THE CLOUD-IN-CLOUD PROBLEM IN THE PRESS-SCHECHTER FORMALISM OF HIERARCHICAL STRUCTURE FORMATION

The formalism by Press and Schechter (PS) is often used to infer number densities of virialized objects of mass M (e.g., quasars, galaxies, clusters of galaxies, etc.) from a count of initially overdense regions in a Gaussian density perturbation field. We reanalyze the PS formalism by explicitly counting underdense regions which are embedded within overdense regions, so-called cloud-in-clouds. In contrast to the original PS formalism, our revised analysis automatically accounts for all the cosmic material. We find that mass distribution functions for virialized objects are altered by the solution of the cloud-in-cloud problem. These altered distribution functions agree much better with distribution functions inferred from N-body simulations than the original PS distribution functions.