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Properties of stellar trajectories in numerical dynamical models of open star clusters

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Abstract

Stellar trajectories in models of open star clusters that are nonstationary in the regular field of the cluster are analyzed. The maximum characteristic Lyapunov exponents λ of the trajectories of the stellar motions in the open cluster are estimated. The mean λ in the open-cluster models considered are \(\bar \lambda \simeq ({\rm M}yr)^{ - 1} \). Cluster cores and halos are regions of highly stochastic and more ordered stellar motions, respectively. The mean Lyapunov exponent, \(\bar \lambda \), increases with the cluster density, as does the size of the highly stochastic region in the cluster core. The stellar trajectories in phase space are “glued” to a domain with a given λ. A Fourier analysis of the stellar trajectories in the open-cluster models is performed. The distributions of the periods of the stellar trajectories with the highest power-spectrum levels are constructed. The distributions of the periods corresponding to the most significant oscillations of the stellar trajectories exhibit peaks with periods commensurable with (or close to) those of the most significant oscillations of the regular field of the system. Specific features of the distributions of the periods of the most significant oscillations of the stellar trajectories and the origins of the formation of these features in the open-cluster models are discussed.

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References

  1. V. M. Danilov, Astron. Zh. 79, 986 (2002) [Astron. Rep. 46, 887 (2002)].

    Google Scholar 

  2. V. M. Danilov, Astron. Zh. 79, 492 (2002) [Astron. Rep. 46, 443 (2002)].

    Google Scholar 

  3. V. M. Danilov, Astron. Zh. 80, 526 (2003) [Astron. Rep. 47, 483(2003)].

    Google Scholar 

  4. H. E. Kandrup, B. L. Eckstein, and B. O. Bradley, Astron. Astrophys. 320, 65 (1997).

    ADS  Google Scholar 

  5. S. Habib, H. E. Kandrup, and M. E. Mahon, Astrophys. J. 480, 155 (1997).

    Article  ADS  Google Scholar 

  6. H. E. Kandrup, Mon. Not. R. Astron. Soc. 301, 960 (1998).

    Article  ADS  Google Scholar 

  7. D. D. Carpintero, J. C. Muzzio, and F. C. Wachlin, Celest. Mech. Dyn. Astron. 73, 159 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  8. J. C. Muzzio et al., Celest. Mech. Dyn. Astron. 81, 167 (2001).

    Article  ADS  MATH  Google Scholar 

  9. D. D. Carpintero et al., Celest. Mech. Dyn. Astron. 85, 247 (2003).

    Article  ADS  MATH  Google Scholar 

  10. J. C. Muzzio and M. E. Mosquera, Celest. Mech. Dyn. Astron. 88, 379 (2004).

    Article  ADS  Google Scholar 

  11. H. E. Kandrup and I. V. Sideris, Celest. Mech. Dyn. Astron. 82, 61 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  12. N. D. Caranicolas and Ch. L. Vozikis, Astron. Astrophys. 349, 70 (1999).

    ADS  Google Scholar 

  13. Ch. L. Vozikis, M. Varvoglis, and K. Tsiganis, Astron. Astrophys. 359, 386 (2000).

    ADS  Google Scholar 

  14. A. A. El-Zant, Astron. Astrophys. 331, 782 (1998).

    ADS  Google Scholar 

  15. C. Efthymiopoulos, G. Contopoulos, and N. Voglis, Celest. Mech. Dyn. Astron. 73, 221 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  16. N. Voglis, G. Contopoulos, and C. Efthymiopoulos, Celest. Mech. Dyn. Astron. 73, 211 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  17. E. Lega and C. Froesle, Celest. Mech. Dyn. Astron. 81, 129 (2001).

    Article  ADS  Google Scholar 

  18. Y. Papaphilippou and J. Laskar, Astron. Astrophys. 307, 427 (1996).

    ADS  Google Scholar 

  19. M. I. Rabinovich and D. I. Trubetskov, Introduction to the Theory of Oscillations and Waves (Nauchno-Izdatel’skii Tsentr “Regulyarnaya i Khaoticheskaya Dinamika,” Moscow-Izhevsk, 2000).

    Google Scholar 

  20. V. M. Danilov and A. F. Seleznev, Astron. Astrophys. Trans. 6, 85 (1994).

    Google Scholar 

  21. S. A. Kutuzov and L. P. Osipkov, Astron. Zh. 57, 28 (1980) [Sov. Astron. 24, 17 (1980)].

    ADS  MathSciNet  Google Scholar 

  22. V. M. Danilov, Astron. Zh. 65, 716 (1988) [Sov. Astron. 32, 374 (1988)].

    ADS  Google Scholar 

  23. V. M. Danilov, Astron. Zh. 77, 345 (2000) [Astron. Rep. 44, 298 (2000)].

    Google Scholar 

  24. V. M. Danilov, Astron. Zh. 74, 188 (1997) [Astron. Rep. 41, 163 (1997)].

    Google Scholar 

  25. I. R. King, Astrophys. J. 67, 471 (1962).

    ADS  Google Scholar 

  26. S. Chandrasekhar, Principles of Stellar Dynamics (Univ. of Chicago, Chicago, 1942; Inostrannaya Literatura, Moscow, 1948).

    Google Scholar 

  27. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1982; Mir, Moscow, 1984).

    Google Scholar 

  28. D. D. Carpintero and L. A. Aguilar, Mon. Not. R. Astron. Soc. 298, 1 (1998).

    Article  ADS  Google Scholar 

  29. J. Laskar, Astron. Astrophys. 198, 341 (1988).

    ADS  Google Scholar 

  30. J. Max, Methodes et Techniques de Traitement du Signal et Applications aux Mesures Physigues (Masson, New York, 1981; Mir, Moscow, 1983), Vol. 1.

    Google Scholar 

  31. V. M. Danilov, Astron. Zh. (2004) (in press).

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Authors and Affiliations

  1. Astronomical Observatory, Ural State University, pr. Lenina 51, Yekaterinburg, 620083, Russia

    V. M. Danilov & E. V. Leskov

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  1. V. M. Danilov
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  2. E. V. Leskov
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__________

Translated from Astronomicheski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Zhurnal, Vol. 82, No. 3, 2005, pp. 219–230.

Original Russian Text Copyright © 2005 by Danilov, Leskov.

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Danilov, V.M., Leskov, E.V. Properties of stellar trajectories in numerical dynamical models of open star clusters. Astron. Rep. 49, 190–200 (2005). https://doi.org/10.1134/1.1882777

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