On application of statistical virial theorems

Statistics

Scientific paper

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Cosmology, Galaxies, Mass Distribution, Statistical Analysis, Virial Theorem, Hubble Diagram, Kinetic Energy, Luminous Intensity, Velocity Distribution, Weighting Functions

Scientific paper

Two effects which could bias statistical virial-theorem determinations of the mean mass density of the universe (Omega) are examined. In order to check for effects due to mass segregation, luminosity-weighted statistics for the galaxy distribution are developed. Systematic error in the determination of the characteristic peculiar velocity dispersion for galaxies is also investigated. Such bias can result from (1) correlation between the peculiar velocities of galaxies and their masses or (2) determining the mean peculiar velocity by averaging over the number of pairs of galaxies rather than the number of individual galaxies in the sample. These effects bias the estimates of Omega toward higher values, but it is found that, taken together, they have at most a 20%-30% effect on estimates of Omega. It is concluded that the value of Omega is in the range from roughly 0.2 to 0.3. The luminosity-weighted statistics offer a basis for a statistical test for relaxation effects in small systems of galaxies. With a sample deeper than those currently available, these tests could be applied effectively to a 'distance-limited' galaxy catalog.

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