Advertisement

Neptune’s resonances in the scattered disk

  • Lei Lan
  • Renu MalhotraEmail author
Original Article

Abstract

The scattered disk objects (SDOs) are thought to be a small fraction of the ancient population of leftover planetesimals in the outer Solar system that were gravitationally scattered by the giant planets and have managed to survive primarily by capture and sticking in Neptune’s exterior mean motion resonances (MMRs). In order to advance understanding of the role of MMRs in the dynamics of the SDOs, we investigate the phase space structure of a large number of Neptune’s MMRs in the semi-major axis range 33–140 au by use of Poincaré sections of the circular planar restricted three-body model for the full range of particle eccentricity pertinent to SDOs. We find that, for eccentricities corresponding to perihelion distances near Neptune’s orbit, distant MMRs have stable regions with widths that are surprisingly large and of similar size to those of the closer-in MMRs. We identify a phase-shifted second resonance zone that exists in the phase space at planet-crossing eccentricities but not at lower eccentricities; this second resonance zone plays an important role in the dynamics of SDOs in lengthening their dynamical lifetimes. Our non-perturbative measurements of the sizes of the stable resonance zones confirm previous results and provide an additional explanation for the prominence of the N : 1 sequence of MMRs over the N : 2, N : 3 sequences and other MMRs in the population statistics of SDOs; our results also provide a tool to more easily identify resonant objects.

Keywords

Restricted three-body problem Kuiper belt Orbital resonance Chaos Resonance sticking Minor planets 

Notes

Acknowledgements

We thank Kathryn Volk for discussions. We also thank Tabare Gallardo and an anonymous reviewer for providing helpful reviews. LL acknowledges funding from National Natural Science Foundation of China (11572166) and China Scholarship Council. RM acknowledges funding from NASA (Grants NNX14AG93G and 80NSSC19K0785) and NSF (Grant AST-1824869).

