Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions

By C. Beaugé, S. Ferraz-Mello, T. Michtchenko. 2002

145 citations recorded by the source corpus.

In recent years several pairs of extrasolar planets have been discovered in the vicinity of mean-motion commensurabilities. In some cases, such as the GJ 876 system, the planets seem to be trapped in a stationary solution, the system exhibiting a simultaneous libration of the resonant angle θ1 = 2λ2 - λ1 - ϖ1 and of the relative position of the pericenters. In this paper we analyze the existence and location of these stable solutions, for the 2 : 1 and 3 : 1 resonances, as functions of the masses and orbital elements of both planets. This is undertaken via an analytical model for the resonant Hamiltonian function. The results are compared with those of numerical simulations of the exact equations. In the 2 : 1 commensurability, we show the existence of three principal families of stationary solutions: (1) aligned orbits, in which θ1 and ϖ1 - ϖ2 both librate around zero, (2) antialigned orbits, in which θ1 = 0 and the difference in pericenter is 180°, and (3) asymmetric stationary solutions, in which both the resonant angle and ϖ1 - ϖ2 are constants with values different from 0° or 180°. Each family exists in a different domain of values of the mass ratio and eccentricities of both planets. Similar results are also found in the 3 : 1 resonance. We discuss the application of these results to the extrasolar planetary systems and develop a chart of possible planetary orbits with apsidal corotation. We estimate, also, the maximum planetary masses in order for the stationary solutions to be dynamically stable.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/e68a28e1cb046baf5e2752891d7a5710ad89c8e7

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In Astronomy and Astrophysics

Citations in the corpus

Migration and the Formation of Systems of Hot Super-Earths and Neptunes (2006, methodology): “The relative orientation of the orbits may be phase–locked at an angle that differs from 0 or 180 deg, depending on their eccentricities and the mass of the planets (Beaugé et al. 2003, Kley et al. 2004).”
THE LICK-CARNEGIE EXOPLANET SURVEY: A URANUS-MASS FOURTH PLANET FOR GJ 876 IN AN EXTRASOLAR LAPLACE CONFIGURATION (2010, background): “Murray et al. (2002), Lee & Peale (2002), Chiang et al. (2002), Thommes & Lissauer (2003), Beauge et al. (2003), Kley et al. (2004), Lee (2004), Kley et al. (2005), and Lee & Thommes (2009) examined scenarios of how the system may have come to be in its current dynamical configuration.”