution of the stability region around the Lagrangian point L4
is investigated in the elliptic restricted three-body problem as the function
of the mass parameter and the orbital eccentricity of the primaries. It is
shown that there are minimum zones in the size distribution of the stability
regions, and these zones are connected with secondary resonances between the
frequencies of librational motions around L4. The results can be applied to
hypothetical Trojan planets for predicting values of the mass parameter and the
eccentricity for which such objects can be expected or their existence is less
probable.Comment: 9 pages, 7 figures, accepted for publication in MNRA
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