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**Session 86 - Measurement of Cosmological Parameters.**

*Oral session, Wednesday, January 17*

*1st Floor, La Villita Assembly Building*

## [86.04] Omega from sigma: Measuring the Cosmological Density with the Redshift Dispersion of Galaxies

*J. Kepner, F. J. Summers, M. Strauss (Princeton)*
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, Ømega. The Cosmic Virial Theorem relates the
average pairwise velocity dispersion of a system of particles to
Ømega 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 Ømega 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 Ømega 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
Ømega 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 Ømega.

**Program
listing for Wednesday**