HD60532, a planetary system in a 3:1 mean motion resonance

In a recent paper it was reported a planetary system around the star HD60532, composed by two giant planets in a possible 3:1 mean motion resonance, that should be confirmed within the next decade. Here we show that the analysis of the global dynamics of the system allows to confirm this resonance. The present best fit to data already corresponds to this resonant configuration and the system is stable for at least 5Gry. The 3:1 resonance is so robust that stability is still possible for a wide variety of orbital parameters around the best fit solution and also if the inclination of the system orbital plane with respect to the plane of the sky is as small as 15 deg. Moreover, if the inclination is taken as a free parameter in the adjustment to the observations, we find an inclination ~ 20 deg, which corresponds to M_b =3.1 M_Jup and M_c = 7.4 M_Jup for the planetary companions.Comment: 4 Pages, 4 Figures, accepted by A&

La2010: A new orbital solution for the long term motion of the Earth

We present here a new solution for the astronomical computation of the orbital motion of the Earth spanning from 0 to -250 Myr. The main improvement with respect to the previous numerical solution La2004 (Laskar et al. 2004) is an improved adjustment of the parameters and initial conditions through a fit over 1 Myr to a special version of the high accurate numerical ephemeris INPOP08 (Fienga et al. 2009). The precession equations have also been entirely revised and are no longer averaged over the orbital motion of the Earth and Moon. This new orbital solution is now valid over more than 50 Myr in the past or in the future with proper phases of the eccentricity variations. Due to chaotic behavior, the precision of the solution decreases rapidly beyond this time span, and we discuss the behavior of various solutions beyond 50 Myr. For paleoclimate calibrations, we provide several different solutions that are all compatible with the most precise planetary ephemeris. We have thus reached the time where geological data are now required to discriminate among planetary orbital solutions beyond 50 Myr.Comment: 17 pages, 14 figure

A pair of planets around HD 202206 or a circumbinary planet?

Long-term precise Doppler measurements with the CORALIE spectrograph reveal the presence of a second planet orbiting the solar-type star HD202206. The radial-velocity combined fit yields companion masses of m_2\sini = 17.4 M_Jup and 2.44 M_Jup, semi-major axes of a = 0.83 AU and 2.55 AU, and eccentricities of e = 0.43 and 0.27, respectively. A dynamical analysis of the system further shows a 5/1 mean motion resonance between the two planets. This system is of particular interest since the inner planet is within the brown-dwarf limits while the outer one is much less massive. Therefore, either the inner planet formed simultaneously in the protoplanetary disk as a superplanet, or the outer Jupiter-like planet formed in a circumbinary disk. We believe this singular planetary system will provide important constraints on planetary formation and migration scenarios.Comment: 9 pages, 14 figures, accepted in A&A, 12-May-200

Tidal Evolution of Exoplanets

Tidal effects arise from differential and inelastic deformation of a planet by a perturbing body. The continuous action of tides modify the rotation of the planet together with its orbit until an equilibrium situation is reached. It is often believed that synchronous motion is the most probable outcome of the tidal evolution process, since synchronous rotation is observed for the majority of the satellites in the Solar System. However, in the 19th century, Schiaparelli also assumed synchronous motion for the rotations of Mercury and Venus, and was later shown to be wrong. Rather, for planets in eccentric orbits synchronous rotation is very unlikely. The rotation period and axial tilt of exoplanets is still unknown, but a large number of planets have been detected close to the parent star and should have evolved to a final equilibrium situation. Therefore, based on the Solar System well studied cases, we can make some predictions for exoplanets. Here we describe in detail the main tidal effects that modify the secular evolution of the spin and the orbit of a planet. We then apply our knowledge acquired from Solar System situations to exoplanet cases. In particular, we will focus on two classes of planets, "Hot-Jupiters" (fluid) and "Super-Earths" (rocky with atmosphere).Comment: 30 pages, 19 figures. Chapter in Exoplanets, ed. S. Seager, to be published by University of Arizona Pres

Dissipation in planar resonant planetary systems

Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that damps the eccentricities. However, the resonant angles appear to librate at the end of the migration process, which is often believed to be an evidence that the systems remain in resonance. Here we provide an analytical model for the dissipation in resonant planetary systems valid for low eccentricities. We confirm that dissipation accounts for an excess of pairs that lie just aside from the nominal periods ratios, as observed by the Kepler mission. In addition, by a global analysis of the phase space of the problem, we demonstrate that these final pairs are non-resonant. Indeed, the separatrices that exist in the resonant systems disappear with the dissipation, and remains only a circulation of the orbits around a single elliptical fixed point. Furthermore, the apparent libration of the resonant angles can be explained using the classical secular averaging method. We show that this artifact is only due to the severe damping of the amplitudes of the eigenmodes in the secular motion.Comment: 18 pages, 20 figures, accepted to A&

Dynamical stability analysis of the HD202206 system and constraints to the planetary orbits

Long-term precise Doppler measurements with the CORALIE spectrograph revealed the presence of two massive companions to the solar-type star HD202206. Although the three-body fit of the system is unstable, it was shown that a 5:1 mean motion resonance exists close to the best fit, where the system is stable. We present here an extensive dynamical study of the HD202206 system aiming at constraining the inclinations of the two known companions, from which we derive possible ranges of value for the companion masses. We study the long term stability of the system in a small neighborhood of the best fit using Laskar's frequency map analysis. We also introduce a numerical method based on frequency analysis to determine the center of libration mode inside a mean motion resonance. We find that acceptable coplanar configurations are limited to inclinations to the line of sight between 30 and 90 degrees. This limits the masses of both companions to roughly twice the minimum. Non coplanar configurations are possible for a wide range of mutual inclinations from 0 to 90 degrees, although $\Delta\Omega = 0 [\pi]$ configurations seem to be favored. We also confirm the 5:1 mean motion resonance to be most likely. In the coplanar edge-on case, we provide a very good stable solution in the resonance, whose $\chi^2$ does not differ significantly from the best fit. Using our method to determine the center of libration, we further refine this solution to obtain an orbit with a very low amplitude of libration, as we expect dissipative effects to have dampened the libration.Comment: 14 pages, 18 figure

Constraints on the location of a possible 9th planet derived from the Cassini data

To explain the unusual distribution of Kuiper Belt objects, several authors have advocated the existence of a super-Earth planet in the outer solar system. It has recently been proposed that a 10 M$_{\oplus}$ object with an orbit of 700 AU semi major axis and 0.6 eccentricity can explain the observed distribution of Kuiper Belt objects around Sedna. Here we use the INPOP planetary ephemerides model as a sensor for testing for an additional body in the solar system. We test the possibility of adding the proposed planet without increasing the residuals of the planetary ephemerides, fitted over the whole INPOP planetary data sample. We demonstrate that the presence of such an object is not compatible with the most sensitive data set, the Cassini radio ranging data, if its true anomaly is in the intervals $[-130^\circ:-100^\circ]$ or $[-65^\circ : 85^\circ]$. Moreover, we find that the addition of this object can reduce the Cassini residuals, with a most probable position given by a true anomaly $v = {117.8^\circ}^{ + 11^\circ}_{ - 10^\circ}$.Comment: Accepted for publication in A&A; 4 pages, 6 figure