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Effect of the rotation and tidal dissipation history of stars on the evolution of close-in planets

A Correction to this article was published on 24 January 2019

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Abstract

Since 20 years, a large population of close-in planets orbiting various classes of low-mass stars (from M-type to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent observational and theoretical works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, stellar spin-up occurring during the Pre-Main-Sequence (PMS) phase because of the contraction of stars and their spin-down because of the torque applied by magnetized stellar winds strongly impact angular momentum exchanges within star–planet systems. Therefore, it is now necessary to take into account the structural and rotational evolution of stars when studying the orbital evolution of close-in planets. At the same time, the presence of planets may modify the rotational dynamics of the host stars and as a consequence their evolution, magnetic activity and mixing. In this work, we present the first study of the dynamics of close-in planets of various masses orbiting low-mass stars (from \(0.6~M_\odot \) to \(1.2~M_\odot \)) where we compute the simultaneous evolution of the star’s structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in Celestial Mechanics, especially during the PMS phase. Moreover, because of this stronger tidal friction in the star, the orbital migration of the planet is now more pronounced and depends more on the stellar mass, rotation and age. This would very weakly affect the planets in the habitable zone because they are located at orbital distances such that stellar tide-induced migration happens on very long timescales. We also demonstrate that the rotational evolution of host stars is only weakly affected by the presence of planets except for massive companions.

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Change history

  • 24 January 2019

    This is an erratum for the publication Bolmont andMathis 2016 (Celestial Mechanics and Dynamical Astronomy, 126, 275-296).

Notes

  1. For a close-in planet, the evolution time scale of its rotation period and obliquity is very short. We therefore expect the planets we consider here to be synchronized and with a null obliquity very early in the evolution (e.g., Leconte et al. 2010).

  2. We point out here that equivalent quality factors \({\overline{Q'}}\) and \({\overline{Q}}\), which are proportional to the inverse of the frequency-averaged dissipation \(\left\langle \mathrm{Im} \left[ k_2^2(\omega )\right] \right\rangle _{\omega }\), where \(\left\langle \ldots \right\rangle _{\omega }=\int _{-\infty }^{\infty }\ldots {\mathrm {d}\omega }/{\omega }\), are not equivalent to potentially defined frequency-averaged quality factors \(\left\langle Q'\left( \omega \right) \right\rangle _{\omega }\) and \(\left\langle Q\left( \omega \right) \right\rangle _{\omega }\). In this framework, the relevant physical quantity being \(\left\langle \mathrm{Im} \left[ k_2^2(\omega )\right] \right\rangle _{\omega }\), we prefer to define directly equivalent quality factors from it.

References

  • Albrecht, S., Winn, J.N., Johnson, J.A., et al.: ApJ 757, 18 (2012)

    ADS  Google Scholar 

  • Alexander, M.E.: Ap&SS 23, 459 (1973)

    ADS  Google Scholar 

  • Auclair-Desrotour, P., Le Poncin-Lafitte, C., Mathis, S.: A&A 561, L7 (2014)

    ADS  Google Scholar 

  • Auclair Desrotour, P., Mathis, S., Le Poncin-Lafitte, C.: A&A 581, A118 (2015)

    ADS  Google Scholar 

  • Amard, L., Palacios, A., Charbonnel, C., Gallet, F., Bouvier, J.: A&A 587, 105 (2016)

    ADS  Google Scholar 

  • Baglin, A., Auvergne, M., Boisnard, L., et al.: In: COSPAR Meeting, 36th COSPAR Scientific Assembly, vol. 36 (2006)

  • Barker, A.J.: MNRAS 414, 1365 (2011)

    ADS  Google Scholar 

  • Barker, A.J., Lithwick, Y.: MNRAS 437, 305 (2014)

    ADS  Google Scholar 

  • Barker, A.J., Ogilvie, G.I.: MNRAS 395, 2268 (2009)

    ADS  Google Scholar 

  • Barker, A.J., Ogilvie, G.I.: MNRAS 404, 1849 (2010)

    ADS  Google Scholar 

  • Barnes, S.A.: ApJ 586, 464 (2003)

    ADS  Google Scholar 

  • Barnes, S.A., Kim, Y.-C.: ApJ 721, 675 (2010)

