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The Lidov-Kozai resonance at different scales

Published online by Cambridge University Press:  30 May 2022

Anne-Sophie Libert Open the ORCID record for Anne-Sophie Libert [Opens in a new window]
Anne-Sophie Libert*
Affiliation:
naXys, Department of Mathematics, University of Namur, 61 Rue de Bruxelles, 5000 Namur, Belgium email: anne-sophie.libert@unamur.be
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Abstract

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The Lidov-Kozai (LK) resonance is one of the most widely discussed topics since the discovery of exoplanets in eccentric orbits. It constitutes a secular protection mechanism for systems with high mutual inclinations, although large variations in eccentricity and inclination are observed. This review aims to illustrate how the LK resonance influences the dynamics of the three-body problem at different scales, namely i) for two-planet extrasolar systems where the orbital variations occur in a coherent way such that the system remains stable, ii) for inclined planets in protoplanetary discs where the LK cycles are produced by the gravitational force exerted by the disc on the planet, iii) for migrating planets in binary star systems, whose dynamical evolution is strongly affected by the LK resonance even without experiencing a resonance capture, and iv) for triple-star systems for which the migration through LK cycles combined with tidal friction is a possible explanation for the short-period pile-up observed in the distribution of multiple stars.

Keywords

Celestial mechanicsplanetary systemsplanetary systems: formationplanetary systems: protoplanetary discsplanets and satellites: dynamical evolution and stabilitybinaries: closestars: kinematics and dynamicsstars: formation
Type
Research Article
Information
Proceedings of the International Astronomical Union , Volume 15 , Symposium S364: Multi-scale (Time and Mass) Dynamics of Space Objects (Oct 2021) , October 2019 , pp. 52 - 64
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of International Astronomical Union

