Substructure in Clusters of Galaxies and the value of $\mathbf{\Omega }$

We investigate the formation of clusters of galaxies in an expanding universe using a new code that regrids at a region of high density. In particular we investigate two models for the initial conditions, both with the standard CDM power spectrum - one has $\mathrm{\Omega }=1$ and the other $\mathrm{\Omega }=0.2$. Both universes have $H_0=100\text{kms}{\text{mpc}}^{-1}$ and $\mathrm{\Lambda }=0$. The level of substructure in the final cluster can be used as a discriminant of the cosmic density. We discuss various statistics which can be measured observationally from clusters of galaxies, that can be used to discriminate between the two models. We find that most of the statistics that use the clusters’ member galaxies may not be the best measures of substructure. Statistics that rely more on X-ray maps and other observables depending more directly on the mass distribution could be better discriminants of $\mathrm{\Omega }$.