Dynamical analysis and constraints for the HD 196885 system

C. A. GIUPPONE, M. H. M. MORAIS, G. BOUÉ, A. C. M. CORREIA

Serra Negra, Sao Paulo

Congreso; XVI Colóquio Brasileiro de Dinâmica Orbital; 2012

Universidade Federal do ABC

About 20% of all known exoplanets have been found to inhabit multiple stellar systems [1]. The theories of planet formation around a star that is part of a binary system found considerable challenges. A brief review of theories can be seen in [2,3]. However, it is very important to know the real masses and the spatial configuration of these systems to better understand the processes involved in their formation. 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 compare numerical results with those using a model with the restricted quadrupolar problem. The numerical integrations of the full problem agree well with the theoretical trajectories of the quadrupolar restricted Hamiltonian. The global behavior of the planet in the HD 196885 system could be dominated by the dynamical regimes Lidov-Kozai equilibrium points, librating or circulating orbits. We find that the most likely configurations for the planet HD 196885b are either nearly coplanar orbits (prograde and retrograde), or highly inclined orbits near the Lidov-Kozai equilibrium points, i = 44º or i = 137º . Among coplanar orbits, the retrograde ones appear to be less chaotic, while for the orbits near the Lidov-Kozai equilibria, those around ω = 270º are more reliable, where ω 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 ) ~ (65º, 80º), (65º , 260º), (115º, 80º), and (115º , 260º ), where I1 is the inclination of the planet and Omega_1 is the longitude of ascending node.