Skip to main content
SpringerLink
Log in

The Role in Sculpting Exoplanetary Systems

  • Chapter
  • First Online:
The Lidov-Kozai Effect - Applications in Exoplanet Research and Dynamical Astronomy

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 441))

  • 901 Accesses

Abstract

In this chapter, it is discussed how the Lidov-Kozai theory has been extended and refined as an important constituent of the new exoplanetary studies. Various phenomena induced by the Lidov-Kozai effect (in particular, the orbital flips from prograde to retrograde orbits and vice versa) in exoplanetary systems are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A planetary system is called multiplanet if it contains more than one planet.

  2. 2.

    This rapid growth has been mostly due to the success of the Kepler space observatory mission.

  3. 3.

    For a description of methods for the discovery of exoplanets, see, e.g., Ferraz-Mello et al. 2005.

  4. 4.

    The essence of the Rossiter–McLaughlin effect is as follows. A planet transiting a rotating star affects the measured radial velocity of the star differently at different phases of the transit, because the eclipsed disk on the star’s disk corresponds to different local radial velocities of the star’s surface. The Rossiter–McLaughlin effect allows one to estimate the angle between the star’s equatorial plane (the plane orthogonal to the rotation axis of the star) and the planet’s orbital plane.

  5. 5.

    Note that this is a third averaging of the original equations of motion, because the secular equations are derived by double averaging of the original equations (over the orbital periods of the particle and the perturber).

References

  • Albrecht, S., Winn, J. N., Johnson, J. A., Howard, A. W., Marcy, G. W., Butler, R. P., et al. (2012) “Obliquities of hot jupiter host stars: evidence for tidal interactions and primordial misalignments.” Astrophys. J., 757, 18 (25pp)

    Article  ADS  Google Scholar 

  • Batygin, K., Laughlin, G., Meschiari, S., Rivera, E., Vogt, S., & Butler, P. (2009) “A quasi-stationary solution to Gliese 436b’s eccentricity.” Astrophys. J., 699, 23–30

    Article  ADS  Google Scholar 

  • Batygin, K., Morbidelli, A., & Tsiganis, K. (2011) “Formation and evolution of planetary systems in presence of highly inclined stellar perturbers.” Astron. Astrophys., 533, A7 (8pp)

    Article  ADS  MATH  Google Scholar 

  • Benest, D. (1988a) “Planetary orbits in the elliptic restricted problem I. The α Centauri system.” Astron. Astrophys., 206, 143–146

    ADS  Google Scholar 

  • Benest, D. (1988b) “Stable planetary orbits around one component in nearby binary stars.” Celest. Mech., 43, 47–53

    Article  ADS  Google Scholar 

  • Benest, D. (1989) “Planetary orbits in the elliptic restricted problem II. The Sirius system.” Astron. Astrophys., 223, 361–364

    ADS  MATH  Google Scholar 

  • Beust, H., & Dutrey, A. (2006) “Dynamics of the young multiple system GG Tauri. II. Relation between the stellar system and the circumbinary disk.” Astron. Astrophys., 446, 137–154

    Article  ADS  Google Scholar 

  • Bodenheimer, P., Hubickyj, O., & Lissauer, J. J. (2000) “Models of the in situ formation of detected extrasolar giant planets.” Icarus, 143, 2–14

    Article  ADS  Google Scholar 

  • Chirikov, B. V. (1979) “A universal instability of many-dimensional oscillator systems.” Phys. Rep., 52, 263–379

    Article  ADS  MathSciNet  Google Scholar 

  • Cochran, W. D., Hatzes, A., Butler, R. P., & Marcy, G. W. (1997) “The discovery of a planetary companion to 16 Cygni B.” Astrophys. J., 483, 457–463

    Article  ADS  Google Scholar 

  • Correia, A. C. M., Boué, G., Laskar, J., & Morais, M. H. M. (2013) “Tidal damping of the mutual inclination in hierarchical systems.” Astron. Astrophys., 553, A39 (15pp)

