A CATALOG OF GALAXY CLUSTER-MODELS

We present a technique to construct a fair sample of simulated galaxy clusters, and build such a sample for a specific cosmological structur e formation scenario. Conventionally one extracts such a sample from a single low-resolution large-scale simulation. Here we simulate the cl usters individually at high resolution. This is made possible by the m ethod of constrained random fields, in which one can put linear constr aints on peaks in the initial smoothed density field. We assume that t hese peaks are the progenitors of present-day rich clusters, and selec t clusters for a catalogue by selecting their initial peak parameters. We find that the final cluster mass can be well approximated by a lin ear function of both the amplitude and the curvature of the initial de nsity peak. Because the probability distributions of these peak parame ters are known, we can construct a model catalogue selected on expecte d final cluster mass. Such a catalogue will not have a well-defined ri chness limit, because the relation between richness and mass is fairly broad. However, by applying the appropriate completeness corrections, the results for the mass-selected catalogue can be compared with obse rvations for richness-selected cluster catalogues. Each cluster model is evolved from its constrained initial conditions by means of an N-bo dy integrator. This includes an algorithm for galaxy formation, so we produce two-component models consisting of dark matter background part icles and galaxies. The latter allow us to obtain directly the observa ble properties of the cluster models, and match these to the observed properties to define the present time in the models, and thus derive t he amplitude of the initial density fluctuation spectrum, sigma(8). We build a model cluster catalogue for the Omega(0) = 1 cold dark matter (CDM) scenario that is designed to mimic the ENACS sample of rich Abe ll clusters. We use the distribution of richness, corrected for incomp leteness, to fix the present epoch. We find sigma(s) = 0.4-0.5, which is consistent with other determinations. The catalogue is 70 per cent complete for a richness larger than 50, but we do have a complete subs ample for richnesses larger than 75. As a first test we compare the cu mulative distribution of line-of-sight velocity dispersions to those f ound for several observational samples, and find that they match best for sigma(8) approximate to 0.4. This means that we fmd consistent val ues for sigma(8) for the CDM Omega(0) = 1 scenario on cluster scales.