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On the stability of circumbinary planetary systems

Abstract

The dynamics of circumbinary planetary systems (the systems in which the planets orbit a central binary) with a small binary mass ratio discovered to date is considered. The domains of chaotic motion have been revealed in the “pericentric distance–eccentricity” plane of initial conditions for the planetary orbits through numerical experiments. Based on an analytical criterion for the chaoticity of planetary orbits in binary star systems, we have constructed theoretical curves that describe the global boundary of the chaotic zone around the central binary for each of the systems. In addition, based on Mardling’s theory describing the separate resonance “teeth” (corresponding to integer resonances between the orbital periods of a planet and the binary), we have constructed the local boundaries of chaos. Both theoretical models are shown to describe adequately the boundaries of chaos on the numerically constructed stability diagrams, suggesting that these theories are efficient in providing analytical criteria for the chaoticity of planetary orbits.

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References

  1. D. Benest, Astron. Astrophys. 206, 143 (1988).

    ADS  Google Scholar 

  2. D. Benest, Astron. Astrophys. 223, 361 (1989).

    ADS  Google Scholar 

  3. D. Benest and R. Gonczi, Earth, Moon, Planets 81, 7 (1998).

    ADS  Article  Google Scholar 

  4. D. Benest and R. Gonczi, Earth, Moon Planets 93, 175 (2004).

    ADS  Article  Google Scholar 

  5. S. Chavez, N. Georgakarakos, S. Prodan, M. Reyes-Ruiz, H. Aceves, F. Betancourt, and E. Perez-Tijerina, Mon. Not. R. Astron. Soc. 446, 1283 (2015).

    ADS  Article  Google Scholar 

  6. B. V. Chirikov, Phys. Rep. 52, 263 (1979).

    ADS  MathSciNet  Article  Google Scholar 

  7. L. Doyle, J. Carter, D. Fabrycky, R. W. Slawson, S. B. Howell, J. N. Winn, J. A. Orosz, A. Prsa, et al., Science 333, 1602 (2011).

    ADS  Article  Google Scholar 

  8. M. J. Holman and P. A. Wiegert, Astron. J. 117, 621 (1999).

    ADS  Article  Google Scholar 

  9. Su-Shu Huang, Publ. Astron. Soc. Pacif. 72, 106 (1960).

    ADS  Article  Google Scholar 

  10. V. Kostov, P. R. McCullough, T. C. Hinse, Z. I. Tsvetanov, G. Hébrard, R. F. Díaz, M. Deleuil, and J. A. Valenti, Astrophys. J. 770, 52 (2013).

    ADS  Article  Google Scholar 

  11. V. Kostov, P. R. McCullough, J. A. Carter, M. Deleuil, R. F. Díaz, D. C. Fabrycky, G. Hébrard, T. C. Hinse, et al., Astron. J. 784, 14 (2014).

    ADS  Article  Google Scholar 

  12. A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics (Springer, New York, 1992).

    Book  MATH  Google Scholar 

  13. J. Lissauer, E. Quintana, J. Chambers, M. J. Duncan, and F. C. Adams, Rev.Mex. Astron.Astrophys. 22, 99 (2004).

    ADS  Google Scholar 

  14. R. Mardling, Lect. Notes Phys. 760, 59 (2008a).

    ADS  MathSciNet  Article  Google Scholar 

  15. R. Mardling, in Proceedings of the IAU Symposium No. 246 on Dynamical Evolution of Dense Stellar Systems, Capri, Italy, Sept. 5–9, 2007, Ed. by E. Vesperini, M. Giersz, and A. Sills (Cambridge Univ. Press, Cambridge, 2008b), p. 199.

  16. A. V. Mel’nikov and I. I. Shevchenko, Solar Syst. Res. 32, 480 (1998).

    ADS  Google Scholar 

  17. J. Orosz, W. F. Welsh, J. A. Carter, E. Brugamyer, L.A. Buchhave, W. D. Cochran, M. Endl, E. B. Ford, et al., Astrophys. J. 758, 87 (2012).

    ADS  Article  Google Scholar 

  18. E. A. Popova, in Proceedings of the IAU Symposium No. 310 on Complex Planetary Systems, Ed. by Z. Knezevic and A. Lemaitre (Cambridge Univ. Press, Cambridge, 2014), p. 98.

  19. E. A. Popova and I. I. Shevchenko, Astron. Lett. 38, 581 (2012a).

    ADS  Article  Google Scholar 

  20. E. A. Popova and I. I. Shevchenko, in Proceedings of the IAU Symposium No. 282 From Interacting Binaries to Exoplanets: Essential Modeling Tools, Ed. by M. T. Richards and I. Hubeny (Cambridge Univ. Press, Cambridge, 2012b), p. 450.

  21. E. A. Popova and I. I. Shevchenko, Astrophys. J. 769, 152 (2013).

    ADS  Article  Google Scholar 

  22. I. I. Shevchenko, in Asteroids, Comets, Meteors, Ed. by B. Warmbein (ESA, Berlin, 2002), p. 367.

  23. I. I. Shevchenko, Astrophys. J. 799, 8 (2015).

    ADS  Article  Google Scholar 

  24. I. I. Shevchenko and A. V. Mel’nikov, JETP Lett. 77, 642 (2003).

    ADS  Article  Google Scholar 

  25. P. Thébault, F. Marzari, and H. Scholl, Mon. Not. R. Astron. Soc. 388, 1528 (2008).

    ADS  Article  Google Scholar 

  26. P. Thébault, F. Marzari, and H. Scholl, Mon. Not. R. Astron. Soc. 393, 21 (2009).

    ADS  Article  Google Scholar 

  27. W. Welsh et al., in Proceedings of the IAU Symposium No. 293 on Formation, Detection, and Characterization of Extrasolar Habitable Planets, August 27–31, 2012, Ed. by N. Haghighipour (2013), p. 1.

  28. P. Wiegert and M. Holman, Astron. J. 113, 1445 (1997).

    ADS  Article  Google Scholar 

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Correspondence to I. I. Shevchenko.

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Original Russian Text © E.A. Popova, I.I. Shevchenko, 2016, published in Pis’ma v Astronomicheskii Zhurnal, 2016, Vol. 42, No. 7, pp. 525–532.

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Popova, E.A., Shevchenko, I.I. On the stability of circumbinary planetary systems. Astron. Lett. 42, 474–481 (2016). https://doi.org/10.1134/S1063773716060050

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  • DOI: https://doi.org/10.1134/S1063773716060050

Keywords

  • celestial mechanics
  • planetary systems
  • binary stars
  • numerical methods