Galaxy Clusters in the Hubble Volume Simulations
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abstract

We report on analyses of cluster samples obtained from the Hubble Volume
Simulations. These simulations, an $\Omega=1$ model named $\tau$CDM and a flat
low $\Omega$ model with a cosmological constant ($\Lambda$CDM), comprise the
largest computational efforts to date in numerical cosmology. We investigate
the presence of massive galaxy clusters at $z\approx 0.8$. The $\tau$CDM model
fails to form clusters at such a redshift. However, due to the small number of
observed clusters around $z\approx 0.8$ and the uncertainties in the
determinations of their masses, this conclusion still is somewhat preliminary.
We produce cluster catalogs at $z=0$ for both cosmologies and investigate their
two--point correlation function $\xi$. We show that the relationship between
the mean density of subsamples of clusters, expressed via their mean separation
$d_{\rm c}$, and the correlation length $r_0$, defined through $\xi(r_0) = 1$,
is not linear but turns over gently for large $d_{\rm c}$. An analytic
prediction by Mo & White (1996) overpredicts $r_0$. The results from the
analysis of the APM cluster data by Croft et al. (1997) are nicely matched by
the $\Lambda$CDM model.