Celestial Mechanics and Dynamical Astronomy

, Volume 126, Issue 1–3, pp 275–296 | Cite as

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

  • Emeline BolmontEmail author
  • Stéphane Mathis
Original Article


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.


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



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).


  1. Albrecht, S., Winn, J.N., Johnson, J.A., et al.: ApJ 757, 18 (2012)ADSGoogle Scholar
  2. Alexander, M.E.: Ap&SS 23, 459 (1973)ADSGoogle Scholar
  3. Auclair-Desrotour, P., Le Poncin-Lafitte, C., Mathis, S.: A&A 561, L7 (2014)ADSGoogle Scholar
  4. Auclair Desrotour, P., Mathis, S., Le Poncin-Lafitte, C.: A&A 581, A118 (2015)ADSGoogle Scholar
  5. Amard, L., Palacios, A., Charbonnel, C., Gallet, F., Bouvier, J.: A&A 587, 105 (2016)ADSGoogle Scholar
  6. Baglin, A., Auvergne, M., Boisnard, L., et al.: In: COSPAR Meeting, 36th COSPAR Scientific Assembly, vol. 36 (2006)Google Scholar
  7. Barker, A.J.: MNRAS 414, 1365 (2011)ADSGoogle Scholar
  8. Barker, A.J., Lithwick, Y.: MNRAS 437, 305 (2014)ADSGoogle Scholar
  9. Barker, A.J., Ogilvie, G.I.: MNRAS 395, 2268 (2009)ADSGoogle Scholar
  10. Barker, A.J., Ogilvie, G.I.: MNRAS 404, 1849 (2010)ADSGoogle Scholar
  11. Barnes, S.A.: ApJ 586, 464 (2003)ADSGoogle Scholar
  12. Barnes, S.A., Kim, Y.-C.: ApJ 721, 675 (2010)ADSGoogle Scholar
  13. Baruteau, C., Rieutord, M.: J. Fluid Mech. 719, 47 (2013)ADSMathSciNetGoogle Scholar
  14. Bolmont, E., Raymond, S.N., Leconte, J.: A&A 535, A94 (2011)ADSGoogle Scholar
  15. Bolmont, E., Raymond, S.N., Leconte, J., Hersant, F., Correia, A.C.M.: A&A 583, A116 (2015)ADSGoogle Scholar
  16. Bolmont, E., Raymond, S.N., Leconte, J., Matt, S.P.: A&A 544, A124 (2012)ADSGoogle Scholar
  17. Bonfils, X., Delfosse, X., Udry, S., et al.: A&A 549, A109 (2013)ADSGoogle Scholar
  18. Borucki, W.J., Koch, D., Basri, G., et al.: Science 327, 977 (2010)ADSGoogle Scholar
  19. Bouvier, J.: A&A 489, L53 (2008)ADSGoogle Scholar
  20. Bouvier, J., Forestini, M., Allain, S.: A&A 326, 1023 (1997)ADSGoogle Scholar
  21. Brun, A.-S.: Magnetic fields throughout stellar evolution. In: Proceedings of the International Astronomical Union, IAU Symposium, vol. 302, p. 114 (2014)Google Scholar
  22. Ceillier, T., van Saders, J., García, R.A., et al.: MNRAS 456, 119 (2016)ADSGoogle Scholar
  23. Charbonneau, D., Brown, T.M., Latham, D.W., Mayor, M.: ApJ 529, L45 (2000)ADSGoogle Scholar
  24. Charbonneau, P.: Ann. Rev. Astron. Astrophys. 52, 251 (2014)ADSGoogle Scholar
  25. Choi, P.I., Herbst, W.: Astron. J. 111, 283 (1996)ADSGoogle Scholar
  26. Correia, A.C.M., Boué, G., Laskar, J., Rodríguez, A.: A&A 571, A50 (2014)ADSGoogle Scholar
  27. Correia, A.C.M., Laskar, J.: J. Geophys. Res. Planets 108, 9 (2003)Google Scholar
  28. Damiani, C., Lanza, A.F.: A&A 574, A39 (2015)ADSGoogle Scholar
  29. Edwards, S., Strom, S.E., Hartigan, P., et al.: Astron. J. 106, 372 (1993)ADSGoogle Scholar
  30. Efroimsky, M.: ApJ 746, 150 (2012)ADSGoogle Scholar