    Article  ADS  Google Scholar 

  • Davies, M. B., Adams, F. C., Armitage, P., Chambers, J., Ford, E., Morbidelli, A., Raymond, S. N., & Veras, D. (2014) “The long-term dynamical evolution of planetary systems.” In: Protostars and Planets VI, ed. by Beuther, H., Klessen, R. S., Dullemond, C. P., & Henning, T. (University of Arizona Press, Tucson) pp. 787–808

    Google Scholar 

  • Demidova, T. V., & Shevchenko, I. I. (2015) “Spiral patterns in planetesimal circumbinary disks.” Astrophys. J., 805, 38 (8pp)

    Article  ADS  Google Scholar 

  • Devaney, R. (1986) An Introduction to Chaotic Dynamical Systems (Benjamin/Cummings, Menlo Park)

    MATH  Google Scholar 

  • Doyle, L. R., Carter, J. A., Fabrycky, D. C., et al. (2011) “Kepler-16: a transiting circumbinary planet.” Science, 333, 1602–1606

    Article  ADS  Google Scholar 

  • Dumusque, X., Pepe, F., Lovis, C., et al. (2012) “An Earth-mass planet orbiting α Centauri B.” Nature, 491, 207–211

    Article  ADS  Google Scholar 

  • Duquennoy, A., & Mayor, M. (1991) “Multiplicity among solar-type stars in the solar neighbourhood. II — Distribution of the orbital elements in an unbiased sample.” Astron. Astrophys., 248, 485–524

    ADS  Google Scholar 

  • Fabrycky, D., & Tremaine, S. (2007) “Shrinking binary and planetary orbits by Kozai cycles with tidal friction.” Astrophys. J., 669, 1298–1315

    Article  ADS  Google Scholar 

  • Fang, J., & Margot, J.-L. (2012) “The role of Kozai cycles in near-Earth binary asteroids.” Astron. J., 143, 59 (8pp)

    Article  ADS  Google Scholar 

  • Ferraz-Mello, S., Michtchenko, T., Beaugé, C., & Callegari, N. Jr. (2005) “Extrasolar planetary systems.” In: Chaos and Stability in Planetary Systems, ed. by Dvorak, R., Freistetter, F., & Kurths, J. (Lect. Notes Phys., v. 683) (Springer, Heidelberg) pp. 219–271

    Google Scholar 

  • Ford, E. B., Kozinsky, B., & Rasio, F. A. (2000) “Secular evolution of hierarchical triple star systems.” Astrophys. J., 535, 385–401

    Article  ADS  Google Scholar 

  • Fragner, M. M., Nelson, R. P., & Kley, W. (2011) “On the dynamics and collisional growth of planetesimals in misaligned binary systems.” Astron. Astrophys., 528, A40 (21pp)

    Article  ADS  Google Scholar 

  • Froeschlé, Cl. (1984) “The Lyapunov characteristic exponents — applications to celestial mechanics.” Celest. Mech., 34, 95–115

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Greenberg, R., & Van Laerhoven, C. (2012) “Aligned major axes in a planetary system without tidal evolution: The 61 Virginis example.” Mon. Not. R. Astron. Soc., 419, 429–435

    Article  ADS  Google Scholar 

  • Haghighipour, N., Dvorak, R., & Pilat-Lohinger, E. (2010) “Planetary dynamics and habitable planet formation in binary star systems.” In: Planets in Binary Star Systems, ed. by Haghighipour, N. (Springer, Dordrecht) pp. 285–327

    Google Scholar 

  • Hauser, H. M., & Marcy, G. W. (1999) “The orbit of 16 Cygni AB.” Publ. Astron. Soc. Pacific, 111, 321–334

    Article  ADS  Google Scholar 

  • Hayes, W. B. (2007) “Is the outer Solar System chaotic?” Nature Phys., 3, 689–691

    Article  ADS  Google Scholar 

  • Hayes, W. B. (2008) “Surfing on the edge: chaos versus near-integrability in the system of Jovian planets.” Mon. Not. R. Astron. Soc., 386, 295–306

