Triaxial collapse and virialisation of dark-matter haloes

TL;DR

This paper refines the ellipsoidal-collapse model for dark matter haloes by introducing a hybrid external shear treatment and a tensor virial theorem-based virialisation criterion, leading to improved predictions of collapse parameters and mass functions.

Contribution

It extends the ellipsoidal-collapse model with a hybrid shear treatment and a physically motivated virialisation criterion, providing more accurate collapse parameters and mass functions.

Findings

Collapse parameters increase with ellipticity and decrease with prolaticity.

Hybrid shear model results are similar to non-linear model, but ellipsoidal collapse impacts parameters by 20-50%.

Mass function aligns well with recent literature, with notable differences at low mass and high redshift.

Abstract

We reconsider the ellipsoidal-collapse model and extend it in two ways: We modify the treatment of the external gravitational shear field, introducing a hybrid model in between linear and non-linear evolution, and we introduce a virialisation criterion derived from the tensor virial theorem to replace the ad-hoc criterion employed so far. We compute the collapse parameters delta_c and Delta_v and find that they increase with ellipticity e and decrease with prolaticity p. We marginalise them over the appropriate distribution of e and p and show the marginalised results as functions of halo mass and virialisation redshift. While the hybrid model for the external shear gives results very similar to those obtained from the non-linear model, ellipsoidal collapse changes the collapse parameters typically by (20...50)%, in a way increasing with decreasing halo mass and decreasing virialisation redshift. We qualitatively confirm the dependence on mass and virialisation redshift of a fitting formula for delta_c, but find noticeable quantitative differences in particular at low mass and high redshift. The derived mass function is in good agreement with mass functions recently proposed in the literature.