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Extrasolar Planetary Systems

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Chaos and Stability in Planetary Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 683))

Abstract

This paper is an updated version of lectures given at the Helmholtz Summer School on Extrasolar Planetary Systems (Potsdam, 2003). It includes five sections: Orbit determination, the known planetary systems, chaos, transition from secular to resonant dynamics and planetary migration. The first section is mainly devoted to problems arising in the orbit determination of systems with 2 or more planets from data on the radial velocity of the central star. In the second section, an attempt of classification is done in which the known planetary systems are grouped in 4 classes, one of which includes 47 UMa and our Solar System (orbits with low period ratio and small eccentricities). The phenomena related to mean-motion resonances (MMR) are studied with some detail in the remaining sections, since they may directly affect the stability of many systems. In the appendix, the FFT techniques used in the paper to assess the stability of a system are reviewed.

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References

  1. C. Allende Prieto and D.L. Lambert: Fundamental parameters of nearby stars from the comparison with evolutionary calculations: masses, radii and effective temperatures. A&A} 352, 555-562 (1999)

    ADS  Google Scholar 

  2. C. Beaugé: Asymmetric librations in exterior resonances. CMDA 60, 225-248 (1994)

    Article  ADS  MATH  Google Scholar 

  3. C. Beaugé, S. Ferraz-Mello and T.A. Michtchenko: Extra-solar planets in mean-motion resonance: Apses alignment and asymmetric stationary solutions. ApJ} 593, 1124-1133 (2003)

    Article  ADS  Google Scholar 

  4. C. Beaugé, S. Ferraz-Mello and T.A. Michtchenko: Planetary migration and extrasolar planets in the 2/1 mean-motion resonance. MNRAS submitted (2005), astro-ph/0404166

    Google Scholar 

  5. F. Benedict, B.E. McArtur, T. Forveille, X. Delfosse, E. Nelan, R.P. Butler, W. Spiesman, G. Marcy, B. Goldman, C. Perrier, W.H. Jefferys and M. Mayor: A mass for the extrasolar planet Gliese 876b determined from Hubble Space Telescope Fine Guidance Sensor 3 astrometry and high-precision radial velocities. ApJ} 581, L115-L118 (2002)

    Article  ADS  Google Scholar 

  6. E. Bois, L. Kiseleva-Eggleton, N. Rambaux and E. Pilat-Lohinger: Conditions of dynamical stability for the HD160691 planetary system. ApJ} 598, 1312-1320 (2003)

    Article  ADS  Google Scholar 

  7. P. Bretagnon: Theory for the motion of all planets – The VSOP82 solution. A&A} 114, 278-288 (1982)

    ADS  MATH  Google Scholar 

  8. P. Bretagnon and G. Francou: `Planetary theories in rectangular and spherical variables. VSOP87 solutions. A&A} 202, 309-315 (1988)

    ADS  MATH  Google Scholar 

  9. P. Butler, G. Marcy, D. Fischer, T. Brown, A. Contos, S. Korzennik, P. Nisenson and R. Noyes: Evidence for multiple companions to upsilon Andromedae. ApJ} 526, 916 (1999)

    Article  ADS  Google Scholar 

  10. N. Callegari Jr., T.A. Michtchenko and S. Ferraz-Mello: Dynamics of two planets in 2:1 mean-motion resonance. CMDA} 89, 201-234 (2004)

    Article  ADS  Google Scholar 

  11. J.F. Chambers: Pulsars and solar-system ephemerides. IAU Symposium} 172, 105-112 (1996)

    ADS  Google Scholar 

  12. M. Chapront-Touze and J. Chapront: The lunar ephemeris ELP 2000. A&A} 124, 50-62 (1983)

    ADS  Google Scholar 

  13. Y.Q. Chen and G. Zhao: Chin. J. Astron. Astrophys.} 2, 151-160 (2002)

    Article  ADS  Google Scholar 

  14. G. Contopoulos: Order and Chaos in Dynamical Astronomy}, (Springer 2002)

    Google Scholar 

  15. Cor A.C.M. Correia, S. Udry, M. Mayor, J. Laskar, D. Naef, F. Pepe, D. Queloz and N.C. Santos: The CORALIE survey for southern extra-solar planets. XIII. A pair of planets around HD 202206 or a circumbinary planet. A&A, in press (2005), astro-ph/0411512

    Google Scholar 

  16. S. Dermott, R. Malhotra and C.D.Murray: Dynamics of the Uranian and Saturnian satellite systems: A chaotic route to melting Miranda. Icarus} 76, 295-334 (1988)