    Article  ADS  Google Scholar 

  • Hayes, W. B., Malykh, A. V., & Danforth, C. M. (2010) “The interplay of chaos between the terrestrial and giant planets.” Mon. Not. R. Astron. Soc., 407, 1859–1865

    Article  ADS  Google Scholar 

  • Heppenheimer, T. A. (1978) “On the formation of planets in binary star systems.” Astron. Astrophys., 65, 421–426

    ADS  Google Scholar 

  • Holman, M. J., & Murray, N. W. (1996) “Chaos in high-order mean motion resonances in the outer asteroid belt.” Astron. J., 112, 1278–1293

    Article  ADS  Google Scholar 

  • Holman, M., Touma, J., & Tremaine, S. (1997) “Chaotic variations in the eccentricity of the planet orbiting 16 Cygni B.” Nature, 386, 254–256

    Article  ADS  Google Scholar 

  • Huang, S.-S. (1960) “Life-supporting regions in the vicinity of binary systems.” Publ. Astron. Soc. Pacific, 72, 106–114

    Article  ADS  Google Scholar 

  • Innanen, K. A., Zheng, J. Q., Mikkola, S., & Valtonen, M. J. (1997) “The Kozai mechanism and the stability of planetary orbits in binary star systems.” Astron. J., 113, 1915–1919

    Article  ADS  Google Scholar 

  • Ivanov, P. B., & Papaloizou, J. C. B. (2004) “On the tidal interaction of massive extra solar planets on highly eccentric orbits.” Mon. Not. R. Astron. Soc., 347, 437–453

    Article  ADS  Google Scholar 

  • Ivanov, P. B., & Papaloizou, J. C. B. (2011) “Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of hot Jupiters.” Celest. Mech. Dyn. Astron., 111, 51–82

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Katz, B., Dong, S., & Malhotra, R. (2011) “Long-term cycling of Kozai–Lidov cycles: Extreme eccentricities and inclinations excited by a distant eccentric perturber.” Phys. Rev. Lett., 107, 181101 (5pp)

    Article  ADS  Google Scholar 

  • Kiseleva, L. G., Eggleton, P. P., & Mikkola, S. (1998) “Tidal friction in triple stars.” Mon. Not. R. Astron. Soc., 300, 292–392

    Article  ADS  Google Scholar 

  • Laskar, J. (1989) “A numerical experiment on the chaotic behaviour of the Solar system.” Nature, 338, 237–238

    Article  ADS  Google Scholar 

  • Laskar, J. (1994) “Large-scale chaos in the solar system.” Astron. Astrophys., 287, L9–L12

    ADS  Google Scholar 

  • Lee, M. H., & Peale, S. (2003) “Secular evolution of hierarchical planetary systems.” Astrophys. J., 592, 1201–1216 [Erratum: (2003) Astrophys. J., 597, 644 (1p)]

    Google Scholar 

  • Li, G., Naoz, S., Kocsis, B., & Loeb, A. (2014a) “Eccentricity growth and orbit flip in near-coplanar hierarchical three-body systems.” Astrophys. J., 785, 116 (8pp)

    Article  ADS  Google Scholar 

  • Li, G., Naoz, S., Holman, M., & Loeb, A. (2014b) “Chaos in the test particle eccentric Kozai–Lidov mechanism.” Astrophys. J., 791, 86 (10pp) [Erratum: (2015) Astrophys. J., 802, 71 (1p)]

    Google Scholar 

  • Libert, A.-S., & Henrard, J. (2007) “Exoplanetary systems: The role of an equilibrium at high mutual inclination in shaping the global behavior of the 3-D secular planetary three-body problem.” Icarus, 191, 469–485

    Article  ADS  Google Scholar 

  • Lichtenberg, A. J., & Lieberman, M. A. (1992) Regular and Chaotic Dynamics. 2nd edition (Springer-Verlag, New York)

