Non-linear Dynamics and Mass Function of Cosmic Structures: I Analytical Results

TL;DR

This paper explores modifications to the Press & Schechter model by incorporating shear and tidal effects, leading to more accurate mass functions that better match observed galaxy luminosity distributions.

Contribution

It introduces analytical prescriptions for collapse times along different axes, improving the modeling of structure formation beyond the spherical approximation.

Findings

Mass function with shear effects predicts more high-mass objects.

Collapse delays along certain axes reduce high-mass object counts.

Shear influences low-mass halo formation, affecting the luminosity function.

Abstract

We investigate some modifications to the Press & Schechter (1974) (PS) prescription resulting from shear and tidal effects. These modifications rely on more realistic treatments of the collapse process than the standard approach based on the spherical model. First, we show that the mass function resulting from a new approximate Lagrangian dynamic (Audit & Alimi 96), contains more objects at high mass, than the classical PS mass function and is well fitted by a PS-like function with a threshold density of $\delta_c \simeq 1.4$. However, such a Lagrangian description can underestimate the epoch of structure formation since it defines it as the collapse of the first principal axis. We therefore suggest some analytical prescriptions, for computing the collapse time along the second and third principal axes, and we deduce the corresponding mass functions. The collapse along the third axis is delayed by the shear and the number of objects of high mass then decreases. Finally, we show that the shear also strongly affects the formation of low-mass halos. This dynamical effect implies a modification of the low-mass slope of the mass function and allows the reproduction of the observed luminosity function of field galaxies. In a companion paper, we present results of numerical simulations which complete this work.