  31. Efroimsky, M., Makarov, V.V.: ApJ 764, 26 (2013)ADSGoogle Scholar
  32. Eggleton, P.P., Kiseleva, L.G., Hut, P.: ApJ 499, 853 (1998)ADSGoogle Scholar
  33. Fabrycky, D.C., Lissauer, J.J., Ragozzine, D., et al.: ApJ 790, 146 (2014)ADSGoogle Scholar
  34. Fang, J., Margot, J.-L.: ApJ 761, 92 (2012)ADSGoogle Scholar
  35. Favier, B., Barker, A.J., Baruteau, C., Ogilvie, G.I.: MNRAS 439, 845 (2014)ADSGoogle Scholar
  36. Ferraz-Mello, S., Tadeu dos Santos, M., Folonier, H., et al.: ApJ 807, 78 (2015)ADSGoogle Scholar
  37. Gallet, F., Bouvier, J.: A&A 556, A36 (2013)ADSGoogle Scholar
  38. Gallet, F., Bouvier, J.: A&A 577, A98 (2015)ADSGoogle Scholar
  39. García, R.A., Ceillier, T., Salabert, D., et al.: A&A 572, A34 (2014)ADSGoogle Scholar
  40. Gizon, L., Ballot, J., Michel, E., et al.: Proc. Natl. Acad. Sci. 110, 13267 (2013)ADSGoogle Scholar
  41. Goodman, J., Dickson, E.S.: ApJ 507, 938 (1998)ADSGoogle Scholar
  42. Goodman, J., Lackner, C.: ApJ 696, 2054 (2009)ADSGoogle Scholar
  43. Guenel, M., Baruteau, C., Mathis, S., & Rieutord, M.: A&A 589, A22 (2016)Google Scholar
  44. Guenel, M., Mathis, S., Remus, F.: A&A 566, L9 (2014)ADSGoogle Scholar
  45. Guillot, T., Lin, D.N.C., Morel, P., Havel, M., Parmentier, V.: EAS Publications Series, vol. 65, pp. 327–336 (2014)Google Scholar
  46. Hansen, B.M.S.: ApJ 723, 285 (2010)ADSGoogle Scholar
  47. Hansen, B.M.S.: ApJ 757, 6 (2012)ADSGoogle Scholar
  48. Henning, W.G., O’Connell, R.J., Sasselov, D.D.: ApJ 707, 1000 (2009)ADSGoogle Scholar
  49. Henry, G.W., Marcy, G.W., Butler, R.P., Vogt, S.S.: ApJ 529, L41 (2000)ADSGoogle Scholar
  50. Husnoo, N., Pont, F., Mazeh, T., et al.: MNRAS 422, 3151 (2012)ADSGoogle Scholar
  51. Hut, P.: A&A 99, 126 (1981)ADSGoogle Scholar
  52. Irwin, J., Berta, Z.K., Burke, C.J., et al.: ApJ 727, 56 (2011)ADSGoogle Scholar
  53. Ivanov, P.B., Papaloizou, J.C.B., Chernov, S.V.: MNRAS 432, 2339 (2013)ADSGoogle Scholar
  54. Jackson, B., Greenberg, R., Barnes, R.: ApJ 681, 1631 (2008)ADSGoogle Scholar
  55. Kaula, W.M.: Rev. Geophys. Space Phys. 2, 661 (1964)ADSGoogle Scholar
  56. Kawaler, S.D.: ApJ 333, 236 (1988)ADSGoogle Scholar
  57. Lai, D.: MNRAS 423, 486 (2012)ADSGoogle Scholar
  58. Lanza, A.F.: A&A 512, A77 (2010)ADSGoogle Scholar
  59. Lanza, A.F., Shkolnik, E.L.: MNRAS 443, 1451 (2014)ADSGoogle Scholar
  60. Leconte, J., Chabrier, G., Baraffe, I., Levrard, B.: A&A 516, A64+ (2010)ADSGoogle Scholar
  61. MacGregor, K.B., Brenner, M.: ApJ 376, 204 (1991)ADSGoogle Scholar
  62. Maeder, A.: Physics, Formation and Evolution of Rotating Stars. Springer, Berlin (2009)Google Scholar
  63. 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)Google Scholar
  64. Mathis, S.: A&A 580, L3 (2015b)ADSGoogle Scholar
  65. Mathis, S., Zahn, J.-P.: A&A 425, 229 (2004)ADSGoogle Scholar
  66. Mathis, S., Le Poncin-Lafitte, C.: A&A 497, 889 (2009)ADSGoogle Scholar
  67. 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)Google Scholar