    Article  ADS  Google Scholar 

  17. Exp} Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, H.M.Stationery Office London 1961

    Google Scholar 

  18. E. Everhart: An efficient integrator that uses Gauss-Radau spacings. In: Dynamics of Comets: Their Origin and Evolution} ed by A. Carusi and G.B. Valsecchi (Reidel, Dordrecht 1985), pp. 185

    Google Scholar 

  19. S. Ferraz-Mello: Dynamics of the Galilean Satellites}, (IAG-USP, Sao Paulo 1979)

    Google Scholar 

  20. S. Ferraz Mello, M. Tsuchida and J.C. Klafke: On symmetric planetary corotations. CMDA} 55, 25-45 (1993)

    Article  ADS  MATH  Google Scholar 

  21. S. Ferraz-Mello: Tidal Acceleration, Rotation and Apses Alignment in Resonant Extra-Solar Planetary Systems. Bull. Amer. Astron. Soc.} 34, 894 (2002)

    ADS  Google Scholar 

  22. S. Ferraz-Mello, C. Beaugé and T.A. Michtchenko: Evolution of migrating planet pairs in resonance. CMDA} 87, 99-112 (2003), astro-ph/0402335

    MathSciNet  Google Scholar 

  23. S. Ferraz-Mello, T.A. Michtchenko and C. Beaugé: Regular motions in extra-solar planetary systems. In: Chaotic worlds} ed by B.A.Steves et al. (Kluwer, Dordrecht 2004) (in press), astro-ph/0402335

    Google Scholar 

  24. S. Ferraz-Mello, T.A. Michtchenko and C. Beaugé: The orbits of the extra-solar planets HD 82943 c,b. ApJ} 621, 473-481 (2005), astro-ph/0411734

    Google Scholar 

  25. D.A. Fischer, G.W. Marcy, R.P. Butler, S.S. Vogt, G.W. Henry, D. Pourbaix, B. Walp, A.A. Misch and J.T. Wright: A planetary companion to HD 40979 and additional planets orbiting HD 12661 and HD 38529. ApJ} 586, 1394-1408 (2003)

    Article  ADS  Google Scholar 

  26. B. Gladman: Dynamics of Systems of Two Close Planets. Icarus} 106, 247-263 (1993)

    Article  ADS  Google Scholar 

  27. R.S. Gomes: {Resonance trapping and evolution of particles subject to Poyinting-Robertson drag: Adiabatic and non-adiabatic approaches. CMDA 61, 97-113 (1995)

    Article  ADS  MATH  Google Scholar 

  28. K. Goździewski, M. Konacki and A.J. Maciejewski: Where is the second planet in the HD 106691 planetary system?. ApJ} 594, 1019-1032 (2003)

    Article  ADS  Google Scholar 

  29. R. Greenberg and A. Brahic: Planetary Rings}, (University of Arizona Press, 1984)

    Google Scholar 

  30. J. Hadjidemetriou: Resonant periodic motion and the stability of extrasolar planetary systems. CMDA} 83, 141-154 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  31. J. Hadjidemetriou and D. Psychoyos: Dynamics of extrasolar planetary systems: 2/1 resonant motion. In: Galaxies and Chaos} ed by G.~Contopoulos and N.~Voglis, (Lectures Notes in Physics, Springer 2003), 412-432

    Google Scholar 

  32. F.C. Henroteau: Double and multiple stars. In: Handbuch der Astrophysik}, (Springer, Berlin 1928), 299-468.

    Google Scholar 

  33. J. Ji, H. Kinoshita, L. Liu, G. Li and H. Nakai: The apsidal antialignment of the HD 82943 system. CMDA} 87, 113-120 (2003)

    Article  ADS  MATH  Google Scholar 

  34. W. Kley: `On the migration of a system of protoplanets. MNRAS} 313, L47-L51 (2001)

    Article  ADS  Google Scholar 

  35. W. Kley: Dynamical evolution of planets in disks. CMDA} 87, 85-97 (2003)

    Article  ADS  MATH  Google Scholar 

  36. KWo M. Konacki and A. Wolszczan: Masses and orbital inclinations of planets in the PSR B1257+12 system. ApJ} 591, L147-150 (2003)

    Article  ADS  Google Scholar 

  37. Kon M. Konacki, G. Torres, D.D. Sasselov, G. Pietrzyński, A. Udalski, S. Jha, M.T. Ruiz, W. Gieren and D. Miniti: The transiting extrasolar giant planet around the star OGLE-TR-113. ApJ} 609, L37-L40 (2004)

