Shear and vorticity in the spherical collapse of dark matter haloes

TL;DR

This paper examines how shear and vorticity influence the spherical collapse of dark matter haloes by incorporating these effects into the Raychaudhuri equation, providing a more detailed understanding of structure formation.

Contribution

It introduces a novel approach to include shear and rotation effects as external influences in the spherical collapse model based on peaks in Gaussian random fields.

Findings

Shear and vorticity significantly modify collapse dynamics.

External shear and rotation alter the critical over-density $\delta_c$.

The model offers improved predictions for halo formation.

Abstract

Traditionally the spherical collapse of objects is studied with respect to a uniform background density, yielding the critical over-density $\delta_\mathrm{c}$ as key ingredient to the mass function of virialized objects. Here we investigate the shear and rotation acting on a peak in a Gaussian random field. By assuming that collapsing objects mainly form at those peaks, we use this shear and rotation as external effects changing the dynamics of the spherical collapse, which is described by the Raychaudhuri equation. We therefore assume that the shear and rotation have no additional dynamics on top of their cosmological evolution and thus only appear as inhomogeneities in the differential equation.