36 research outputs found

### Dynamical analysis of the Gliese-876 Laplace resonance

The existence of multiple planetary systems involved in mean motion
conmensurabilities has increased significantly since the Kepler mission.
Although most correspond to 2-planet resonances, multiple resonances have also
been found. The Laplace resonance is a particular case of a three-body
resonance where the period ratio between consecutive pairs is n_1/n_2 near to
n_2/n_3 near to 2/1. It is not clear how this triple resonance can act in order
to stabilize (or not) the systems.
The most reliable extrasolar system located in a Laplace resonance is GJ876
because it has two independent confirmations. However best-fit parameters were
obtained without previous knowledge of resonance structure and no exploration
of all the possible stable solutions for the system where done.
In the present work we explored the different configurations allowed by the
Laplace resonance in the GJ876 system by varying the planetary parameters of
the third outer planet. We find that in this case the Laplace resonance is a
stabilization mechanism in itself, defined by a tiny island of regular motion
surrounded by (unstable) highly chaotic orbits. Low eccentric orbits and mutual
inclinations from -20 to 20 degrees are compatible with the observations. A
definite range of mass ratio must be assumed to maintain orbital stability.
Finally we give constrains for argument of pericenters and mean anomalies in
order to assure stability for this kind of systems.Comment: 7 pages, 7 figures, accepted in MNRA

### A semi-empirical stability criterion for real planetary systems

We test a crossing orbit stability criterion for eccentric planetary systems,
based on Wisdom's criterion of first order mean motion resonance overlap
(Wisdom, 1980).
We show that this criterion fits the stability regions in real exoplanet
systems quite well. In addition, we show that elliptical orbits can remain
stable even for regions where the apocenter distance of the inner orbit is
larger than the pericenter distance of the outer orbit, as long as the initial
orbits are aligned.
The analytical expressions provided here can be used to put rapid constraints
on the stability zones of multi-planetary systems. As a byproduct of this
research, we further show that the amplitude variations of the eccentricity can
be used as a fast-computing stability indicator.Comment: 11 pages, 11 figures. MNRAS accepte

### 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

### Dynamical analysis and constraints for the HD 196885 system

The HD\,196885 system is composed of a binary star and a planet orbiting the
primary. The orbit of the binary is fully constrained by astrometry, but for
the planet the inclination with respect to the plane of the sky and the
longitude of the node are unknown. Here we perform a full analysis of the
HD\,196885 system by exploring the two free parameters of the planet and
choosing different sets of angular variables. We find that the most likely
configurations for the planet is either nearly coplanar orbits (prograde and
retrograde), or highly inclined orbits near the Lidov-Kozai equilibrium points,
i = 44^{\circ} or i = 137^{\circ} . Among coplanar orbits, the retrograde ones
appear to be less chaotic, while for the orbits near the Lidov-Kozai
equilibria, those around \omega= 270^{\circ} are more reliable, where \omega_k
is the argument of pericenter of the planet's orbit with respect to the
binary's orbit.
From the observer's point of view (plane of the sky) stable areas are
restricted to (I1, \Omega_1) \sim (65^{\circ}, 80^{\circ}),
(65^{\circ},260^{\circ}), (115^{\circ},80^{\circ}), and
(115^{\circ},260^{\circ}), where I1 is the inclination of the planet and
\Omega_1 is the longitude of ascending node.Comment: 10 pages, 7 figures. A&A 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 $(\sigma,\Delta\omega) = (\pm 60\deg, \mp 120\deg)$, 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

### Mapping the $\nu_\odot$ Secular Resonance for Retrograde Irregular Satellites

Constructing dynamical maps from the filtered output of numerical
integrations, we analyze the structure of the $\nu_\odot$ secular resonance for
fictitious irregular satellites in retrograde orbits. This commensurability is
associated to the secular angle $\theta = \varpi - \varpi_\odot$, where
$\varpi$ is the longitude of pericenter of the satellite and $\varpi_\odot$
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 $\theta$ 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