References

  1. Beaugè, C.: Asymmetric librations in exterior resonance. Celest. Mech. Dyn. Astron. 60, 225 (1994)ADSMathSciNetCrossRefGoogle Scholar
  2. Chiang, E.I., Jordan, A.B.: On the Plutinos and Twotinos of the Kuiper belt. Astron. J. 124, 3430 (2002)ADSCrossRefGoogle Scholar
  3. Di Sisto, R.P., Brunini, A.: The origin and distribution of the Centaur population. Icarus 190, 224 (2007)ADSCrossRefGoogle Scholar
  4. Duncan, M.J., Levison, H.F.: A disk of scattered icy objects and the origin of Jupiter-family comets. Science 276, 1670 (1997)ADSCrossRefGoogle Scholar
  5. Emel’yanenko, V.V., Asher, D.J., Bailey, M.E.: Centaurs from the Oort cloud and the origin of Jupiter-family comets. MNRAS 361, 1345 (2005)ADSCrossRefGoogle Scholar
  6. Fehlberg, E.: Runge-Kutta formulas of high order with stepsize control through leading truncation error term. NASA TR. R-287, 1 (1968)Google Scholar
  7. Fernández, J.A., Gallardo, T., Brunini, A.: The scattered disk population as a source of Oort cloud comets: evaluation of its current and past role in populating the Oort cloud. Icarus 172, 372 (2004)ADSCrossRefGoogle Scholar
  8. Forgács-Dajka, E., Sándor, Z., Érdi, B.: A fast method to identify mean motion resonances. MNRAS 477, 3383 (2018)ADSCrossRefGoogle Scholar
  9. Gallardo, T.: Atlas of the mean motion resonances in the solar system. Icarus 184, 29 (2006)ADSCrossRefGoogle Scholar
  10. Gallardo, T.: Resonances in the asteroid and trans-Neptunian belts: a brief review. Planet. Space Sci. 157, 96 (2018)ADSCrossRefGoogle Scholar
  11. Gallardo, T.: Strength, stability and three dimensional structure of mean motion resonances in the solar system. Icarus 317, 121 (2019)ADSCrossRefGoogle Scholar
  12. Gallardo, T., Ferraz-Mello, S.: Understanding libration via time-frequency analysis. Astron. J. 113, 863 (1997)ADSCrossRefGoogle Scholar
  13. Gallardo, T., Ferraz-Mello, S.: Dynamics in the exterior 2:3 resonance with Neptune. Planet. Space Sci. 46, 945 (1998)ADSCrossRefGoogle Scholar
  14. Gladman, B., Marsden, B.G., Vanlaerhoven, C.: Nomenclature in the outer solar system. In: Barucci, M.A., Boehnhardt, H., Cruikshank, D.P., Morbidelli, A., Dotson, R. (eds.) The Solar System Beyond Neptune, pp. 43–57. University of Arizona Press, Tucson (2008)Google Scholar
  15. Gomes, R.S., Fernández, J.A., Gallardo, T., Brunini, A.: The scattered disk: origins, dynamics, and end states. In: Barucci, M.A., Boehnhardt, H., Cruikshank, D.P., Morbidelli, A., Dotson, R. (eds), The Solar System Beyond Neptune, pp. 259–273 (2008)Google Scholar
  16. Henrard, J., Lemaitre, A.: A second fundamental model for resonance. Celest. Mech. 30, 197 (1983)ADSMathSciNetCrossRefGoogle Scholar
  17. Kotoulas, T.A.: The dynamics of the 1:2 resonant motion with Neptune in the 3D elliptic restricted three-body problem. Astron. Astrophys. 429, 1107 (2005)ADSCrossRefGoogle Scholar
  18. Kotoulas, T., Voyatzis, G.: Comparative study of the 2:3 and 3:4 resonant motion with Neptune: an application of symplectic mappings and low frequency analysis. Celest. Mech. Dyn. Astron. 88, 343 (2004)ADSMathSciNetCrossRefGoogle Scholar
  19. Levison, H.F., Duncan, M.J.: From the Kuiper belt to Jupiter-family comets: the spatial distribution of ecliptic comets. Icarus 127, 13 (1997)ADSCrossRefGoogle Scholar
  20. Levison, H.F., Duncan, M.J., Dones, L., Gladman, B.J.: The scattered disk as a source of Halley-type comets. Icarus 184, 619 (2006)ADSCrossRefGoogle Scholar
  21. Luu, J.X., Jewitt, D.C.: Kuiper belt objects: relics from the accretion disk of the Sun. Ann. Rev. Astron. Astrophys. 40, 63 (2002)ADSCrossRefGoogle Scholar
  22. Lykawka, P.S., Mukai, T.: Dynamical classification of trans-neptunian objects: probing their origin, evolution, and interrelation. Icarus 189, 213 (2007a)ADSCrossRefGoogle Scholar
  23. Lykawka, P.S., Mukai, T.: Resonance sticking in the scattered disk. Icarus 192, 238 (2007b)ADSCrossRefGoogle Scholar
  24. Malhotra, R.: The origin of Pluto’s orbit: implications for the Solar System beyond Neptune. Astron. J. 110, 420 (1995)ADSCrossRefGoogle Scholar
  25. Malhotra, R.: The phase space structure near Neptune resonances in the Kuiper belt. Astron. J. 111, 504 (1996)ADSCrossRefGoogle Scholar