    Article  ADS  Google Scholar 

  38. J. Laskar: Frequency analysis for multi-dimensional systems. Global dynamics and diffusion. Physica D} 67, 257-281 (1993)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. J. Laskar: On the spacing of planetary systems, Phys. Rev. Let.} 84, 3240-3243 (2000)

    Article  ADS  Google Scholar 

  40. G. Laughlin and J.E. Chambers: Short-term dynamical interactions among extrasolar planets. ApJ} 551, L109-L113 (2001), astro-ph/0407441

    Google Scholar 

  41. G. Laughlin, R.P. Butler, D.A. Fischer, G.W. Marcy, S.S. Vogt and A. Wolf: The GJ 876 Planetary System – A progress report. ApJ}, in press (2005)

    Google Scholar 

  42. M.H. Lee and S.J. Peale: Dynamics and origin of the 2:1 orbital resonances of the GJ 876 planets” ApJ 567, 596-609 (2002)

    Article  ADS  Google Scholar 

  43. M.H. Lee and S.J. Peale: Secular Evolution of hierarchical planetary systems. ApJ} 592, 1201-1216 (2003)

    Article  ADS  Google Scholar 

  44. M.H. Lee: Diversity and origin of 2:1 orbital resonances in extra-solar planetary systems. ApJ} 611, 517-527 (2004)

    Article  ADS  Google Scholar 

  45. R. Malhotra, D. Black, A. Eck and A. Jackson: Constraints on the putative companions to PSR 1257+12. Nature} 355, 583-585 (1992)

    Article  ADS  Google Scholar 

  46. G.W. Marcy, R.P. Butler, D. Fischer, S.S. Vogt, J.J. Lissauer and E.J. Rivera: A pair of resonant planets orbiting GJ 876. ApJ} 556, 296-301 (2001)

    Article  ADS  Google Scholar 

  47. G.W. Marcy, R.P. Butler, D. Fischer, G. Laughlin, S.S. Vogt, G.W. Henry and D. Pourbaix: A planet at 5 AU around 55 Cancri. ApJ} 581, 1375-1388 (2002)

    Article  ADS  Google Scholar 

  48. M. Mayor, S. Udry, D. Naef, F. Pepe, D. Queloz, N.C. Santos and M. Burnet: The CORALIE survey for southern extra-solar planets. XII. Orbital solutions for 16 extra-solar planets discovered with CORALIE. A&A} 415, 391-402 (2004)

    Article  ADS  Google Scholar 

  49. B.E. McArthur, M. Endl, W.D. Cochran, G.F. Benedict, D.A. Fischer, G.W. Marcy, R.P. Butler, D. Naef, M. Mayor, D. Queloz, S. Udry and T.E. Harrison: Detection of a Neptune-mass planet in the ρ{1}Cancri system using the Hobby-Eberly telescope. ApJ} 614, L81-l84 (2004)

    Article  ADS  Google Scholar 

  50. C. McCarthy, R.P. Butler, C.G. Tinney, H.R.A. Jones, G.W. Marcy, B. Carter, A.J. Penny and D.A. Fischer: Multiple companions to HD 154857 and HD 160691. ApJ} 617, 575-579 (2004)

    Article  ADS  Google Scholar 

  51. T.A. Michtchenko and S. Ferraz-Mello: Comparative study of the asteroidal motion in the 3:2 and 2:1 resonances with Jupiter. I. Planar model. A&A} 303, 945-963 (1995)

    ADS  Google Scholar 

  52. T.A. Michtchenko and S. Ferraz-Mello: Resonant structure of the Outer Solar System in the neighborhood of the Planets. AJ 122, 474-481 (2001)

    Article  ADS  Google Scholar 

  53. T.A. Michtchenko and S. Ferraz-Mello: Modeling the 5:2 mean-motion resonance in the Jupiter-Saturn planetary system. Icarus 149, 357-374 (2001)

    Article  ADS  Google Scholar 

  54. T.A. Michtchenko and R. Malhotra: Secular dynamics of the three-body problem: Application to the ν Andromedae planetary system. Icarus 168, 237-248 (2004)

    Article  ADS  Google Scholar 

  55. A. Morbidelli: Modern Celestial Mechanics: Aspects of Solar System Dynamics}, (Taylor and Francis, London 2002)

    Google Scholar 

  56. D. Naef, M. Mayor, J.L. Beuzit, C. Perrier, D. Queloz, J.P. Sivan and S. Udry: `The ELODIE survey for northern extra-solar planets. III. Three planetary candidates detected with ELODIE. A&A 414, 351-359 (2004)