  68. Matt, S.P., Brun, A.S., Baraffe, I., Bouvier, J., Chabrier, G.: ApJ 799, L23 (2015)ADSGoogle Scholar
  69. Mayor, M., Queloz, D.: Nature 378, 355 (1995)ADSGoogle Scholar
  70. McQuillan, A., Mazeh, T., Aigrain, S.: ApJ 775, L11 (2013)ADSGoogle Scholar
  71. McQuillan, A., Mazeh, T., Aigrain, S.: ApJS 211, 24 (2014)ADSGoogle Scholar
  72. Mignard, F.: Moon Planets 20, 301 (1979)ADSGoogle Scholar
  73. Ogilvie, G.I.: MNRAS 429, 613 (2013)ADSGoogle Scholar
  74. Ogilvie, G.I.: ARA&A 52, 171 (2014)ADSGoogle Scholar
  75. Ogilvie, G.I., Lin, D.N.C.: ApJ 610, 477 (2004)ADSGoogle Scholar
  76. Ogilvie, G.I., Lin, D.N.C.: ApJ 661, 1180 (2007)ADSGoogle Scholar
  77. Paz-Chinchón, F., Leão, I.C., Bravo, J.P., et al.: ApJ 803, 69 (2015)ADSGoogle Scholar
  78. Penev, K., Zhang, M., Jackson, B.: PASP 126, 553 (2014)ADSGoogle Scholar
  79. Perryman, M.: The Exoplanet Handbook. Cambridge University Press (2011)Google Scholar
  80. Pont, F.: MNRAS 396, 1789 (2009)ADSGoogle Scholar
  81. Poppenhaeger, K., Wolk, S.J.: A&A 565, L1 (2014)ADSGoogle Scholar
  82. Rebull, L.M., Stauffer, J.R., Megeath, S.T., Hora, J.L., Hartmann, L.: ApJ 646, 297 (2006)ADSGoogle Scholar
  83. Rebull, L.M., Wolff, S.C., Strom, S.E.: Astron. J. 127, 1029 (2004)ADSGoogle Scholar
  84. Remus, F., Mathis, S., Zahn, J.-P.: A&A 544, A132 (2012a)ADSGoogle Scholar
  85. Remus, F., Mathis, S., Zahn, J.-P., Lainey, V.: A&A 541, A165 (2012b)ADSGoogle Scholar
  86. Réville, V., Brun, A.S., Matt, S.P., Strugarek, A., Pinto, R.F.: ApJ 798, 116 (2015)ADSGoogle Scholar
  87. Savonije, G.-J.: In: Goupil, M.-J., Zahn J.-P. (eds.) EAS Publications Series, vol. 29, pp. 91–125 (2008)Google Scholar
  88. Siess, L., Dufour, E., Forestini, M.: A&A 358, 593 (2000)ADSGoogle Scholar
  89. Skumanich, A.: ApJ 171, 565 (1972)ADSGoogle Scholar
  90. Teitler, S., Königl, A.: ApJ 786, 139 (2014)ADSGoogle Scholar
  91. Terquem, C., Papaloizou, J.C.B., Nelson, R.P., Lin, D.N.C.: ApJ 502, 788 (1998)ADSGoogle Scholar
  92. Tobie, G., Mocquet, A., Sotin, C.: Icarus 177, 534 (2005)ADSGoogle Scholar
  93. 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)Google Scholar
  94. Winn, J.N., Fabrycky, D., Albrecht, S., Johnson, J.A.: ApJ 718, L145 (2010)ADSGoogle Scholar
  95. Witte, M.G., Savonije, G.J.: A&A 350, 129 (1999)ADSGoogle Scholar
  96. Zahn, J.P.: Ann. Astrophys. 29, 489 (1966)ADSGoogle Scholar
  97. Zahn, J.-P.: A&A 41, 329 (1975)ADSGoogle Scholar
  98. Zahn, J.-P.: A&A 57, 383 (1977)ADSGoogle Scholar
  99. Zahn, J.-P.: A&A 220, 112 (1989)ADSGoogle Scholar
  100. Zahn, J.-P., Bouchet, L.: A&A 223, 112 (1989)ADSGoogle Scholar
  101. Zahn, J.-P.: A&A 265, 115 (1992)ADSGoogle Scholar
  102. Zahn, J.-P.: A&A 288, 829 (1994)ADSGoogle Scholar

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.NaXys, Department of MathematicsUniversity of NamurNamurBelgium
  2. 2.Laboratoire AIM Paris-SaclayCEA/DRF - CNRS - Univ. Paris Diderot - IRFU/SAp, Centre de SaclayGif-sur-Yvette CedexFrance

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