The peak-patch picture of cosmic catalogs .1. Algorithms

We develop a picture of cosmic structure formation that identifies virialized cosmological objects with a point process of ''peak patches'' in the initial (Lagrangian) space. The strongly nonlinear internal dynamics of the collapsing patch is largely decoupled from the weakly nonlinear dynamics describing peak-patch flow. A modest set of local field measurements on the patch region suffices to approximately determine the fate of the peak. The candidate peak points are identified using a hierarchy of smoothing operations on the density field. Patch size and mass are found by requiring complete collapse of a homogeneous ellipsoid model for internal patch dynamics which includes the important influence of the external tidal field. Exclusion algorithms that prevent peak-patch overlaps trim the candidate list into the final ''hierarchical peak'' list. The Zeldovich approximation with locally adaptive filtering of the displacement field is used for external dynamics to move the surviving patches to their final state (Eulerian) positions, augmented by a quadratic nonlinear correction where necessary. Thus both statistical and dynamical clustering of the peaks are included. Our technique is the natural generalization of both the Press-Schechter method (to include nonlocal effects) and the BBKS single-filter peaks theory (to allow a mass spectrum and solve the cloud-in-cloud problem). It allows efficient Monte Carlo constructions of three-dimensional catalogs of objects such as groups and clusters of galaxies, and, with more selection criteria, of galaxies in their formation phases.