    ADS  Google Scholar 

  • Baruteau, C., Rieutord, M.: J. Fluid Mech. 719, 47 (2013)

    ADS  MathSciNet  Google Scholar 

  • Bolmont, E., Raymond, S.N., Leconte, J.: A&A 535, A94 (2011)

    ADS  Google Scholar 

  • Bolmont, E., Raymond, S.N., Leconte, J., Hersant, F., Correia, A.C.M.: A&A 583, A116 (2015)

    ADS  Google Scholar 

  • Bolmont, E., Raymond, S.N., Leconte, J., Matt, S.P.: A&A 544, A124 (2012)

    ADS  Google Scholar 

  • Bonfils, X., Delfosse, X., Udry, S., et al.: A&A 549, A109 (2013)

    ADS  Google Scholar 

  • Borucki, W.J., Koch, D., Basri, G., et al.: Science 327, 977 (2010)

    ADS  Google Scholar 

  • Bouvier, J.: A&A 489, L53 (2008)

    ADS  Google Scholar 

  • Bouvier, J., Forestini, M., Allain, S.: A&A 326, 1023 (1997)

    ADS  Google Scholar 

  • Brun, A.-S.: Magnetic fields throughout stellar evolution. In: Proceedings of the International Astronomical Union, IAU Symposium, vol. 302, p. 114 (2014)

  • Ceillier, T., van Saders, J., García, R.A., et al.: MNRAS 456, 119 (2016)

    ADS  Google Scholar 

  • Charbonneau, D., Brown, T.M., Latham, D.W., Mayor, M.: ApJ 529, L45 (2000)

    ADS  Google Scholar 

  • Charbonneau, P.: Ann. Rev. Astron. Astrophys. 52, 251 (2014)

    ADS  Google Scholar 

  • Choi, P.I., Herbst, W.: Astron. J. 111, 283 (1996)

    ADS  Google Scholar 

  • Correia, A.C.M., Boué, G., Laskar, J., Rodríguez, A.: A&A 571, A50 (2014)

    ADS  Google Scholar 

  • Correia, A.C.M., Laskar, J.: J. Geophys. Res. Planets 108, 9 (2003)

    Google Scholar 

  • Damiani, C., Lanza, A.F.: A&A 574, A39 (2015)

    ADS  Google Scholar 

  • Edwards, S., Strom, S.E., Hartigan, P., et al.: Astron. J. 106, 372 (1993)

    ADS  Google Scholar 

  • Efroimsky, M.: ApJ 746, 150 (2012)

    ADS  Google Scholar 

  • Efroimsky, M., Makarov, V.V.: ApJ 764, 26 (2013)

    ADS  Google Scholar 

  • Eggleton, P.P., Kiseleva, L.G., Hut, P.: ApJ 499, 853 (1998)

    ADS  Google Scholar 

  • Fabrycky, D.C., Lissauer, J.J., Ragozzine, D., et al.: ApJ 790, 146 (2014)

    ADS  Google Scholar 

  • Fang, J., Margot, J.-L.: ApJ 761, 92 (2012)

    ADS  Google Scholar 

  • Favier, B., Barker, A.J., Baruteau, C., Ogilvie, G.I.: MNRAS 439, 845 (2014)

    ADS  Google Scholar 

  • Ferraz-Mello, S., Tadeu dos Santos, M., Folonier, H., et al.: ApJ 807, 78 (2015)

    ADS  Google Scholar 

  • Gallet, F., Bouvier, J.: A&A 556, A36 (2013)

    ADS  Google Scholar 

  • Gallet, F., Bouvier, J.: A&A 577, A98 (2015)

    ADS  Google Scholar 

  • García, R.A., Ceillier, T., Salabert, D., et al.: A&A 572, A34 (2014)

    ADS  Google Scholar 

  • Gizon, L., Ballot, J., Michel, E., et al.: Proc. Natl. Acad. Sci. 110, 13267 (2013)

    ADS  Google Scholar 

  • Goodman, J., Dickson, E.S.: ApJ 507, 938 (1998)

    ADS  Google Scholar 

  • Goodman, J., Lackner, C.: ApJ 696, 2054 (2009)

    ADS  Google Scholar 

  • Guenel, M., Baruteau, C., Mathis, S., & Rieutord, M.: A&A 589, A22 (2016)

