44 research outputs found
Tidal evolution of close-in exoplanets in co-orbital configurations
In this paper, we study the behavior of a pair of co-orbital planets, both
orbiting a central star on the same plane and undergoing tidal interactions.
Our goal is to investigate final orbital configurations of the planets,
initially involved in the 1/1 mean-motion resonance (MMR), after long-lasting
tidal evolution. The study is done in the form of purely numerical simulations
of the exact equations of motions accounting for gravitational and tidal
forces. The results obtained show that, at least for equal mass planets, the
combined effects of the resonant and tidal interactions provoke the orbital
instability of the system, often resulting in collision between the planets. We
first discuss the case of two hot-super-Earth planets, whose orbital dynamics
can be easily understood in the frame of our semi-analytical model of the 1/1
MMR. Systems consisting of two hot-Saturn planets are also briefly discussed.Comment: 18 pages, 8 figures. Accepted for publication in Celestial Mechanics
and Dynamical Astronom
Secular Dynamics of S-type Planetary Orbits in Binary Star Systems: Applicability Domains of First- and Second-Order Theories
We analyse the secular dynamics of planets on S-type coplanar orbits in tight
binary systems, based on first- and second-order analytical models, and compare
their predictions with full N-body simulations. The perturbation parameter
adopted for the development of these models depends on the masses of the stars
and on the semimajor axis ratio between the planet and the binary.
We show that each model has both advantages and limitations. While the
first-order analytical model is algebraically simple and easy to implement, it
is only applicable in regions of the parameter space where the perturbations
are sufficiently small. The second-order model, although more complex, has a
larger range of validity and must be taken into account for dynamical studies
of some real exoplanetary systems such as -Cephei and HD 41004A.
However, in some extreme cases, neither of these analytical models yields
quantitatively correct results, requiring either higher-order theories or
direct numerical simulations.
Finally, we determine the limits of applicability of each analytical model in
the parameter space of the system, giving an important visual aid to decode
which secular theory should be adopted for any given planetary system in a
close binary.Comment: 32 pages, 8 figures, accepted for publication in Celestial Mechanics
and Dynamical Astrophysic
Spin-orbit coupling for tidally evolving super-Earths
We investigate the spin behavior of close-in rocky planets and the
implications for their orbital evolution. Considering that the planet rotation
evolves under simultaneous actions of the torque due to the equatorial
deformation and the tidal torque, both raised by the central star, we analyze
the possibility of temporary captures in spin-orbit resonances. The results of
the numerical simulations of the exact equations of motions indicate that,
whenever the planet rotation is trapped in a resonant motion, the orbital decay
and the eccentricity damping are faster than the ones in which the rotation
follows the so-called pseudo-synchronization. Analytical results obtained
through the averaged equations of the spin-orbit problem show a good agreement
with the numerical simulations. We apply the analysis to the cases of the
recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The
simulated dynamical history of these systems indicates the possibility of
capture in several spin-orbit resonances; particularly, GJ 3634 b and 55 Cnc e
can currently evolve under a non-synchronous resonant motion for suitable
values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation
behavior by evolving towards synchronization through successive temporary
resonant trappings.Comment: Accepted for publication in MNRA
Chaotic diffusion in the action and frequency domains: estimate of instability times
Purpose: Chaotic diffusion in the non-linear systems is commonly studied in
the action framework. In this paper, we show that the study in the frequency
domain provides good estimates of the sizes of the chaotic regions in the phase
space, also as the diffusion timescales inside these regions.
Methods: Applying the traditional tools, such as Poincar\'e Surfaces of
Section, Lyapunov Exponents and Spectral Analysis, we characterise the phase
space of the Planar Circular Restricted Three Body Problem (PCR3BP). For the
purpose of comparison, the diffusion coefficients are obtained in the action
domain of the problem, applying the Shannon Entropy Method (SEM), also as in
the frequency domain, applying the Mean Squared Displacement (MSD) method and
Laskar's Equation of Diffusion. We compare the diffusion timescales defined by
the diffusion coefficients obtained to the Lyapunov times and the instability
times obtained through direct numerical integrations.
Results: Traditional tools for detecting chaos tend to misrepresent regimes
of motion, in which either slow-diffusion or confined-diffusion processes
dominates. The SEM shows a good performance in the regions of slow chaotic
diffusion, but it fails to characterise regions of strong chaotic motion. The
frequency-based methods are able to precisely characterise the whole phase
space and the diffusion times obtained in the frequency domain present
satisfactory agreement with direct integration instability times, both in weak
and strong chaotic motion regimes. The diffusion times obtained by means of the
SEM fail to match correctly the instability times provided by numerical
integrations.
Conclusion: We conclude that the study of dynamical instabilities in the
frequency domain provides reliable estimates of the diffusion timescales, and
also presents a good cost-benefit in terms of computation-time.Comment: 9 pages, 2 figures, accepted for publication in EPJS
Modelling resonances and orbital chaos in disk galaxies. Application to a Milky Way spiral model
Context: Resonances in the stellar orbital motion under perturbations from
spiral arms structure play an important role in the evolution of the disks of
spiral galaxies. The epicyclic approximation allows the determination of the
corresponding resonant radii on the equatorial plane (for nearly circular
orbits), but is not suitable in general.
Aims: We expand the study of resonant orbits by analysing stellar motions
perturbed by spiral arms with Gaussian-shaped profiles without any restriction
on the stellar orbital configurations, and we expand the concept of Lindblad
(epicyclic) resonances for orbits with large radial excursions.
Methods: We define a representative plane of initial conditions, which covers
the whole phase space of the system. Dynamical maps on representative planes
are constructed numerically, in order to characterize the phase-space structure
and identify the precise location of resonances. The study is complemented by
the construction of dynamical power spectra, which provide the identification
of fundamental oscillatory patterns in the stellar motion.
Results: Our approach allows a precise description of the resonance chains in
the whole phase space, giving a broader view of the dynamics of the system when
compared to the classical epicyclic approach, even for objects in retrograde
motion. The analysis of the solar neighbourhood shows that, depending on the
current azimuthal phase of the Sun with respect to the spiral arms, a star with
solar kinematic parameters may evolve either inside the stable co-rotation
resonance or in a chaotic zone.
Conclusions: Our approach contributes to quantifying the domains of resonant
orbits and the degree of chaos in the whole Galactic phase-space structure. It
may serve as a starting point to apply these techniques to the investigation of
clumps in the distribution of stars in the Galaxy, such as kinematic moving
groups.Comment: 17 pages, 15 figures. Matches accepted version in A&
Tidal evolution of a close-in planet with a more massive outer companion
We investigate the motion of a two-planet coplanar system under the combined effects of mutual interaction and tidal dissipation. The secular behavior of the system is analyzed using two different approaches, restricting to the case of a more massive outer planet. First, we solve the exact equations of motion through the numerical simulation of the system evolution. We also compute the stationary solutions of the mean equations of motion based on a Hamiltonian formalism. An application to the real system CoRoT-7 is investigated.Facultad de Ciencias Astronómicas y Geofísica