    Book  MATH  Google Scholar 

  • Lithwick, Y., & Naoz, S. (2011) “The eccentric Kozai mechanism for a test particle.” Astrophys. J., 742, 94 (8pp)

    Article  ADS  Google Scholar 

  • Lovis, C., Ségransan, D., Mayor, M., Udry, S., Benz, W., Bertaux, J.-L., Bouchy, F., Correia, A. C. M., Laskar, J., Lo Curto, G., Mordasini, C., Pepe, F., Queloz, D., & Santos, N. C. (2011) “The HARPS search for southern extra-solar planets. XXVIII. Up to seven planets orbiting HD 10180: probing the architecture of low-mass planetary systems.” Astron. Astrophys., 528, A112 (16pp)

    Google Scholar 

  • Malmberg, D., Davies, M. B., & Chambers, J. E. (2007) “The instability of planetary systems in binaries: how the Kozai mechanism leads to strong planet-planet interactions.” Mon. Not. R. Astron. Soc., 377, L1–L4

    Article  ADS  Google Scholar 

  • Marchal, C. (1990) The Three-Body Problem (Elsevier, Amsterdam)

    MATH  Google Scholar 

  • Marzari, F., & Barbieri, M. (2007) “Planet dispersal in binary systems during transient multiple star phases.” Astron. Astrophys., 472, 643–647

    Article  ADS  Google Scholar 

  • Mathieu, R. D., Ghez, A. M., Jensen, E. L. N., & Simon, M. (2000) “Young binary stars and associated disks.” In: Protostars and Planets IV (Univ. Arizona Press, Tucson) pp. 703–730

    Google Scholar 

  • Mayor, M., & Queloz, D. (1995) “A Jupiter-mass companion to a solar-type star.” Nature, 378, 355–359

    Article  ADS  Google Scholar 

  • Mazeh, T., & Shaham, J. (1979) “The orbital evolution of close triple systems — the binary eccentricity.” Astron. Astrophys., 77, 145–151

    ADS  Google Scholar 

  • Mazeh, T., Krymolowski, Y., & Rosenfeld, G. (1997) “The high eccentricity of the planet orbiting 16 Cygni B.” Astrophys. J., 477, L103–L106

    Article  ADS  Google Scholar 

  • Meiss, J.D. (1992) “Symplectic maps, variational principles, and transport.” Rev. Mod. Phys., 64, 795–848

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Melnikov, A. V. (2016) “On the chaotic orbital dynamics of the planet in the system 16 Cyg.” Astron. Lett., 42, 115–125

    Article  ADS  Google Scholar 

  • Meschiari, S. (2012a) “Circumbinary planet formation in the Kepler-16 system. I. N-body simulations.” Astrophys. J., 752, 71 (6pp)

    Google Scholar 

  • Meschiari, S. (2012b) “Planet formation in circumbinary configurations: Turbulence inhibits planetesimal accretion.” Astrophys. J., 761, L7 (5pp)

    Article  ADS  Google Scholar 

  • Meschiari, S. (2014) “Circumbinary planet formation in the Kepler-16 system. II. A toy model for in-situ planet formation within a debris belt.” Astrophys. J., 790, 41 (14pp)

    Google Scholar 

  • Moriwaki, K., & Nakagawa, Y. (2004) “A planetesimal accretion zone in a circumbinary disk.” Astrophys. J., 609, 1065–1070

    Article  ADS  Google Scholar 

  • Murray, N. W., & Holman, M. J. (1997) “Diffusive chaos in the outer asteroid belt.” Astron. J., 114, 1246–1259

    Article  ADS  Google Scholar 

  • Murray, N., & Holman, M. (1999) “The origin of chaos in the outer Solar system.” Science, 283, 1877–1881

    Article  ADS  Google Scholar 

  • Nagasawa, M., Ida, S., & Bessho, T. (2008) “Formation of hot planets by a combination of planet scattering, tidal circularization, and the Kozai mechanism.” Astrophys. J., 678, 498–508