  • Guenel, M., Mathis, S., Remus, F.: A&A 566, L9 (2014)

    ADS  Google Scholar 

  • Guillot, T., Lin, D.N.C., Morel, P., Havel, M., Parmentier, V.: EAS Publications Series, vol. 65, pp. 327–336 (2014)

  • Hansen, B.M.S.: ApJ 723, 285 (2010)

    ADS  Google Scholar 

  • Hansen, B.M.S.: ApJ 757, 6 (2012)

    ADS  Google Scholar 

  • Henning, W.G., O’Connell, R.J., Sasselov, D.D.: ApJ 707, 1000 (2009)

    ADS  Google Scholar 

  • Henry, G.W., Marcy, G.W., Butler, R.P., Vogt, S.S.: ApJ 529, L41 (2000)

    ADS  Google Scholar 

  • Husnoo, N., Pont, F., Mazeh, T., et al.: MNRAS 422, 3151 (2012)

    ADS  Google Scholar 

  • Hut, P.: A&A 99, 126 (1981)

    ADS  Google Scholar 

  • Irwin, J., Berta, Z.K., Burke, C.J., et al.: ApJ 727, 56 (2011)

    ADS  Google Scholar 

  • Ivanov, P.B., Papaloizou, J.C.B., Chernov, S.V.: MNRAS 432, 2339 (2013)

    ADS  Google Scholar 

  • Jackson, B., Greenberg, R., Barnes, R.: ApJ 681, 1631 (2008)

    ADS  Google Scholar 

  • Kaula, W.M.: Rev. Geophys. Space Phys. 2, 661 (1964)

    ADS  Google Scholar 

  • Kawaler, S.D.: ApJ 333, 236 (1988)

    ADS  Google Scholar 

  • Lai, D.: MNRAS 423, 486 (2012)

    ADS  Google Scholar 

  • Lanza, A.F.: A&A 512, A77 (2010)

    ADS  Google Scholar 

  • Lanza, A.F., Shkolnik, E.L.: MNRAS 443, 1451 (2014)

    ADS  Google Scholar 

  • Leconte, J., Chabrier, G., Baraffe, I., Levrard, B.: A&A 516, A64+ (2010)

    ADS  Google Scholar 

  • MacGregor, K.B., Brenner, M.: ApJ 376, 204 (1991)

    ADS  Google Scholar 

  • Maeder, A.: Physics, Formation and Evolution of Rotating Stars. Springer, Berlin (2009)

  • Mathis, S.: In: Martins, F., Boissier, S., Buat, V., Cambrésy, L., Petit, P. (eds.) SF2A-2015: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics, pp.401–405 (2015a)

  • Mathis, S.: A&A 580, L3 (2015b)

    ADS  Google Scholar 

  • Mathis, S., Zahn, J.-P.: A&A 425, 229 (2004)

    ADS  Google Scholar 

  • Mathis, S., Le Poncin-Lafitte, C.: A&A 497, 889 (2009)

    ADS  Google Scholar 

  • Mathis, S. & Remus, F.: In: Rozelot, J.-P., Neiner C. (eds.) Lecture Notes in Physics. The Environments of the Sun and the Stars), vol. 857, p. 111 (2013)

  • Matt, S.P., Brun, A.S., Baraffe, I., Bouvier, J., Chabrier, G.: ApJ 799, L23 (2015)

    ADS  Google Scholar 

  • Mayor, M., Queloz, D.: Nature 378, 355 (1995)

    ADS  Google Scholar 

  • McQuillan, A., Mazeh, T., Aigrain, S.: ApJ 775, L11 (2013)

    ADS  Google Scholar 

  • McQuillan, A., Mazeh, T., Aigrain, S.: ApJS 211, 24 (2014)

    ADS  Google Scholar 

  • Mignard, F.: Moon Planets 20, 301 (1979)

    ADS  Google Scholar 

  • Ogilvie, G.I.: MNRAS 429, 613 (2013)

    ADS  Google Scholar 

  • Ogilvie, G.I.: ARA&A 52, 171 (2014)

    ADS  Google Scholar 

  • Ogilvie, G.I., Lin, D.N.C.: ApJ 610, 477 (2004)

    ADS  Google Scholar 

  • Ogilvie, G.I., Lin, D.N.C.: ApJ 661, 1180 (2007)

