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A cosmic virial theorem

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A new type of cosmic virial theorem is derived, representing a relation among the two-point and three-point galaxy correlation functions and the mean square relative peculiar velocity 〈v 2(r)〉 averaged over pairs of galaxies separated by distancer. The two correlation functions seem to be fairly well known, but 〈v 2(r)〉 at best is only very roughly estimated from available data. It might be possible to improve the estimate through a systematic program of redshift measurements in sample areas. If so, the cosmic virial theorem might yield an interesting measure of the mean mass density due to galaxies.

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  1. Dmitriev, N. A. and Zel'dovich, Ya. B.: 1963,Zhurn. Eksp. Teor. Fiz. 45, 1150; Engl. tr. inSoviet Physics — J.E.T.P. 18, 793, 1964.

  2. Fall, S. M.: 1975,Monthly Notices Roy. Astron. Soc. 172, 23p.

  3. Gott, J. R., Wrixon, G. T., and Wannier, P.: 1973,Astrophys. J. 186, 777.

  4. Geller, M. J. and Davis, M.: 1975,Bull. Am. Astr. Soc. 7, 414.

  5. Geller, M. J. and Peebles, P. J. E.: 1973,Astrophys. J. 184, 329.

  6. Irvine, W. M.: 1961,Local Irregularities in a Universe Satisfying the Cosmological Principle, Doctoral Thesis, Harvard Univ., Cambridge.

  7. Irvine, W. M.: 1965,Ann. Phys. (N.Y.) 32, 322.

  8. Layzer, D.: 1963,Astrophys. J. 138, 174.

  9. Peebles, P. J. E.: 1971,Physical Cosmology, Princeton Univ. Press, Princeton, N.J.

  10. Peebles, P. J. E.: 1973,Astrophys. J. 185, 413.

  11. Peebles, P. J. E.: 1974,Astron. Astrophys. 32, 197.

  12. Peebles, P. J. E.: 1975,Astrophys. J. 196, 647.

  13. Peebles, P. J. E. and Groth, E. J.: 1975,Astrophys. J. 196, 1.

  14. Roberts, M. S.: 1967 (private communication).

  15. Soneira, R. and Peebles, P. J. E.: 1976, to be published.

  16. Vaucouleurs, A. de and Vaucouleurs, G. de: 1967,Astron. J. 72, 730.

  17. Vaucouleurs, G. de and Vaucouleurs, A. de: 1964,Reference Catalogue of Bright Galaxies, Univ. of Texas Press, Austin.

  18. Zel'dovich, Ya. B.: 1965,Adv. Astron. Astrophys. 3, 241.

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Research supported in part by the National Science Foundation.

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Peebles, P.J.E. A cosmic virial theorem. Astrophys Space Sci 45, 3–19 (1976). https://doi.org/10.1007/BF00642136

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  • Correlation Function
  • Mass Density
  • Sample Area
  • Systematic Program
  • Virial Theorem