### Unveiling hidden companions in post-common-envelope binaries: A robust strategy and uncertainty exploration

Some post-common-envelope binaries are binary stars with short periods that
exhibit significant period variations over long observational time spans. These
eclipse timing variations (ETVs) are most likely to be accounted for by the
presence of an unseen massive companion, potentially of planetary or substellar
nature, and the light-travel time (LTT) effect. In this study, our main
objective is to describe the diversity of compatible nontransit companions
around PCEBs and explore the robustness of the solutions by employing tools for
uncertainty estimation. We select the controversial data of the QS Vir binary
star, which previous studies have suggested hosts a planet. We employ a
minimizing strategy, using genetic algorithms to explore the global parameter
space followed by refinement of the solution using the simplex method. We
evaluate errors through the classical MCMC approach and discuss the error range
for parameters. Our results highlight the strong dependence of ETV models for
close binaries on the dataset used, which leads to relatively loose constraints
on the parameters of the unseen companion. We find that the shape of the $O-C$
curve is influenced by the dataset employed. We propose an alternative method
to evaluate errors on the orbital fits based on a grid search surrounding the
best-fit values, obtaining a wider range of plausible solutions that are
compatible with goodness-of-fit statistics. We also analyze how the parameter
solutions are affected by the choice of the dataset, and find that this system
continuously changes the compatible solutions as new data are obtained from
eclipses. The best-fit parameters for QS Vir correspond to a low-mass stellar
companion (57.71 $M_{jup}$ ranging from 40 to 64 $M_{jup}$) on an eccentric
orbit ($e=0.91^{+0.07}_{-0.17}$) with a variety of potential periods ($P =
16.69 ^{+0.47}_{-0.42}$ yr.)Comment: 13 Pages. 14 Figures. A&A A&A approved. article aa47030-2

### The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits

We present families of symmetric and asymmetric periodic orbits at the 1/1
resonance, for a planetary system consisting of a star and two small bodies, in
comparison to the star, moving in the same plane under their mutual
gravitational attraction. The stable 1/1 resonant periodic orbits belong to a
family which has a planetary branch, with the two planets moving in nearly
Keplerian orbits with non zero eccentricities and a satellite branch, where the
gravitational interaction between the two planets dominates the attraction from
the star and the two planets form a close binary which revolves around the
star. The stability regions around periodic orbits along the family are
studied. Next, we study the dynamical evolution in time of a planetary system
with two planets which is initially trapped in a stable 1/1 resonant periodic
motion, when a drag force is included in the system. We prove that if we start
with a 1/1 resonant planetary system with large eccentricities, the system
migrates, due to the drag force, {\it along the family of periodic orbits} and
is finally trapped in a satellite orbit. This, in principle, provides a
mechanism for the generation of a satellite system: we start with a planetary
system and the final stage is a system where the two small bodies form a close
binary whose center of mass revolves around the star.Comment: to appear in Cel.Mech.Dyn.Ast

### A new analysis of the GJ581 extrasolar planetary system

We have done a new analysis of the available observations for the GJ581
exoplanetary system. Today this system is controversial due to choices that can
be done in the orbital determination. The main ones are the ocurrence of
aliases and the additional bodies - the planets f and g - announced in Vogt et
al. 2010. Any dynamical study of exoplanets requires the good knowledge of the
orbital elements and the investigations involving the planet g are particularly
interesting, since this body would lie in the Habitable Zone (HZ) of the star
GJ581. This region,for this system, is very attractive of the dynamical point
of view due to several resonances of two and three bodies present there. In
this work, we investigate the conditions under which the planet g may exist. We
stress the fact that the planet g is intimately related with the orbital
elements of the planet d; more precisely, we conclude that it is not possible
to disconnect its existence from the determination of the eccentricity of the
planet d. Concerning the planet f, we have found one solution with period
$\approx 450$ days, but we are judicious about any affirmation concernig this
body because its signal is in the threshold of detection and the high period is
in a spectral region where the ocorruence of aliases is very common. Besides,
we outline some dynamical features of the habitable zone with the dynamical map
and point out the role played by some resonances laying there.Comment: 12 pages, 9 figure