, Volume 39, Issue 1, pp 63–70 | Cite as

Necessary criteria for spatial uniformity of groups of galaxies

  • G. A. Saiyan


In order to search for spatially uniform groups of galaxies, two necessary criteria for systems of this type are constructed. The pairwise distribution of galaxies (the distribution of their mutual distances) in the picture plane is used in both cases. This distribution is derived theoretically (in the limit N → ∞, where N is the number of galaxies in the group) and numerically for finite N. For this we considered the orthogonal projection onto a plane of a uniform Poisson process in a sphere of some radius. In the first criterion we use the Kolmogorov criterion to compare the calculated and observed integral pairwise distributions. In the second criterion we use dimensionless statistics associated with the moments of the pairwise distribution. An investigation of the Geller-Huchra and Mahtessian catalogs, in which groups of galaxies were selected based on the condition 9 ≤ N ≤ 30, showed that the overwhelming majority of these systems are spatially nonuniform. Some dynamical consequences of these results are discussed.


Poisson Process Orthogonal Projection Dynamical Consequence Overwhelming Majority Mutual Distance 
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  1. 1.
    V. Trimble, Annu. Rev. Astron. Astrophys.,25, 425 (1987).CrossRefGoogle Scholar
  2. 2.
    V. A. Ambartsumian, Scientific Works [in Russian], Izd. Akad. Nauk Arm. SSR, Erevan (1960).Google Scholar
  3. 3.
    G. B. Field and W. C. Saslaw, Astrophys. J.,170, 199 (1971).CrossRefGoogle Scholar
  4. 4.
    S. J. Aarseth and W. C. Saslaw, Astrophys. J.172, 17 (1972).CrossRefGoogle Scholar
  5. 5.
    H. J. Rood and J. R. Dickel, Astrophys. J.,224, 724 (1978).CrossRefGoogle Scholar
  6. 6.
    F. R. Klinkhammer, Astron. Astrophys.,91, 365 (1980).Google Scholar
  7. 7.
    B. A. Williams, in: Clusters and Groups of Galaxies. Proceedings of International Meeting Held in Trieste, Italy, September 13–16, F. Mardirosian, G. Giuricin, and M. Mezzetti, eds. (1983), p. 375.Google Scholar
  8. 8.
    L. A. Santaló, Integral Geometry and Geometric Probability, Cambridge University Press, Cambridge (1984), 404 pp.Google Scholar
  9. 9.
    M. Geller and J. Huchra, Astrophys. J. Suppl. Ser.,52, 61 (1983).CrossRefGoogle Scholar
  10. 10.
    A. P. Mahtessian, Groups of Galaxies II. General List, Preprint of Byurakan Astrophysical Observatory (1995).Google Scholar
  11. 11.
    R. D. Lord, Ann. Math. Stat.,25, 794 (1954).Google Scholar
  12. 12.
    H. Bateman, Higher Transcendental Functions, Bateman Manuscript Project, A. Erdelyi, Dir., McGraw-Hill, New York (1953).Google Scholar
  13. 13.
    G. N. Watson, A Treatise on the Theory of Bessel Functions, Vol. 1, University Press, Cambridge — New York (1944).Google Scholar
  14. 14.
    M. Sanroma and E. Salvador-Sole, Astrophys. J.,342, 17 (1989).CrossRefGoogle Scholar
  15. 15.
    E. Salvador-Sole and M. Sanroma, Astrophys. J.,345, 660 (1989).CrossRefGoogle Scholar
  16. 16.
    S. M. Kudryavtsev, Vestn. Leningr. Gos. Univ.,15, 74 (1985).Google Scholar
  17. 17.
    G. A. Saiyan, Astron. Zh.,68, No. 5, 1036 (1991) [G. A. Sahian, Sov. Astron.,35, No. 5, 518 (1991)].Google Scholar
  18. 18.
    J. M. Hammersley, Ann. Math. Stat.,21, 447 (1950).Google Scholar
  19. 19.
    Yu. A. Kaz'min, "The moment problem," in: Mathematical Encyclopedia [in Russian], Vol. 3, Moscow (1982), p. 794.Google Scholar
  20. 20.
    M. Ramella, M. Geller, and J. Huchra, Astrophys. J.,344, 57 (1989).CrossRefGoogle Scholar
  21. 21.
    J. P. Huchra and M. J. Geller, Astrophys. J. Suppl. Ser.,99, 391 (1995).CrossRefGoogle Scholar
  22. 22.
    R. A. Vardanyan and Yu. K. Melik-Alaverdyan, Astrofizika,14, No. 1, 195 (1978).Google Scholar
  23. 23.
    N. A. Bahcall, Astrophys. J.,198, 249 (1975).CrossRefGoogle Scholar
  24. 24.
    N. A. Bahcall, Annu. Rev. Astron. Astrophys.,15, 505 (1977).CrossRefGoogle Scholar
  25. 25.
    S. A. Gregory and W. G. Tifft, Astrophys. J.,206, 934 (1976).CrossRefGoogle Scholar
  26. 26.
    C. A. Sarazin, Rev. Mod. Phys.,58, 1 (1986).CrossRefGoogle Scholar
  27. 27.
    P. Hickson, Astrophys. J.,217, 16 (1977).CrossRefGoogle Scholar
  28. 28.
    P. Hickson, Z. Ninkov, J. P. Huchra, and G. A. Mamon, in: Clusters and Groups of Galaxies. Proceedings of International Meeting Held in Trieste, Italy, September 13–16, F. Mardirosian, G. Giuricin, and M. Mezzetti, eds., (1983), p. 367.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • G. A. Saiyan
    • 1
  1. 1.Byurakan Astrophysical ObservatoryArmenia

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