    Article  ADS  Google Scholar 

  • Naoz, S., Farr, W. M., & Rasio, F. A. (2012) “On the formation of hot Jupiters in stellar binaries.” Astrophys. J., 754, L36 (6pp)

    Article  ADS  Google Scholar 

  • Naoz, S., Perets, H. B., & Ragozzine, D. (2010) “The observed orbital properties of binary minor planets.” Astrophys. J., 719, 1775–1783

    Article  ADS  Google Scholar 

  • Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J. (2011) “Hot Jupiters from secular planet-planet interactions.” Nature, 473, 187–189

    Article  ADS  Google Scholar 

  • Orosz, J. A., Welsh, W. F., Carter, J. A., Fabrycky, D. C., Cochran, W. D., et al. (2012) “Kepler-47: a transiting circumbinary multiplanet system.” Science, 337, 1511–1514

    Article  ADS  Google Scholar 

  • Paardekooper, S.-J., Leinhardt, Z. M., Thébault, T., & Baruteau, C. (2012) “How not to build Tatooine: the difficulty of in situ formation of circumbinary planets Kepler 16b, Kepler 34b, and Kepler 35b.” Astrophys. J., 754, L16 (5pp)

    Article  ADS  Google Scholar 

  • Perets, H. B., & Naoz, S. (2009) “Kozai cycles, tidal friction, and the dynamical evolution of binary minor planets.” Astrophys. J., 699, L17–L21

    Article  ADS  Google Scholar 

  • Rein, H. (2012) “Period ratios in multiplanetary systems discovered by Kepler are consistent with planet migration.” Mon. Not. R. Astron. Soc., 427, L21–L24

    ADS  Google Scholar 

  • Sahu, K. C., Casertano, S., Bond, H. E., et al. (2006) “Transiting extrasolar planetary candidates in the Galactic bulge.” Nature, 443, 534–540

    Article  ADS  Google Scholar 

  • Shappee, B. J., & Thompson, T. A. (2013) “The mass-loss-induced eccentric Kozai mechanism: a new channel for the production of close compact object–stellar binaries.” Astrophys. J., 766, 64 (12pp)

    Article  ADS  Google Scholar 

  • Shevchenko, I. I. (2000) “Geometry of a chaotic layer.” J. Exp. Theor. Phys., 91, 615–625

    Article  ADS  Google Scholar 

  • Shevchenko, I. I. (2002) “On the maximum Lyapunov exponents of the chaotic rotation of natural planetary satellites.” Cosmic Research, 40, 296

    Article  ADS  Google Scholar 

  • Shevchenko, I. I. (2007) “On the Lyapunov exponents of the asteroidal motion subject to resonances and encounters.” In: Near Earth Objects, our Celestial Neighbors: Opportunity and Risk (Proc. IAU Symp. 236), ed. by Milani, A., Valsecchi, G. B., & Vokrouhlický, D. (Cambridge Univ. Press, Cambridge) pp. 15–29

    Google Scholar 

  • Shevchenko, I. I. (2011a) “Lyapunov and diffusion timescales in the solar neighborhood.” Astrophys. J., 733, 39 (8pp)

    Article  ADS  Google Scholar 

  • Shevchenko, I. I. (2014) “Lyapunov exponents in resonance multiplets.” Phys. Lett. A, 378, 34–42

    Article  ADS  MathSciNet  Google Scholar 

  • Shevchenko, I. I. (2015) “Chaotic zones around gravitating binaries.” Astrophys. J., 799, 8 (7pp)

    Article  ADS  Google Scholar 

  • Soter, S. (2006) “What is a planet?” Astron. J., 132, 2513–2519

    Article  ADS  Google Scholar 

  • Stern, S. A., & Levison, H. F. (2002) “Regarding the criteria for planethood and proposed planetary classification schemes.” Highlights of Astronomy, 12, 205–213

    Article  ADS  Google Scholar 

  • Steffen, J. H., et al. (2012) “Kepler constraints on planets near hot Jupiters.” Proceedings of the National Academy of Science, 109, 7982–7987

