Secular dynamics of S-type planetary orbits in binary star systems: applicability domains of first- and second-order theories
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We analyse the secular dynamics of planets on S-type coplanar orbits in tight binary systems, based on first- and second-order analytical models, and compare their predictions with full N-body simulations. The perturbation parameter adopted for the development of these models depends on the masses of the stars and on the semimajor axis ratio between the planet and the binary. We show that each model has both advantages and limitations. While the first-order analytical model is algebraically simple and easy to implement, it is only applicable in regions of the parameter space where the perturbations are sufficiently small. The second-order model, although more complex, has a larger range of validity and must be taken into account for dynamical studies of some real exoplanetary systems such as \(\gamma \) Cephei and HD 41004A. However, in some extreme cases, neither of these analytical models yields quantitatively correct results, requiring either higher-order theories or direct numerical simulations. Finally, we determine the limits of applicability of each analytical model in the parameter space of the system, giving an important visual aid to decode which secular theory should be adopted for any given planetary system in a close binary.
KeywordsSecular dynamics Binary star Second-order Perturbation theory Planets in binaries
Part of this work was developed during a visit of E.A-I. to the Universidad Nacional de Cordoba. We wish to express our gratitude to FAPESP (Grants 2010/01209-2 and 2013/17102-0), CNPq, CONICET and Secyt/UNC for their support.
- Eggenberger, A., Udry, S.: Probing the impact of stellar duplicity on planet occurrence with spectroscopic and imaging observations. Planets Bin. Star Syst. 366, 19 (2010)Google Scholar
- Ellis, K.-M., Murray, C.-D.: The disturbing function in solar system dynamics. Icarus. 147, 129–144 (2000)Google Scholar
- Laskar, J.: Introduction to Frequency Map Analysis, Hamiltonian Systems with Three or More Degrees of Freedom. Springer, New York (1999)Google Scholar
- Plummer, H.C.K.: An Introductory Treatise on Dynamical Astronomy. University Press, Cambridge (1918)Google Scholar