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Tidal evolution of hierarchical and inclined systems

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Abstract

We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20°). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to various situations in the HD 11964, HD 80606, and HD 98800 systems.

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Authors and Affiliations

  1. Department of Physics, I3N, University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    Alexandre C. M. Correia

  2. Astronomie et Systèmes Dynamiques, IMCCE-CNRS UMR 8028, Observatoire de Paris, 77 Av. Denfert-Rochereau, 75014, Paris, France

    Jacques Laskar & François Farago

  3. Centro de Astrofísica, University of Porto, Rua das Estrelas, 4150-762, Porto, Portugal

    Gwenaël Boué

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  1. Alexandre C. M. Correia
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  2. Jacques Laskar
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  3. François Farago
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  4. Gwenaël Boué
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Correspondence to Alexandre C. M. Correia.

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Correia, A.C.M., Laskar, J., Farago, F. et al. Tidal evolution of hierarchical and inclined systems. Celest Mech Dyn Astr 111, 105–130 (2011). https://doi.org/10.1007/s10569-011-9368-9

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  • DOI: https://doi.org/10.1007/s10569-011-9368-9

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