    Google Scholar 

  • Sussman, G.J., & Wisdom, J. (1988) “Numerical evidence that Pluto is chaotic.” Science, 241, 433–437

    Article  ADS  Google Scholar 

  • Sussman, G. J., & Wisdom, J. (1992) “Chaotic evolution of the solar system.” Science, 257, 56–62

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Takeda, G., & Rasio, F. A. (2005) “High orbital eccentricities of extrasolar planets induced by the Kozai mechanism.” Astrophys. J., 627, 1001–1010

    Article  ADS  Google Scholar 

  • Thébault, P., Marzari, F., Scholl, H. (2006) “Relative velocities among accreting planetesimals in binary systems: The circumprimary case.” Icarus, 183, 193–206

    Article  ADS  Google Scholar 

  • Van Laerhoven, C., & Greenberg, R. (2012) “Characterizing multi-planet systems with classical secular theory.” Celest. Mech. Dyn. Astron., 113, 215–234

    Article  ADS  Google Scholar 

  • Welsh, W. F., Orosz, J. A., Carter, J. A., Fabrycky, D. C., Ford, E. B., et al. (2012) “Transiting circumbinary planets Kepler-34b and Kepler-35b.” Nature, 481, 475–479

    Article  ADS  Google Scholar 

  • Whitmire, D., Matese, J., Criswell, L., & Mikkola, S. (1998) “Habitable planet formation in binary star systems.” Icarus, 132, 196–203

    Article  ADS  Google Scholar 

  • Winn, J. N., Fabrycky, D., Albrecht, S., & Johnson, J. A. (2010) “Hot stars with hot Jupiters have high obliquities.” Astrophys. J., 718, L145–L149

    Article  ADS  Google Scholar 

  • Winn, J. N., Johnson, J. A., Albrecht, S., Howard, A. W., Marcy, G. W., Crossfield, I. J., et al. (2009) “HAT-P-7: a retrograde or polar orbit, and a third body.” Astrophys. J., 703, L99–L103

    Article  ADS  Google Scholar 

  • Wright, J. T., Fakhouri, O., Marcy, G. W., Han, E., Feng, Y., Johnson, J. A., Howard, A. W., Fischer, D. A., Valenti, J. A., Anderson, J., & Piskunov, N. (2011) “The exoplanet orbit database.” Publ. Astron. Soc. Pacific, 123, 412–422

    Article  ADS  Google Scholar 

  • Wu, Y., & Murray, N. (2003) “Planet migration and binary companions: The case of HD 80606b.” Astrophys. J., 589, 605–614

    Article  ADS  Google Scholar 

  • Wu, Y., Murray, N. W., & Ramsahai, J. M. (2007) “Hot Jupiters in binary star systems.” Astrophys. J., 670, 820–825

    Article  ADS  Google Scholar 

  • Xie, J.-W., Payne, M. J., Thébault, P., Zhou, J.-L., & Ge, J. (2011) “Planet formation in highly inclined binary systems. I. Planetesimals jump inward and pile up.” Astrophys. J., 735, 10 (18pp)

    Google Scholar 

  • Zapatero Osorio, M. R., Béjar, V. J. S., Martín, E. L., Rebolo, R., Barrado y Navascués, D., Bailer-Jones, C. A. L., & Mundt, R. (2000) “Discovery of young, isolated planetary mass objects in the σ Orionis star cluster.” Science, 290, 103–107

    Google Scholar 

  • Zinnecker, H. (2001) “A free-floating planet population in the Galaxy?” In: ASP Conf. Series, 239, 223–228

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pulkovo Observatory of the Russian Academy of Sciences, St. Petersburg, Russia

    Ivan I. Shevchenko

Authors
  1. Ivan I. Shevchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Shevchenko, I.I. (2017). The Role in Sculpting Exoplanetary Systems. In: The Lidov-Kozai Effect - Applications in Exoplanet Research and Dynamical Astronomy. Astrophysics and Space Science Library, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-43522-0_8

Download citation

Publish with us

Policies and ethics

Search

Navigation