Nonlinear Dynamics

, Volume 74, Issue 3, pp 831–847 | Cite as

Exploring the origin, the nature, and the dynamical behavior of distant stars in galaxy models

Original Paper


We explore the regular or chaotic nature of orbits moving in the meridional plane of an axially symmetric galactic gravitational model with a disk, a dense spherical nucleus, and some additional perturbing terms corresponding to influence from nearby galaxies. In order to obtain this, we use the Smaller ALingment Index (SALI) technique integrating extensive samples of orbits. Of particular interest is the study of distant, remote stars moving in large galactocentric orbits. Our extensive numerical experiments indicate that the majority of the distant stars perform chaotic orbits. However, there are also distant stars displaying regular motion as well. Most distant stars are ejected into the galactic halo on approaching the dense and massive nucleus. We study the influence of some important parameters of the dynamical system, such as the mass of the nucleus and the angular momentum, by computing in each case the percentage of regular and chaotic orbits. A second-order polynomial relationship connects the mass of the nucleus and the critical angular momentum of the distant star. Some heuristic semi-theoretical arguments to explain and justify the numerically derived outcomes are also given. Our numerical calculations suggest that the majority of distant stars spend their orbital time in the halo where it is easy to be observed. We present evidence that the main cause for driving stars to distant orbits is the presence of the dense nucleus combined with the perturbation caused by nearby galaxies. The origin of young O and B stars observed in the halo is also discussed.


Galaxies: kinematics and dynamics Numerical methods 



I would like to express my warmest thanks to the two anonymous referees for the careful reading of the manuscript and for all the aptly suggestions and comments, which improved both the quality and the clarity of the paper.


