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We focus on the influence of cosmological model on the process of formation of clusters of galaxies. Richstone, Loeb and Turner (1992 ApJ 393, 477) have shown that under the assumptions of hierarchical formation and a Gaussian random field of perturbations, the rate at which matter is currently being added to the most massive virialized structures is a strong function of $\Omega_0$, and suggested that the observed frequency of substructure in clusters might be a probe of $\Omega$. Evrard, Mohr, Fabricant and Geller (1993 ApJ Letters 419, L9) have shown that it is possible to compare SPH simulations of clusters to X-ray images of clusters using a test measuring the skewness of the image, to explore this effect. We report on calculations done in collaboration with Crone and Evrard, which explore the cosmological dependence of the cluster density profile and various tests of substructure in N-body simulations.
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