Mathematics – Logic
Scientific paper
Dec 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995aas...187.8604k&link_type=abstract
American Astronomical Society, 187th AAS Meeting, #86.04; Bulletin of the American Astronomical Society, Vol. 27, p.1413
Mathematics
Logic
Scientific paper
We present theoretical and N-body results on the correlation between velocity dispersion and local density measured in a redshift survey, as a means of constraining the cosmological density parameter, Omega . The Cosmic Virial Theorem relates the average pairwise velocity dispersion of a system of particles to Omega and the two point correlation function. We show that the Cosmic Virial Theorem is valid for suitable particle subsets, including sets corresponding to surfaces of constant density. In particular, the velocity dispersion of particles on such a surface is proportional to Omega and the density of the surface. We have calculated the velocity dispersion as a function of density for N-body simulations of several cosmological models. We find that the proportionality between velocity dispersion, density and Omega holds over redshift scales in the range 50 km s(-1) to 500 km s(-1) . This relationship is independent of the shape and the amplitude of the initial power spectrum for the range of models we address. We suggest an application of these results to redshift surveys by calculating the redshift dispersion of galaxies as a function of density on the sky. By not averaging over all densities, we can take advantage of the Omega dependence of the velocity dispersion in a way that is insensitive to the effects of a small number of high-density regions. Currently available redshift surveys are too sparse to apply this method, but a volume-limited subsample of the Sloan Digital Sky Survey should be adequate to discriminate cleanly between low and high values of Omega .
Kepner Jeremy
Strauss Michael
Summers F. J.
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