Analytic Approach to the Cloud‐in‐Cloud Problem for Non‐Gaussian Density Fluctuations

Abstract

We revisit the cloud-in-cloud problem for non-Gaussian density fluctuations. We show that the extended Press-Schechter (EPS) formalism for non-Gaussian fluctuations has a flaw in describing mass functions regardless of the type of filtering. As an example, we consider non-Gaussian models in which density fluctuations at a point obey a χ2 distribution with ν degrees of freedom. We find that mass functions predicted by using an integral formula proposed by Jedamzik and Yano, Nagashima, and Gouda, properly taking into account correlation between objects at different scales, deviate from those predicted by using the EPS formalism, especially for strongly non-Gaussian fluctuations. Our results for the mass function at large mass scales are consistent with those by Avelino and Viana obtained from numerical simulations.