  26. Malhotra, R., Williams, J.G.: Pluto’s heliocentric orbit. In: Stern, S.A., Tholen, D.J. (eds.) Pluto and Charon, p. 127. University of Arizona Press, Tucson (1997)Google Scholar
  27. Malhotra, R., Lan, L., Volk, K., Wang, X.: Neptune’s 5:2 resonance in the Kuiper belt. Astron. J. 156, 55 (2018)ADSCrossRefGoogle Scholar
  28. Milani, A., Nobili, A.M., Carpino, M.: Dynamics of Pluto. Icarus 82, 200 (1989)ADSCrossRefGoogle Scholar
  29. Morbidelli, A.: Chaotic diffusion and the origin of comets from the 2/3 resonance in the Kuiper belt. Icarus 127, 1 (1997)ADSCrossRefGoogle Scholar
  30. Morbidelli, A., Brown, M.E.: The Kuiper belt and the primordial evolution of the solar system. In: Festou, M.C., Keller, H.U., Weaver, H.A. (eds.) Comets II, pp. 175–191. University of Arizona Press, Tucson (2004)Google Scholar
  31. Morbidelli, A., Thomas, F., Moons, M.: The resonant structure of the Kuiper belt and the dynamics of the first five trans-Neptunian objects. Icarus 118, 322 (1995)ADSCrossRefGoogle Scholar
  32. Murray, C.D., Dermott, S.F.: Solar System Dynamics, 1st edn. Cambridge University Press, New York (1999)zbMATHGoogle Scholar
  33. Murray-Clay, R.A., Chiang, E.I.: A signature of planetary migration: the origin of asymmetric capture in the 2:1 resonance. Astrophys. J. 619, 623 (2005)ADSCrossRefGoogle Scholar
  34. Nesvorný, D., Roig, F.: Mean motion resonances in the trans-Neptunian region: I. The 2:3 resonance with Neptune. Icarus 148, 282 (2000)ADSCrossRefGoogle Scholar
  35. Nesvorný, D., Roig, F.: Mean motion resonances in the transneptunian region: part II: the 1:2, 3:4, and weaker resonances. Icarus 150, 104 (2001)ADSCrossRefGoogle Scholar
  36. Pan, M., Sari, R.: A generalization of the Lagrangian points: studies of resonance for highly eccentric orbits. Astron. J. 128, 1418 (2004)ADSCrossRefGoogle Scholar
  37. Robutel, P., Laskar, J.: Frequency map and global dynamics in the solar system I: short period dynamics of massless particles. Icarus 152, 4 (2001)ADSCrossRefGoogle Scholar
  38. Saillenfest, M., Lari, G.: The long-term evolution of known resonant trans-Neptunian objects. Astron. Astrophys. 603, A79 (2017)ADSCrossRefGoogle Scholar
  39. Saillenfest, M., Fouchard, M., Tommei, G., Valsecchi, G.B.: Long-term dynamics beyond Neptune: secular models to study the regular motions. Celest. Mech. Dyn. Astron. 126, 369 (2016)ADSMathSciNetCrossRefGoogle Scholar
  40. Tiscareno, M.S., Malhotra, R.: The dynamics of known Centaurs. Astron. J. 126, 3122 (2003)ADSCrossRefGoogle Scholar
  41. Tiscareno, M.S., Malhotra, R.: Chaotic diffusion of resonant Kuiper belt objects. Astron. J. 138, 827 (2009)ADSCrossRefGoogle Scholar
  42. Volk, K., Malhotra, R.: The scattered disk as the source of the Jupiter family comets. Astrophys. J. 687, 714 (2008)ADSCrossRefGoogle Scholar
  43. Volk, K., Murray-Clay, R., Gladman, B., et al.: OSSOS III—resonant trans-Neptunian populations: constraints from the first quarter of the Outer Solar System Origins Survey. Astron. J. 152, 23 (2016)ADSCrossRefGoogle Scholar
  44. Volk, K., Murray-Clay, R.A., Gladman, B.J., et al.: OSSOS. IX. Two objects in Neptune’s 9:1 resonance—implications for resonance sticking in the scattering population. Astron. J. 155, 260 (2018)ADSCrossRefGoogle Scholar
  45. Voyatzis, G., Kotoulas, T.: Planar periodic orbits in exterior resonances with Neptune. Planet. Space Sci. 53, 1189 (2005)ADSCrossRefGoogle Scholar
  46. Voyatzis, G., Kotoulas, T., Hadjidemetriou, J.D.: Symmetric and nonsymmetric periodic orbits in the exterior mean motion resonances with Neptune. Celest. Mech. Dyn. Astron. 91, 191 (2005)ADSMathSciNetCrossRefGoogle Scholar
  47. Wang, X., Malhotra, R.: Mean motion resonances at high eccentricities: the 2:1 and the 3:2 interior resonances. Astron. J. 154, 20 (2017)ADSCrossRefGoogle Scholar
  48. Yu, T.Y.M., Murray-Clay, R., Volk, K.: Trans-Neptunian objects transiently stuck in Neptune’s mean-motion resonances: numerical simulations of the current population. Astron. J. 156, 33 (2018)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Tsinghua UniversityBeijingChina
  2. 2.The University of ArizonaTucsonUSA

Personalised recommendations