    Article  ADS  Google Scholar 

  57. J.C.B. Papaloizou: Disc-planet interactions: Migration and resonances in extrasolar planetary systems. CMDA 87, 53-83 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  58. T. Pauwels: Secular orbit-orbit resonance between two satellites with non-zero masses. CMDA 30, 229-247 (1983)

    MATH  Google Scholar 

  59. M.A.C. Perryman: Extra-solar Planets. Rep. Progr. Phys. 63, 1209-1272 (2000)

    ADS  Google Scholar 

  60. Plu H.C. Plummer: An Introductory Treatise on Dynamical Astronomy, (Cambridge Univ. Press 1918 - reprint Dover 1960)

    Google Scholar 

  61. G.E. Powell and I.C. Percival: Spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems. JPhA 12, 2053-2071 (1979)

    ADS  Google Scholar 

  62. F.A. Rasio, P.D. Nicholson, S.L. Shapiro and S.A. Teukolsky: Planetary system in PSR 1257+12: A crucial test. Nature 355, 325-356 (1992)

    Article  ADS  Google Scholar 

  63. C. Ron and J. Vondrák: Expansion of annual aberration into trigonometric series. Bull. Astron. Inst. Czech. 37 96-103 (1986)

    ADS  Google Scholar 

  64. N. Santos, F. Bouchy, M. Mayor, F. Pepe, D. Queloz, S. Udry, C. Lovis, M. Bazot,W. Benz, J.L. Bertaux, G. LoCurto, X. Delfosse, C. Mordasini, D. Naef, J.P. Sivan and S. Vauclair: The HARPS survey for southern extra-solar planets. II. A 14 Earth-masses exoplanet around μ Arae. A&A 426, L19-L23 (2004)

    Article  ADS  Google Scholar 

  65. M.D. Snellgrove, J.C.B. Papaloizou and R.P. Nelson: `On disk driven inward migration of resonantly coupled planets with application to the system around GJ876. A&A 374, 1092-1099 (2001)

    Article  ADS  Google Scholar 

  66. P. Stumpff: Two self-consistent Fortran subroutines for the computation of the Earth's motion. A&AS 41 1-8 (1980)

    ADS  Google Scholar 

  67. F. Tisserand: Traité de Mécanique Céleste vol. I}, (Gauthier-Villars, Paris 1889 - reprint 1960)

    Google Scholar 

  68. S. Udry, M. Mayor, D. Naef, F. Pepe, D. Queloz, N.C. Santos and M. Burnet: The CORALIE survey for southern extra-solar planets. VIII. The very low-mass companions of HD 141937, HD 162020, HD 168443 and HD 202206. Brown dwarfs or superplanets?. A&A 390, 267-279 (2002)

    Article  ADS  Google Scholar 

  69. P. van de Kamp: Astrometry with long-focus telescopes. In: Astronomical Techniques} ed by W.A.Hiltner, (Chicago Univ. Press 1962), pp. 487-536.

    Google Scholar 

  70. A. Wolszczan and D.A. Frail: A planetary system around the millisecond pulsar PSR 1257+12. Nature 355, 145-147 (1992)

    Article  ADS  Google Scholar 

  71. L.Y. Zhou, H.J. Lehto, Y.S. Sun and J.Q. Zheng: The apsidal corotation in mean-motion resonance: the 55 Cancri as an example. MNRAS 350, 1495-1502 (2004)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Instituto de Astronomia Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Brasil

    S Ferraz-Mello & T.A Michtchenko

  2. Observatorio Astronómico, Universidad Nacional de Córdoba, Argentina

    C. Beaugé

  3. Departamento de Matemática, Universidade Federal de São Carlos, Brasil

    N. Callegari Jr.

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  1. S Ferraz-Mello
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  2. T.A Michtchenko
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  3. C. Beaugé
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  4. N. Callegari Jr.
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Rudolf Dvorak Florian Freistetter Jürgen Kurths

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Ferraz-Mello, S., Michtchenko, T., Beaugé, C., Callegari, N. Extrasolar Planetary Systems. In: Dvorak, R., Freistetter, F., Kurths, J. (eds) Chaos and Stability in Planetary Systems. Lecture Notes in Physics, vol 683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10978337_4

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  • DOI: https://doi.org/10.1007/10978337_4

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