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We present the first self-consistently computed results on the evolution of X-ray properties of galaxy clusters in a cold + hot dark matter (CHDM) model. We have performed a hydrodynamic plus N-body simulation for the COBE-compatible CHDM model with standard mass components: Omega(sub hot) = 0.3, Omega (sub cold) = 0.6 and Omega(sub baryon) = 0.1 (h = 0.5). In contrast with the CDM model, which fails to reproduce the observed temperature distribution function dN/dT (Bryan et al. 1994b), the CHDM model fits the observational dN/dT quite well. Our results on X-ray luminosity are less firm but even more intriguing. We find that the resulting X-ray luminosity functions at redshifts z = 0.0, 0.2, 0.4, 0.7 are well fit by observations, where they overlap. The fact that both temperatures and luminosities provide a reasonable fit to the available observational data indicates that, unless we are missing some essential physics, there is neither room nor need for a large fraction of gas in rich clusters: 10% (or less) in baryons is sufficient to explain their X-ray properties. We also see a tight correlation between X-ray luminosity and gas temperature.

We propose that the Coma cluster has recently undergone a collision with the NGC 4839 galaxy group. The ROSAT X-ray morphology, the Coma radio halo, the presence of poststarburst galaxies in the bridge between Coma and NGC 4839, the usually high velocity dispersion for the NGC 4839 group, and the position of a large-scale galaxy filament to the NE of Coma are all used to argue that the NGC 4839 group passed through the core of Coma approximately 2 Gyr ago. We present a new Hydro/N-body simulation of the merger between a galaxy group and a rich cluster that reproduces many of the observed X-ray and optical properties of Coma/NGC 4839.

We study percolation in mass and galaxy distributions obtained in 3D simulations of the CDM, C + HDM, and the power law (n = -1) models in the Omega = 1 universe. Percolation statistics is used here as a quantitative measure of the degree to which a mass or galaxy distribution is of a filamentary or cellular type. The very fast code used calculates the statistics of clusters along with the direct detection of percolation. We found that the two parameters mu(infinity), characterizing the size of the largest cluster, and mu-squared, characterizing the weighted mean size of all clusters excluding the largest one, are extremely useful for evaluating the percolation threshold. An advantage of using these parameters is their low sensitivity to boundary effects. We show that both the CDM and the C + HDM models are extremely filamentary both in mass and galaxy distribution. The percolation thresholds for the mass distributions are determined.

We present a new criterion for formation of second-generation filaments. The criterion called the kinetic energy ratio, KR, is based on comparison of peculiar velocities at different scales. We suggest that the clumpiness of the distribution in some cases might be less important than the 'coldness' or 'hotness' of the flow for formation of coherent structures. The kinetic energy ratio is analogous to the Mach number except for one essential difference. If at some scale KR is greater than 1, as estimated at the linear stage, then when fluctuations of this scale reach nonlinearity, the objects they produce must be anisotropic ('filamentary'). In the case of power-law initial spectra the kinetic ratio criterion suggests that the border line is the power-spectrum with the slope n = -1.