228 research outputs found
Mapping the Secular Resonance for Retrograde Irregular Satellites
Constructing dynamical maps from the filtered output of numerical
integrations, we analyze the structure of the secular resonance for
fictitious irregular satellites in retrograde orbits. This commensurability is
associated to the secular angle , where
is the longitude of pericenter of the satellite and
corresponds to the (fixed) planetocentric orbit of the Sun. Our study is
performed in the restricted three-body problem, where the satellites are
considered as massless particles around a massive planet and perturbed by the
Sun. Depending on the initial conditions, the resonance presents a diversity of
possible resonant modes, including librations of around zero (as found
for Sinope and Pasiphae) or 180 degrees, as well as asymmetric librations (e.g.
Narvi). Symmetric modes are present in all giant planets, although each regime
appears restricted to certain values of the satellite inclination. Asymmetric
solutions, on the other hand, seem absent around Neptune due to its almost
circular heliocentric orbit. Simulating the effects of a smooth orbital
migration on the satellite, we find that the resonance lock is preserved as
long as the induced change in semimajor axis is much slower compared to the
period of the resonant angle (adiabatic limit). However, the librational mode
may vary during the process, switching between symmetric and asymmetric
oscillations. Finally, we present a simple scaling transformation that allows
to estimate the resonant structure around any giant planet from the results
calculated around a single primary mass.Comment: 11 pages, 13 figure
MAMA: An Algebraic Map for the Secular Dynamics of Planetesimals in Tight Binary Systems
We present an algebraic map (MAMA) for the dynamical and collisional
evolution of a planetesimal swarm orbiting the main star of a tight binary
system (TBS). The orbital evolution of each planetesimal is dictated by the
secular perturbations of the secondary star and gas drag due to interactions
with a protoplanetary disk. The gas disk is assumed eccentric with a constant
precession rate. Gravitational interactions between the planetesimals are
ignored. All bodies are assumed coplanar. A comparison with full N-body
simulations shows that the map is of the order of 100 times faster, while
preserving all the main characteristics of the full system.
In a second part of the work, we apply MAMA to the \gamma-Cephei, searching
for friendly scenarios that may explain the formation of the giant planet
detected in this system. For low-mass protoplanetary disks, we find that a
low-eccentricity static disk aligned with the binary yields impact velocities
between planetesimals below the disruption threshold. All other scenarios
appear hostile to planetary formation
The Resonance Overlap and Hill Stability Criteria Revisited
We review the orbital stability of the planar circular restricted three-body
problem, in the case of massless particles initially located between both
massive bodies. We present new estimates of the resonance overlap criterion and
the Hill stability limit, and compare their predictions with detailed dynamical
maps constructed with N-body simulations. We show that the boundary between
(Hill) stable and unstable orbits is not smooth but characterized by a rich
structure generated by the superposition of different mean-motion resonances
which does not allow for a simple global expression for stability.
We propose that, for a given perturbing mass and initial eccentricity
, there are actually two critical values of the semimajor axis. All values
are
unstable in the Hill sense. The first limit is given by the Hill-stability
criterion and is a function of the eccentricity. The second limit is virtually
insensitive to the initial eccentricity, and closely resembles a new resonance
overlap condition (for circular orbits) developed in terms of the intersection
between first and second-order mean-motion resonances.Comment: 33 pages, 14 figures, accepte
Secular dynamics of planetesimals in tight binary systems: Application to Gamma-Cephei
The secular dynamics of small planetesimals in tight binary systems play a
fundamental role in establishing the possibility of accretional collisions in
such extreme cases. The most important secular parameters are the forced
eccentricity and secular frequency, which depend on the initial conditions of
the particles, as well as on the mass and orbital parameters of the secondary
star. We construct a second-order theory (with respect to the masses) for the
planar secular motion of small planetasimals and deduce new expressions for the
forced eccentricity and secular frequency. We also reanalyze the radial
velocity data available for Gamma-Cephei and present a series of orbital
solutions leading to residuals compatible with the best fits. Finally, we
discuss how different orbital configurations for Gamma-Cephei may affect the
dynamics of small bodies in circunmstellar motion. For Gamma-Cephei, we find
that the classical first-order expressions for the secular frequency and forced
eccentricity lead to large inaccuracies around 50 % for semimajor axes larger
than one tenth the orbital separation between the stellar components. Low
eccentricities and/or masses reduce the importance of the second-order terms.
The dynamics of small planetesimals only show a weak dependence with the
orbital fits of the stellar components, and the same result is found including
the effects of a nonlinear gas drag. Thus, the possibility of planetary
formation in this binary system largely appears insensitive to the orbital fits
adopted for the stellar components, and any future alterations in the system
parameters (due to new observations) should not change this picture. Finally,
we show that planetesimals migrating because of gas drag may be trapped in
mean-motion resonances with the binary, even though the migration is divergent.Comment: 11 pages, 9 figure
Dynamics of two planets in co-orbital motion
We study the stability regions and families of periodic orbits of two planets
locked in a co-orbital configuration. We consider different ratios of planetary
masses and orbital eccentricities, also we assume that both planets share the
same orbital plane. Initially we perform numerical simulations over a grid of
osculating initial conditions to map the regions of stable/chaotic motion and
identify equilibrium solutions. These results are later analyzed in more detail
using a semi-analytical model. Apart from the well known quasi-satellite (QS)
orbits and the classical equilibrium Lagrangian points L4 and L5, we also find
a new regime of asymmetric periodic solutions. For low eccentricities these are
located at , where \sigma is
the difference in mean longitudes and \Delta\omega is the difference in
longitudes of pericenter. The position of these Anti-Lagrangian solutions
changes with the mass ratio and the orbital eccentricities, and are found for
eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation
to one of the planets, and analyzed its effect on an initially asymmetric
periodic orbit. We found that the resonant solution is preserved as long as the
mass variation is adiabatic, with practically no change in the equilibrium
values of the angles.Comment: 9 pages, 11 figure
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
On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets
We study the dynamics of planetary systems with two planets moving in the
same plane, when frictional forces act on the two planets, in addition to the
gravitational forces. The model of the general three-body problem is used.
Different laws of friction are considered. The topology of the phase space is
essential in understanding the evolution of the system. The topology is
determined by the families of stable and unstable periodic orbits, both
symmetric and non symmetric. It is along the stable families, or close to them,
that the planets migrate when dissipative forces act. At the critical points
where the stability along the family changes, there is a bifurcation of a new
family of stable periodic orbits and the migration process changes route and
follows the new stable family up to large eccentricities or to a chaotic
region. We consider both resonant and non resonant planetary systems. The 2/1,
3/1 and 3/2 resonances are studied. The migration to larger or smaller
eccentricities depends on the particular law of friction. Also, in some cases
the semimajor axes increase and in other cases they are stabilized. For
particular laws of friction and for special values of the parameters of the
frictional forces, it is possible to have partially stationary solutions, where
the eccentricities and the semimajor axes are fixed.Comment: Accepted in Celestial Mechanics and Dynamical Astronom
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