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

Characterizing Multi-planet Systems with Classical Secular Theory

Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help identify tidal effects, early planet-planet scattering, and dynamical coupling among the planets, for systems in which mean-motion resonances do not play a role. Although tidal damping can result in aligned major axes after all but one eigenmode have damped away, such alignment may simply be fortuitous. An example of this is 55 Cancri (orbital solution of Fischer et al., 2008) where multiple eigenmodes remain undamped. Various solutions for 55 Cancri are compared, showing differing dynamical groupings, with implications for the coupling of eccentricities and for the partitioning of damping among the planets. Solutions for orbits that include expectations of past tidal evolution with observational data, must take into account which eigenmodes should be damped, rather than expecting particular eccentricities to be near zero. Classical secular theory is only accurate for low eccentricity values, but comparison with other results suggests that it can yield useful qualitative descriptions of behavior even for moderately large eccentricity values, and may have advantages for revealing underlying physical processes and, as large numbers of new systems are discovered, for triage to identify where more comprehensive dynamical studies should have priority.Comment: Published in Celestial Mechanics and Dynamical Astronomy, 25 pages, 10 figure

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

The Relativistic Factor in the Orbital Dynamics of Point Masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations

Angular momentum exchange during secular migration of two-planet systems

We investigate the secular dynamics of two-planet coplanar systems evolving under mutual gravitational interactions and dissipative forces. We consider two mechanisms responsible for the planetary migration: star-planet (or planet-satellite) tidal interactions and interactions of a planet with a gaseous disc. We show that each migration mechanism is characterized by a specific law of orbital angular momentum exchange. Calculating stationary solutions of the conservative secular problem and taking into account the orbital angular momentum leakage, we trace the evolutionary routes followed by the planet pairs during the migration process. This procedure allows us to recover the dynamical history of two-planet systems and constrain parameters of the involved physical processes.Comment: 20 pages, 9 figures, accepted for publication in Celestial Mechanics and Dynamical Astronomy (special issue on Exoplanets

Resonances of low orders in the planetary system of HD37124

The full set of published radial velocity data (52 measurements from Keck + 58 ones from ELODIE + 17 ones from CORALIE) for the star HD37124 is analysed. Two families of dynamically stable high-eccentricity orbital solutions for the planetary system are found. In the first one, the outer planets c and d are trapped in the 2/1 mean-motion resonance. The second family of solutions corresponds to the 5/2 mean-motion resonance between these planets. In both families, the planets are locked in (or close to) an apsidal corotation resonance. In the case of the 2/1 MMR, it is an asymmetric apsidal corotation (with the difference between the longitudes of periastra $\Delta\omega\sim 60^\circ$), whereas in the case of the 5/2 MMR it is a symmetric antialigned one ($\Delta\omega = 180^\circ$). It remains also possible that the two outer planets are not trapped in an orbital resonance. Then their orbital eccentricities should be relatively small (less than, say, 0.15) and the ratio of their orbital periods is unlikely to exceed $2.3-2.5$.Comment: 28 pages, 10 figures, 3 tables; Accepted to Celestial Mechanics and Dynamical Astronom

A resonant-term-based model including a nascent disk, precession, and oblateness: application to GJ 876

Investigations of two resonant planets orbiting a star or two resonant satellites orbiting a planet often rely on a few resonant and secular terms in order to obtain a representative quantitative description of the system's dynamical evolution. We present a semianalytic model which traces the orbital evolution of any two resonant bodies in a first- through fourth-order eccentricity or inclination-based resonance dominated by the resonant and secular arguments of the user's choosing. By considering the variation of libration width with different orbital parameters, we identify regions of phase space which give rise to different resonant ''depths,'' and propose methods to model libration profiles. We apply the model to the GJ 876 extrasolar planetary system, quantify the relative importance of the relevant resonant and secular contributions, and thereby assess the goodness of the common approximation of representing the system by just the presumably dominant terms. We highlight the danger in using ''order'' as the metric for accuracy in the orbital solution by revealing the unnatural libration centers produced by the second-order, but not first-order, solution, and by demonstrating that the true orbital solution lies somewhere ''in-between'' the third- and fourth-order solutions. We also present formulas used to incorporate perturbations from central-body oblateness and precession, and a protoplanetary or protosatellite thin disk with gaps, into a resonant system. We quantify these contributions to the GJ 876 system, and thereby highlight the conditions which must exist for multi-planet exosystems to be significantly influenced by such factors. We find that massive enough disks may convert resonant libration into circulation; such disk-induced signatures may provide constraints for future studies of exoplanet systems.Comment: 39 pages of body text, 21 figures, 5 tables, 1 appendix, accepted for publication in Celestial Mechanics and Dynamical Astronom