Long-term effects of the Galactic tide on cometary dynamics

  • Marc Fouchard
  • Christiane Froeschlé
  • Giovanni Valsecchi
  • Hans Rickman
Original Article

Abstract

We introduce a model for integrating the effects of Galactic tides on Oort cloud comets, which involves two procedures, according to the values of the osculating semi-major axis a and eccentricity e. Ten simulations of the dynamics of 106 comets over 5 Gyr are performed using this model. We thus investigate the long-term effects of the Galactic tide with and without a radial component, the effects of the local density of the Galactic disk, and those of the Oort constants. Most of the results may be understood in terms of the integrability or non-integrability of the system. For an integrable system, which occurs for moderate semi-major axes with or without radial component, the dynamics is explained by periodic variation of the cometary perihelion, inducing the depletion of the outer region of the Oort cloud, a constant flux from the inner region after 500 Myr, and the quick formation of a reservoir of comets with argument of perihelion near 26.6°. When the system is non-integrable, the efficiency of the tide in reducing the cometary perihelion distance is enhanced both by replenishing the Oort cloud domain from which comets are sent toward the planetary system, and by reducing the minimal value that the perihelion distance may reach. No effects of varying the Oort constants were observed, showing that the flat rotation curve is a satisfactory approximation in Oort cloud dynamics.

Keywords

Galactic dynamics Numerical model Long-period comets Oort cloud 

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References

  1. Bahcall J.N., Flynn C., Gould A. (1992). Local dark matter from a carefully selected sample. ApJ 389:234–250CrossRefADSGoogle Scholar
  2. Bailey M.E. (1983). The structure and evolution of the solar system comet cloud. MNRAS 204:603–633MATHADSGoogle Scholar
  3. Brasser R. (2001). Some properties of a two-body system under the influence of the Galactic tidal field. MNRAS 324:1109–1116CrossRefADSGoogle Scholar
  4. Breiter S., Ratajczak R. (2005). Vectorial elements for the Galactic disc tide effects in cometary motion. MNRAS 364:1222–1228CrossRefADSGoogle Scholar
  5. Breiter S., Dybczyński P.A., Elipe A. (1996). The action of the galactic disk on the Oort cloud comets. Qualitative study. A & A 315:618–624Google Scholar
  6. Duncan M., Quinn T., Tremaine S. (1987). The formation and extent of the solar system comet cloud. AJ 94:1330–1338CrossRefADSGoogle Scholar
  7. Dybczyński P.A. (2005). Simulating observable comets II. Simultaneous stellar and galactic action. A & A 441:783–790Google Scholar
  8. Elipe A., Ferrer S. (1994). Reductions, relative equilibria, and bifurcations in the generalized van der Waals potential: relation to the integrable cases. Phys. Rev. Lett. 72:985–988CrossRefADSGoogle Scholar
  9. Everhart, E.: An efficient integrator that uses Gauss-Radau spacings. In: Carusi, A., Valsecchi, G.B. (eds.) Proc. IAU Colloq. 83, Dynamics of Comets: Their Origin and Evolution, p. 185, Reidel, Dordrecht (1985)Google Scholar
  10. Fouchard M. (2004). New fast models of the galactic tide. MNRAS 349:347–356CrossRefADSGoogle Scholar
  11. Fouchard M., Froeschlé C., Matese J.J., Valsecchi G.B. (2005). Comparison between different models of the galactic tidal effects on cometary orbits. Celest. Mech. Dyn. Astron. 93:231–264CrossRefADSGoogle Scholar
  12. García-Sánchez J., Weissman P.R., Preston R.A., Jones D.L., Lestrade J.-F., Latham D.W., Stefanik R.P., Paredes J.M. (2001). Stellar encounters with the solar system. A & A 379:634–659ADSGoogle Scholar
  13. Hills J.G. (1981). Comet showers and the steady-state infall of comets from the Oort cloud, Astron. J. 86:1730–1740ADSGoogle Scholar
  14. Heisler J. (1990). Monte Carlo simulations of the Oort comet cloud. Icarus 75:104–121CrossRefADSGoogle Scholar
  15. Heisler J., Tremaine S. (1986). The influence of the galactic tidal field on the Oort comet cloud, Icarus 65:13–26Google Scholar
  16. Holmberg J., Flynn C. (2000). The local density of matter mapped by Hipparcos. MNRAS 313:209–216CrossRefADSGoogle Scholar
  17. Levison H., Dones L., Duncan M.J. (2001). The origin of Halley-type comets: probing the inner Oort cloud. Astron. J. 121: 2253–2267CrossRefADSGoogle Scholar
  18. Matese J.J., Lissauer J.J. (2002). Characteristics and frequency of weak stellar impulses of the Oort cloud. Icarus 157:228–240CrossRefADSGoogle Scholar
  19. Matese J.J., Lissauer J.J. (2004). Perihelion evolution of observed new comets implies the dominance of the galactic tide in making Oort cloud comets discernable. Icarus 170:508–513CrossRefADSGoogle Scholar
  20. Matese J.J., Whitman P.G. (1989). The galactic disk tidal field and the nonrandom distribution of observed Oort cloud comets. Icarus 82:389–401CrossRefADSGoogle Scholar
  21. Matese J.J., Whitman P.G. (1992). A model of the galactic tidal interaction with the Oort comet cloud, Celest. Mech. Dyn. Astron. 54:13–35CrossRefADSGoogle Scholar
  22. Mignard F. (2000). Local galactic kinematics from Hipparcos proper motions. A & A 354:522–536ADSGoogle Scholar
  23. Neslušan L., Jakubík M. (2005). Some characteristics of the outer Oort cloud as inferred from observations of new comets. A & A 437:1093–1108ADSGoogle Scholar
  24. Olling R.P., Dehnen W. (2003). The Oort constants measured from proper motions. ApJ 599:275–296CrossRefADSGoogle Scholar
  25. Olling R.P., Merrifield M.R. (1998). Refining the Oort and Galactic constants. MNRAS 297:943–952CrossRefADSGoogle Scholar
  26. Oort J.H. (1950). The structure of the cloud of comets surrounding the Solar System and a hypothesis concerning its origin. Bull. Astron. Inst. Neth. 11:91–110ADSGoogle Scholar
  27. Tommei G (2006). Canonical elements for Öpik theory. Celest. Mech. Dyn. Astron., 94:173–195MATHMathSciNetCrossRefADSGoogle Scholar
  28. Tremaine S. (2000). Canonical elements for collision orbits. Celest. Mech. Dyn. Astron. 79:231–233CrossRefADSGoogle Scholar
  29. Wiegert P., Tremaine S. (1999). The evolution of long-period comets. Icarus 137:84–121CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Marc Fouchard
    • 1
    • 2
  • Christiane Froeschlé
    • 3
  • Giovanni Valsecchi
    • 1
  • Hans Rickman
    • 4
  1. 1.INAF-IASFRomaItaly
  2. 2.IMCCE/SYRTEParisFrance
  3. 3.Observatoire de la Côte d’Azur, UMR 6202Bv. de l’ObservatoireNice cedex 4France
  4. 4.Uppsala Astronomical ObservatoryUppsalaSweden

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