Dynamical instabilities and the formation of extrasolar planetary systems

Science

Volumn 274, Issue 5289, 1996, Pages 954-956

  Rasio, Frederic A ^a   Ford, Eric B ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; COMPUTER SIMULATION; GRAVITATION; ORBITS; PLANETS; SPACE RESEARCH; STABILITY; UNITS OF MEASUREMENT;

ASTRONOMICAL UNITS; HILL STABILITY LIMIT; PLANETARY SYSTEMS; STARS;

SOLAR SYSTEM;

ARTICLE; ASTRONOMY; COMPUTER SIMULATION; DYNAMICS; PRIORITY JOURNAL;

EID: 0030575876     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.274.5289.954     Document Type: Article

References (20)

1. See A. P. Boss, Science 267, 360 (1995); Lunar Planet. Sci. XXVII, 139 (1996). For a more general review of planet formation models, see J. J. Lissauer, Annu. Rev. Astron. Astrophys. 31, 129 (1993).
2. See A. P. Boss, Science 267, 360 (1995); Lunar Planet. Sci. XXVII, 139 (1996). For a more general review of planet formation models, see J. J. Lissauer, Annu. Rev. Astron. Astrophys. 31, 129 (1993).
3. See A. P. Boss, Science 267, 360 (1995); Lunar Planet. Sci. XXVII, 139 (1996). For a more general review of planet formation models, see J. J. Lissauer, Annu. Rev. Astron. Astrophys. 31, 129 (1993).
4. M. Mayor and D. Queloz, Nature 378, 355 (1995); R. P. Butler and G. W. Marcy, Astrophys. J. 464, L153 (1996); G. W. Marcy and R. P. Butler, ibid., L147 (1996): _, E. Williams, L. Bildsten, J. R. Graham, in preparation.
5. M. Mayor and D. Queloz, Nature 378, 355 (1995); R. P. Butler and G. W. Marcy, Astrophys. J. 464, L153 (1996); G. W. Marcy and R. P. Butler, ibid., L147 (1996): _, E. Williams, L. Bildsten, J. R. Graham, in preparation.
6. M. Mayor and D. Queloz, Nature 378, 355 (1995); R. P. Butler and G. W. Marcy, Astrophys. J. 464, L153 (1996); G. W. Marcy and R. P. Butler, ibid., L147 (1996): _, E. Williams, L. Bildsten, J. R. Graham, in preparation.
7. M. Mayor and D. Queloz, Nature 378, 355 (1995); R. P. Butler and G. W. Marcy, Astrophys. J. 464, L153 (1996); G. W. Marcy and R. P. Butler, ibid., L147 (1996): _, E. Williams, L. Bildsten, J. R. Graham, in preparation.
8. See the summary of the Fifth International Conference on Bioastronomy by G. Schilling, Science 273, 429 (1996).
9. D.N.C. Lin, P. Bodenheimer, D. C. Richardson, Nature 380, 606 (1996).
10. F. A. Rasio, C. A. Tout, S. H. Lubow, M. Livio, Astrophys. J. 470, 1187 (1996).
11. The orbit of Jupiter may have evolved significantly by interaction with the protoplanetary disk during the formation of our solar system; P. Goldreich and S. Tremaine, Astrophys. J. 241, 425 (1980).
12. See B. Gladman, Icarus 106, 247 (1993) for a very thorough discussion of this instability.
13. J. E. Chambers, G. W. Wetherill, A. P. Boss, Icarus 119, 261 (1996) have studied the generalization to more than two planets. Alternatively, chaotic evolution of two or more planets well outside the Hill stability limit could also lead to instabilities and strong interactions on much longer time scales; G. D. Quinlan, in Proceedings of the 152nd Symposium of the International Astronomical Union, Angra dos Reis, Brazil, 15 to 19 July 1991, S. Ferraz-Mello, Ed. (Kluwer, Dordrecht, Netherlands, 1992), p. 25.
14. J. E. Chambers, G. W. Wetherill, A. P. Boss, Icarus 119, 261 (1996) have studied the generalization to more than two planets. Alternatively, chaotic evolution of two or more planets well outside the Hill stability limit could also lead to instabilities and strong interactions on much longer time scales; G. D. Quinlan, in Proceedings of the 152nd Symposium of the International Astronomical Union, Angra dos Reis, Brazil, 15 to 19 July 1991, S. Ferraz-Mello, Ed. (Kluwer, Dordrecht, Netherlands, 1992), p. 25.
15. 9.
16. The ejected planet is usually the one that was initially outside in the equal-mass case studied here, otherwise we expect the less massive one to be ejected preferentially.
17. See P. J. Ioannou and R. S. Lindzen, Astrophys. J. 406, 266 (1993) and references therein.
18. The time scale for the initial e to decrease significantly, say from ≃1 to 0.5, is determined by the dissipation of dynamical tides in the star and is likely to be considerably shorter. The evolution of the system during this early phase will be similar to that of a tidal-capture binary; R. A. Mardling, Astrophys. J. 450, 732 (1995). Once dissipation in the equilibrium tide becomes dominant, the circutarization can be studied using the standard weak-friction model; P. Hut [Astron. Astrophys. 99, 126 (1981)], provides the needed generalization to high-eccentricity orbits. The outer planet is not expected to play a significant role during the circularization, since its dynamical coupling to the inner orbit is now very weak. This weak coupling is already evident at the end of the simulation (Fig. 2), which shows that the system has entered a quasiperiodic regime (7).
19. The time scale for the initial e to decrease significantly, say from ≃1 to 0.5, is determined by the dissipation of dynamical tides in the star and is likely to be considerably shorter. The evolution of the system during this early phase will be similar to that of a tidal-capture binary; R. A. Mardling, Astrophys. J. 450, 732 (1995). Once dissipation in the equilibrium tide becomes dominant, the circutarization can be studied using the standard weak-friction model; P. Hut [Astron. Astrophys. 99, 126 (1981)], provides the needed generalization to high-eccentricity orbits. The outer planet is not expected to play a significant role during the circularization, since its dynamical coupling to the inner orbit is now very weak. This weak coupling is already evident at the end of the simulation (Fig. 2), which shows that the system has entered a quasiperiodic regime (7).
20. This work was supported by an Alfred P. Sloan Foundation Fellowship (F.A.R.) and by the MIT UROP program (E.B.F.). Computations were performed at the Cornell Theory Center. We thank P. Morrison for stimulating discussions.