Secular models and Kozai resonance for planets in coorbital non-coplanar motion

In this work, we construct and test an analytical and a semianalytical secular models for two planets locked in a coorbital non-coplanar motion, comparing some results with the case of restricted three body problem. The analytical average model replicates the numerical N-body integrations, even for moderate eccentricities ($\lesssim$ 0.3) and inclinations ($\lesssim10^\circ$), except for the regions corresponding to quasi-satellite and Lidov-Kozai configurations. Furthermore, this model is also useful in the restricted three body problem, assuming very low mass ratio between the planets. We also describe a four-degree-of-freedom semianalytical model valid for any type of coorbital configuration in a wide range of eccentricities and inclinations. {Using a N-body integrator, we have found that the phase space of the General Three Body Problem is different to the restricted case for inclined systems, and establish the location of the Lidov-Kozai equilibrium configurations depending on mass ratio. We study the stability of periodic orbits in the inclined systems, and find that apart from the robust configurations $L_4$, $AL_4$, and $QS$ is possible to harbour two Earth-like planets in orbits previously identified as unstable $U$ and also in Euler $L_3$ configurations, with bounded chaos.Comment: 15 pages. 20 figure

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

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

A semi-empirical stability criterion for real multi-planetary systems with eccentric orbits

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom´s criterion of first order mean motion resonance overlap citep{Wisdom1980AJ}. 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.Fil: Giuppone, Cristian Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Instituto de Astronomía Teórica y Experimental; Argentina; Universidade de Aveiro. Departamento de Física, I3N; Portugal;Fil: Morais, M.H.M.. Universidade de Aveiro. Departamento de Física, I3N; Portugal;Fil: Correia, A.C.M.. Centre National de la Recherche Scientifique. Observatoire de Paris; Francia; Universidade de Aveiro. Departamento de Física, I3N; Portugal

Movimientos propios en la zona del cúmulo abierto Collinder 132

Tesis (Lic. en Astronomía)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2006.El conocimiento actualizado de las posiciones y los movimientos de las estrellas es imprescindible en Astronomía, no sólo para saber dónde se encuentran los astros sino también para la determinación del sistema de referencia celeste y el estudio de la cinemática y dinámica de nuestra galaxia, por ejemplo. En este trabajo se realizó la determinación de movimientos propios estableciendo posiciones de primera época a partir placas digitalizadas de las colecciones Carte du Ciel y Catálogo Astrográfico de la zona Córdoba. Como posiciones de segunda época las brindadas por los catálogos más modernos (USNO-B1.0 y UCAC2) y como catálogo de referencia, el Tycho2. Para el desarrollo de la metodología se trabajó en la zona del cúmulo abierto Collinder 132 presentando y discutiendo los resultados obtenidos.Cristian Andrés Giuppone

Ajustes orbitales y dinámica de sistemas planetarios extrasolares /

Tesis (Doctor en Astronomía)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2011.El presente trabajo explica y desarrolla estrategias para la determinación de parámetros orbitales de sistemas exoplanetarios a partir de datos de velocidad radial, que son un requisito fundamental para cualquier estudio dinámico. Muchas veces los descubrimientos de exoplanetas muestran configuraciones dinámicamente inestables, implicando que no es consistente con la configuración real de los mismos. Debido a que muchas veces los resultados de los ajustes orbitales son muy sensibles al método numérico y/o conjunto de datos, desarrollamos varias estrategias que permiten identificar los extremos globales de la función residual, estimando los niveles de confianza en los parámetros determinados. Por último, abordamos la generación de datos sintéticos para planetas que se encuentran en resonancias de movimientos medios. Nuestros resultados permiten explicar algunas de las posibles características en la distribución de elementos orbitales, que indican tendencias a sobreestimar parámetros como excentricidades y amplitudes de oscilación de los ángulos resonantes.Cristian Andrés Giuppone ; dirigido por Cristián Beaugé

Semianalytical model for planetary resonances: Application to planets around single and binary stars

Context. Planetary resonances are a common dynamical mechanism acting on planetary systems. However, no general model for describing their properties exists, particularly for commensurabilities of any order and arbitrary eccentricity and inclination values. Aims. We present a semianalytical model that describes the resonance strength, width, location and stability of fixed points, and periods of small-amplitude librations. The model is valid for any two gravitationally interacting massive bodies, and is thus applicable to planets around single or binary stars. Methods. Using a theoretical framework in the Poincaré and Jacobi reference system, we developed a semianalytical method that employs a numerical evaluation of the averaged resonant disturbing function. Validations of the model are presented that compare its predictions with dynamical maps for real and fictitious systems. Results. The model describes many dynamical features of planetary resonances very well. Notwithstanding the good agreement found in all cases, a small deviation is noted in the location of the resonance centers for circumbinary systems. As a consequence of its application to the HD 31527 system, we found that the updated best-fit solution leads to a high-eccentricity stable libration between the middle and outer planets inside the 16/3 mean-motion resonance (MMR). This is the first planetary system whose long-term dynamics appears dominated by such a high-order commensurability. In the case of circumbinary planets, the overlap of N/1 mean-motion resonances coincides very well with the size of the global chaotic region close to the binary, as well as its dependence on the mutual inclination.Fil: Gallardo, Tabaré. Universidad de la República; UruguayFil: Beauge, Cristian. Observatorio Astronomico de la Universidad Nacional de Cordoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Giuppone, Cristian Andrés. Observatorio Astronomico de la Universidad Nacional de Cordoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; Argentin