    ADS  Google Scholar 

  • Paz-Chinchón, F., Leão, I.C., Bravo, J.P., et al.: ApJ 803, 69 (2015)

    ADS  Google Scholar 

  • Penev, K., Zhang, M., Jackson, B.: PASP 126, 553 (2014)

    ADS  Google Scholar 

  • Perryman, M.: The Exoplanet Handbook. Cambridge University Press (2011)

  • Pont, F.: MNRAS 396, 1789 (2009)

    ADS  Google Scholar 

  • Poppenhaeger, K., Wolk, S.J.: A&A 565, L1 (2014)

    ADS  Google Scholar 

  • Rebull, L.M., Stauffer, J.R., Megeath, S.T., Hora, J.L., Hartmann, L.: ApJ 646, 297 (2006)

    ADS  Google Scholar 

  • Rebull, L.M., Wolff, S.C., Strom, S.E.: Astron. J. 127, 1029 (2004)

    ADS  Google Scholar 

  • Remus, F., Mathis, S., Zahn, J.-P.: A&A 544, A132 (2012a)

    ADS  Google Scholar 

  • Remus, F., Mathis, S., Zahn, J.-P., Lainey, V.: A&A 541, A165 (2012b)

    ADS  Google Scholar 

  • Réville, V., Brun, A.S., Matt, S.P., Strugarek, A., Pinto, R.F.: ApJ 798, 116 (2015)

    ADS  Google Scholar 

  • Savonije, G.-J.: In: Goupil, M.-J., Zahn J.-P. (eds.) EAS Publications Series, vol. 29, pp. 91–125 (2008)

  • Siess, L., Dufour, E., Forestini, M.: A&A 358, 593 (2000)

    ADS  Google Scholar 

  • Skumanich, A.: ApJ 171, 565 (1972)

    ADS  Google Scholar 

  • Teitler, S., Königl, A.: ApJ 786, 139 (2014)

    ADS  Google Scholar 

  • Terquem, C., Papaloizou, J.C.B., Nelson, R.P., Lin, D.N.C.: ApJ 502, 788 (1998)

    ADS  Google Scholar 

  • Tobie, G., Mocquet, A., Sotin, C.: Icarus 177, 534 (2005)

    ADS  Google Scholar 

  • van Saders, J.L., Ceillier, T., Metcalfe, T.S., Silva Aguirre, V., Pinsonneault, M.H., García, R.A., Mathur, S., Davies, G.R.: Nature 529, 181–184 (2016)

  • Winn, J.N., Fabrycky, D., Albrecht, S., Johnson, J.A.: ApJ 718, L145 (2010)

    ADS  Google Scholar 

  • Witte, M.G., Savonije, G.J.: A&A 350, 129 (1999)

    ADS  Google Scholar 

  • Zahn, J.P.: Ann. Astrophys. 29, 489 (1966)

    ADS  Google Scholar 

  • Zahn, J.-P.: A&A 41, 329 (1975)

    ADS  Google Scholar 

  • Zahn, J.-P.: A&A 57, 383 (1977)

    ADS  Google Scholar 

  • Zahn, J.-P.: A&A 220, 112 (1989)

    ADS  Google Scholar 

  • Zahn, J.-P., Bouchet, L.: A&A 223, 112 (1989)

    ADS  Google Scholar 

  • Zahn, J.-P.: A&A 265, 115 (1992)

    ADS  Google Scholar 

  • Zahn, J.-P.: A&A 288, 829 (1994)

    ADS  Google Scholar 

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Acknowledgments

We thank the referee for the useful comments. E. B. acknowledges that this work is part of the F.R.S.-FNRS “ExtraOrDynHa” research project. 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).

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Correspondence to Emeline Bolmont.

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Bolmont, E., Mathis, S. Effect of the rotation and tidal dissipation history of stars on the evolution of close-in planets. Celest Mech Dyn Astr 126, 275–296 (2016). https://doi.org/10.1007/s10569-016-9690-3

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  • DOI: https://doi.org/10.1007/s10569-016-9690-3

Keywords

  • Planets and satellites: dynamical evolution and stability
  • Planet–star interactions
  • Terrestrial planets
  • Gaseous planets
  • Stars: evolution
  • Stars: rotation