Non-linear dynamics and mass function of cosmic structures. II Numerical results

TL;DR

This paper compares analytical and numerical mass functions of cosmic structures, demonstrating that the extended Press & Schechter formalism combined with the friend-of-friend algorithm best matches simulation results and captures structure formation properties.

Contribution

It shows for the first time that the extended PS formalism can reproduce not only mass functions but also initial properties and collapse times of cosmic structures.

Findings

Friend-of-friend algorithm best matches extended PS predictions.

Extended PS formalism reproduces initial statistical properties.

The approach provides a coherent picture of structure formation.

Abstract

We compare the mass functions obtained analytically, in the framework of an extended Press & Schechter (PS) formalism, in a previous paper to the numerical mass functions obtained in N -- body simulations, using different algorithms to define objects in the density field. After discussing the properties of the algorithms, we show that the mass function obtained using the friend -- of -- friend algorithm reproduces best the scaling behaviors predicted in the extended PS formalism. Following this statistical analysis, we show that it is possible in the framework of our extended PS formalism to reproduce the mass function but also, and for the first time, the initial statistical properties of structures and their collapse time. This allow to present a ``coherent'' picture of structure formation which can account for the initial, final and dynamical properties of structures.