Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

Abstract

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.

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Notes

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    For more details, the reader can apply the integral calculator available through the Wolfram website at: http://www.wolframalpha.com/calculators/integral_calculator.

  2. 2.

    http://www.astro.wisc.edu/~townsend/static.php?ref=ez-web.

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Acknowledgments

The authors would like to thank an anonymous Referee for a careful reading of the manuscript and valuable comments that helped to improve their work. They are also grateful to the Editors of this special issue on tides for their kind invitation to contribute. S. M. acknowledges funding by the European Research Council through ERC Grant SPIRE 647383. This work was also supported by the ANR Blanc TOUPIES SIMI5-6 020 01, the Programme National de Planétologie (CNRS/INSU) and PLATO CNES Grant at Service d’Astrophysique (CEA-Saclay). The authors gratefully acknowledge use of the EZ-web stellar evolution resources. Exoplanet studies at INAF-Osservatorio Astrofisico di Catania have been funded also through the Progetti Premiali of the Italian Ministero dell’Istruzione, Università e Ricerca.

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Lanza, A.F., Mathis, S. Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model. Celest Mech Dyn Astr 126, 249–274 (2016). https://doi.org/10.1007/s10569-016-9714-z

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Keywords

  • Planet-star interactions
  • Stars rotation
  • Binaries
  • Hydrodynamics
  • Turbulence
  • Physical model