References

Albrecht, S., Winn, J. N., Johnson, J. A., Howard, A. W., Marcy, G. W., Butler, R. P., Arriagada, P., Crane, J. D., Shectman, S. A., Thompson, I. B., Hirano, T., Bakos, G., & Hartman, J. D. 2012, ApJ, 757(1), 18.CrossRefGoogle Scholar
Anderson, K. R., Lai, D., & Storch, N. I. 2017, Monthly Notices of the Royal Astronomical Society, 467, 3066–3082.CrossRefGoogle Scholar
Anderson, K. R., Storch, N. I., & Lai, D. 2016, MNRAS, 456(4), 3671–3701.CrossRefGoogle Scholar
Bailey, M. E. 1992, Celestial Mechanics and Dynamical Astronomy, 54(1-3), 49–61.CrossRefGoogle Scholar
Bataille, M., Libert, A.-S., & Correia, A. C. M. 2018, Monthly Notices of the Royal Astronomical Society, 479(4), 4749–4759.CrossRefGoogle Scholar
Batygin, K., Morbidelli, A., & Tsiganis, K. 2011, A&A, 533, A7.Google Scholar
Bitsch, B., Crida, A., Libert, A. S., & Lega, E. 2013, A&A, 555, A124.Google Scholar
Carruba, V., Burns, J. A., Nicholson, P. D., & Gladman, B. J. 2002, Icarus, 158(2), 434–449.CrossRefGoogle Scholar
Cincotta, P. M., Giordano, C. M., & Simó, C. 2003, Physica D Nonlinear Phenomena, 182(3–4), 151–178.CrossRefGoogle Scholar
Correia, A. C. M., Boué, G., & Laskar, J. 2016, Celestial Mechanics and Dynamical Astronomy, 126, 189–225.CrossRefGoogle Scholar
Deitrick, R., Barnes, R., McArthur, B., Quinn, T. R., Luger, R., Antonsen, A., & Benedict, G. F. 2015, ApJ, 798(1), 46.CrossRefGoogle Scholar
Duquennoy, A. & Mayor, M. 1991, A&A, 248, 485–524.Google Scholar
Eggleton, P. P. & Kiseleva-Eggleton, L. 2001, The Astrophysical Journal, 562, 1012–1030.CrossRefGoogle Scholar
Fabrycky, D. & Tremaine, S. 2007, ApJ, 669(2), 1298–1315.CrossRefGoogle Scholar
Ford, E. B., Kozinsky, B., & Rasio, F. A. 2000, ApJ, 535(1), 385–401.CrossRefGoogle Scholar
Gallardo, T., Hugo, G., & Pais, P. 2012, Icarus, 220(2), 392–403.CrossRefGoogle Scholar
Innanen, K. A., Zheng, J. Q., Mikkola, S., & Valtonen, M. J. 1997, AJ, 113, 1915.CrossRefGoogle Scholar
Ito, T. & Ohtsuka, K. 2019, Monographs on Environment, Earth and Planets, 7(1), 1–113.CrossRefGoogle Scholar
Jacobi, M. 1842, Astronomische Nachrichten, 20(6), 81.CrossRefGoogle Scholar
Kinoshita, H. & Nakai, H. 1999, Celestial Mechanics and Dynamical Astronomy, 75(2), 125–147.CrossRefGoogle Scholar
Kozai, Y. 1962, AJ, 67, 591.CrossRefGoogle Scholar
Kozai, Y. 1985, Celestial Mechanics, 36(1), 47–69.CrossRefGoogle Scholar
Laskar, J. 1997, A&A, 317, L75–L78.Google Scholar
Lee, M. H. & Peale, S. J. 2003, ApJ, 592(2), 1201–1216.CrossRefGoogle Scholar
Libert, A.-S. & Henrard, J. 2007, Icarus, 191(2), 469–485.CrossRefGoogle Scholar
Libert, A.-S. & Tsiganis, K. 2009, A&A, 493(2), 677–686.Google Scholar
Lidov, M. L. 1962, Planetary Space Science, 9, 719–759.CrossRefGoogle Scholar
Liu, B., Mu noz, D. J., & Lai, D. 2015, Monthly Notices of the Royal Astronomical Society, 447, 747–764.CrossRefGoogle Scholar
Michel, P. & Thomas, F. 1996, A&A, 307, 310.Google Scholar
Michtchenko, T. A., Ferraz-Mello, S., & Beaugé, C. 2006, Icarus, 181(2), 555–571.CrossRefGoogle Scholar
Migaszewski, C. & Goździewski, K. 2009, MNRAS, 395(4), 1777–1794.CrossRefGoogle Scholar
Moe, M. & Kratter, K. M. 2018, ApJ, 854(1), 44.CrossRefGoogle Scholar
Naoz, S. 2016, ARAA, 54, 441–489.CrossRefGoogle Scholar
Naoz, S. & Fabrycky, D. C. 2014, The Astrophysical Journal, 793, 137.CrossRefGoogle Scholar
Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J. 2011, Nature, 473(7346), 187–189.CrossRefGoogle Scholar
Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J. 2013, MNRAS, 431(3), 2155–2171.CrossRefGoogle Scholar
Nesvorný, D., Alvarellos, J. L. A., Dones, L., & Levison, H. F. 2003, AJ, 126(1), 398–429.CrossRefGoogle Scholar
Petrovich, C. 2015, ApJ, 799(1), 27.CrossRefGoogle Scholar
Poincaré, H. 1892, Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars et fils.Google Scholar
Quinn, T., Tremaine, S., & Duncan, M. 1990, ApJ, 355, 667.CrossRefGoogle Scholar
Raghavan, D., McAlister, H. A., Henry, T. J., Latham, D. W., Marcy, G. W., Mason, B. D., Gies, D. R., White, R. J., & ten Brummelaar, T. A. 2010, The Astrophysical Journal Supplement, 190, 1–42.CrossRefGoogle Scholar
Roisin, A. & Libert, A. S. 2021, A&A, 645, A138.Google Scholar
Roisin, A., Teyssandier, J., & Libert, A.-S. 2021, MNRAS, 506(4), 5005–5014.CrossRefGoogle Scholar
Sansottera, M., Grassi, L., & Giorgilli, A. On the relativistic Lagrange-Laplace secular dynamics for extrasolar systems. In Complex Planetary Systems, Proceedings of the International Astronomical Union 2014, volume 310, pp. 74–77.CrossRefGoogle Scholar
Sansottera, M. & Libert, A. S. 2019, Celestial Mechanics and Dynamical Astronomy, 131(8), 38.CrossRefGoogle Scholar
Schwarz, R., Funk, B., Zechner, R., & Bazsó, Á. 2016, MNRAS, 460(4), 3598–3609.CrossRefGoogle Scholar
Terquem, C. & Ajmia, A. 2010, MNRAS, 404(1), 409–414.Google Scholar
Teyssandier, J., Terquem, C., & Papaloizou, J. C. B. 2013, MNRAS, 428(1), 658–669.CrossRefGoogle Scholar
Thébault, P. & Haghighipour, N. 2015, Planet Formation in Binaries, pp. 309–340. Springer.Google Scholar
Thomas, F. & Morbidelli, A. 1996, Celestial Mechanics and Dynamical Astronomy, 64(3), 209–229.CrossRefGoogle Scholar
Tokovinin, A. 2014, AJ, 147, 87.CrossRefGoogle Scholar
Toonen, S., Hamers, A., & Portegies Zwart, S. 2016, Computational Astrophysics and Cosmology, 3, 6.CrossRefGoogle Scholar
Tuomi, M. & Kotiranta, S. 2009, A&A, 496(2), L13–L16.Google Scholar
Veras, D. & Ford, E. B. 2010, ApJ, 715(2), 803–822.CrossRefGoogle Scholar
Volpi, M., Roisin, A., & Libert, A.-S. 2019, A&A, 626, A74.Google Scholar
von Zeipel, H. 1910, Astronomische Nachrichten, 183(22), 345.CrossRefGoogle Scholar
Wittenmyer, R. A., Wang, S., Horner, J., Tinney, C. G., Butler, R. P., Jones, H. R. A., O’Toole, S. J., Bailey, J., Carter, B. D., Salter, G. S., Wright, D., & Zhou, J.-L. 2013, The Astrophysical Journal Supplement, 208(1), 2.CrossRefGoogle Scholar
Wu, Y. & Murray, N. 2003, ApJ, 589(1), 605–614.CrossRefGoogle Scholar
Wu, Y., Murray, N. W., & Ramsahai, J. M. 2007, ApJ, 670(1), 820–825.CrossRefGoogle Scholar
Xiang-Gruess, M. & Papaloizou, J. C. B. 2013, MNRAS, 431(2), 1320–1336.CrossRefGoogle Scholar
Zanazzi, J. J. & Lai, D. 2018, MNRAS, 478(1), 835–851.CrossRefGoogle Scholar