Are retrograde resonances possible in multi-planet systems?

Abstract
Context. Most multi-planetary systems are characterized by hot-Jupiters close to their central star, moving on eccentric orbits. From a dynamical point of view, compact multi-planetary systems form a specific class of the general N-body problem (where ). Moreover, extrasolar planets are found in prograde orbits about their host star, and often in mean motion resonances (MMR).
Aims. In a first step, we study theoretically a new stabilizing mechanism suitable for compact two-planet systems. This mechanism involves counter-revolving orbits forming a retrograde MMR. In a second step, we investigate the feasibility of planetary systems hosting counter-revolving planets. Dynamical stability, observations, and formation processes of these systems are analyzed and discussed.
Methods. To characterize the dynamical behavior of multi-dimensional planetary systems, we apply our technique of global dynamics analysis based on the MEGNO indicator (Mean Exponential Growth factor of Nearby Orbits) that provides the fine structure of the phase space. In a few cases of possible counter-revolving configurations, we carry out new fits to the observations using the Pikaia genetic algorithm. A statistical study of the stability in the neighborhood of different observed, planetary-systems is completed using a Monte-Carlo method.
Results. We analyse the observational data for the HD 73526 planetary system and find that counter-revolving configurations may be consistent with the observational data. We highlight the fine and characteristic structure of retrograde MMRs. We demonstrate that retrograde resonances open a family of stabilizing mechanisms involving new apsidal precession behaviors.
Conclusions. Considering two possible formation mechanisms (free-floating planet and Slingshot model), we conclude that counter-revolving configurations are feasible.

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