  1. 1.
    Allen, C., Martos, M.A.: A simple, realistic model of the galactic mass distribution for orbit computations. Rev. Mex. Astron. Astrofis. 13, 137–147 (1986) Google Scholar
  2. 2.
    Bahcall, J.N., Schmidt, M., Soneira, R.M.: On the interpretation of rotation curves measured at large galactocentric distances. Astrophys. J. 258, L23–L27 (1982) CrossRefGoogle Scholar
  3. 3.
    Binney, J., Tremaine, S.: Galactic Dynamics. Princeton Univ. Press, Princeton (2008) MATHGoogle Scholar
  4. 4.
    Blitz, L., Fich, M., Kulkarni, S.: The new Milky Way. Science 220, 1233–1240 (1983) CrossRefGoogle Scholar
  5. 5.
    Brosche, P., Geffert, M., Doerenkamp, P., Tucholke, H.-J., Klemola, A.R., Ninkovic, S.: Space motions of globular clusters NGC 362 and NGC 6218 (M12). Astron. J. 102, 2022–2027 (1991) CrossRefGoogle Scholar
  6. 6.
    Caldwell, J.A.R., Ostriker, J.P.: The mass distribution within our galaxy—a three component model. Astrophys. J. 251, 61–87 (1981) CrossRefGoogle Scholar
  7. 7.
    Caranicolas, N.D.: The structure of motion in a 4-component galaxy mass model. Astrophys. Space Sci. 246, 15–28 (1997) CrossRefMATHGoogle Scholar
  8. 8.
    Caranicolas, N.D.: A map for a group of resonant cases in a quartic galactic Hamiltonian. J. Astrophys. Astron. 22, 309–319 (2001) CrossRefGoogle Scholar
  9. 9.
    Caranicolas, N.D., Innanen, K.A.: Chaos in a galaxy model with nucleus and bulge components. Astron. J. 102, 1343–1347 (1991) CrossRefGoogle Scholar
  10. 10.
    Caranicolas, N.D., Papadopoulos, N.J.: Chaotic orbits in a galaxy model with a massive nucleus. Astron. Astrophys. 399, 957–960 (2003) CrossRefGoogle Scholar
  11. 11.
    Caranicolas, N.D., Zotos, E.E.: Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits. Nonlinear Dyn. 69, 1795–1805 (2012) MathSciNetCrossRefGoogle Scholar
  12. 12.
    Carlberg, R.G., Innanen, K.A.: Galactic chaos and the circular velocity at the sun. Astron. J. 94, 666–670 (1987) CrossRefGoogle Scholar
  13. 13.
    Clutton-Brock, M., Innanen, K.A., Papp, K.A.: A theory for the gravitational potentials of spheroidal stellar systems and its application to the galaxy. Astrophys. Space Sci. 47, 299–314 (1977) CrossRefGoogle Scholar
  14. 14.
    Croswell, K., Latham, D.W., Carney, B.W., Schuster, W., Aguilar, L.: A search for distant stars in the Milky Way galaxy’s halo and thick disk. Astron. J. 101, 2078–2096 (1991) CrossRefGoogle Scholar
  15. 15.
    Dauphole, B., Geffert, M., Colin, J., Ducourant, C., Odenkirchen, M., Tucholke, H.-J.: The kinematics of globular clusters, apocentric distances and a halo metallicity gradient. Astron. Astrophys. 313, 119–128 (1996) Google Scholar
  16. 16.
    Deprit, A.: The Lissajous transformation. I Basics. Celest. Mech. Dyn. Astron. 51(3), 202–225 (1991) Google Scholar
  17. 17.
    Elipe, A.: Complete reduction of oscillators in resonance p:q. Phys. Rev. E 61, 6477–6484 (2000) CrossRefGoogle Scholar
  18. 18.
    Elmegreen, D.M.: Spiral structure of the Milky Way and external galaxies. In: The Milky Way Galaxy; Proceedings of the 106th Symposium, Groningen, Netherlands, pp. 255–272 (1983) Google Scholar
  19. 19.
    Gerhard, O.: Mass distribution in our galaxy. Space Sci. Rev. 100, 129–138 (2002) CrossRefGoogle Scholar
  20. 20.
    Hasan, H., Norman, C.A.: Chaotic orbits in barred galaxies with central mass concentrations. Astrophys. J. 361, 69–77 (1990) CrossRefGoogle Scholar
  21. 21.
    Hasan, H., Pfenniger, D., Norman, C.: Galactic bars with central mass concentrations—three-dimensional dynamics. Astrophys. J. 409, 91–109 (1993) CrossRefGoogle Scholar
  22. 22.
    Henon, M., Heiles, C.: The applicability of the third integral of motion: some numerical experiments. Astron. J. 69, 73–79 (1964) MathSciNetCrossRefGoogle Scholar
  23. 23.
    Huang, R.Q.: Evolution of rotating binary stars. Astron. Astrophys. 422, 981–986 (2004) CrossRefMATHGoogle Scholar
  24. 24.
    Huang, R.Q., Taam, R.E.: The non-conservative evolution of massive binary systems. Astron. Astrophys. 236, 107–116 (1990) Google Scholar
  25. 25.
    Miyamoto, M., Nagai, R.: Three-dimensional models for the distribution of mass in galaxies. Publ. Astron. Soc. Jpn. 27, 533–543 (1975) Google Scholar
  26. 26.
    Mülläri, A.A., Mülläri, T.B., Orlov, V.V., Petrova, A.V.: Catalogue of orbits of nearby stars: preliminary results. Astron. Astrophys. Trans. 15, 19–30 (1998) CrossRefGoogle Scholar
  27. 27.
    Papadopoulos, N.J., Caranicolas, N.D.: Chaotic orbits of distant stars. Astron. Astrophys. Trans. 24, 113–120 (2005) CrossRefGoogle Scholar
  28. 28.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in FORTRAN. Cambridge University Press, Cambridge (1992) MATHGoogle Scholar
  29. 29.
    Richstone, D.O.: Scale-free models of galaxies. II—A complete survey of orbits. Astrophys. J. 252, 496–507 (1982) CrossRefGoogle Scholar
  30. 30.
    Saha, A.: A search for distant halo RR Lyrae stars. Astrophys. J. 283, 580–597 (1984) CrossRefGoogle Scholar
  31. 31.
    Saha, A.: RR Lyrae stars and the distant galactic halo—distribution, chemical composition, kinematics, and dynamics. Astrophys. J. 289, 310–319 (1985) CrossRefGoogle Scholar
  32. 32.
    Saha, A., Oke, J.B.: Spectroscopy and spectrophotometry of distant halo RR Lyrae stars. Astrophys. J. 285, 688–697 (1985) CrossRefGoogle Scholar
  33. 33.
    Skokos, C.: Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits. J. Phys. A, Math. Gen. 34, 10029–10043 (2001) MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Skokos, Ch., Antonopoulos, Ch., Bountis, T.C., Vrahatis, M.N.: Detecting order and chaos in Hamiltonian systems by the SALI method. J. Phys. A, Math. Gen. 37, 6269–6284 (2004) MathSciNetCrossRefGoogle Scholar
  35. 35.
    Zotos, E.E.: A new dynamical model for the study of galactic structure. New Astron. 16, 391–401 (2011) CrossRefGoogle Scholar
  36. 36.
    Zotos, E.E.: Trapped and escaping orbits in an axially symmetric galactic-type potential. Publ. Astron. Soc. Aust. 29, 161–173 (2012) CrossRefGoogle Scholar
  37. 37.
    Zotos, E.E.: Application of new dynamical spectra of orbits in Hamiltonian systems. Nonlinear Dyn. 69, 2041–2063 (2012) MathSciNetCrossRefGoogle Scholar
  38. 38.
    Zotos, E.E.: Exploring the nature of orbits in a galactic model with a massive nucleus. New Astron. 17, 576–588 (2012) CrossRefGoogle Scholar
  39. 39.
    Zotos, E.E.: The fast norm vector indicator (FNVI) method: a new dynamical parameter for detecting order and chaos in Hamiltonian systems. Nonlinear Dyn. 70, 951–978 (2012) MathSciNetCrossRefGoogle Scholar
  40. 40.
    Zotos, E.E., Caranicolas, N.D.: Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials? Nonlinear Dyn. 70, 279–287 (2012) MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Physics, School of ScienceAristotle University of ThessalonikiThessalonikiGreece

Personalised recommendations