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 proper solution of the cloud-in-cloud problem. These altered distribution functions agree much better with distribution functions inferred form N-body simulations than the original PS-distribution functions.