The Peak-Patch Picture of Cosmic Catalogs. II. Validation

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Abstract
We compare hierarchical peak-patch catalogs with groups and clusters constructed using Couchman's adaptive P(3)M simulations of a ''standard'' CDM model with amplitude parameter sigma(8) approximate to 1. The N-body groups are found using an identification algorithm based on average cluster overdensity and the peak-patch properties were determined using algorithms from Paper I. We show that the best agreement is obtained if we use (1) density peaks rather than shear eigenvalue peaks as candidate points, (2) ellipsoidal rather than spherical collapse dynamics, thereby including external tidal effects, and (3) a binary reduction method as opposed to a full exclusion method for solving the cloud-in-cloud problem of peak theory. These are also the best choices physically. The mass and internal energy distributions of the peaks and groups are quite similar, but the group kinetic energy distribution is offset by similar to 12% in velocity dispersion, reflecting our finding that the N-body clusters are invariably out of isolated virial equilibrium. Individual peak-to-group comparisons show good agreement for high-mass, tightly bound groups, with growing scatter for lower masses and looser binding. The final state (Eulerian) spatial distribution of peak patches and N-body clusters are shown to be satisfyingly close. There is indication for the necessity of a small nonlinear correction to the Zeldovich peak velocities.

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