Shear and vorticity in the spherical collapse of dark matter haloes

Abstract

Traditionally the spherical collapse of objects is studied with respect to a uniform background density, yielding the critical over-density δ 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.We find that the shear will always be larger than the rotation at peaks of the random field, which automatically results into a lower critical over-density δ c , since the shear always supports the collapse, while the rotation acts against it. Within this model δ c naturally inherits a mass dependence from the Gaussian random field, since smaller objects are exposed to more modes of the field. The overall effect on δ c is approximately of the order of a few percent with a decreasing trend to high masses.

Quasi-spherical collapse of matter in ΛCDM

“…Instead one is led to investigate the collapse directly at the level of the equations of motion. This is for example necessary when incorporating the effect of shear or rotation, as has been done by Reischke et al (2018). Another interesting example is when investigating the collapse within the framework of general modifications of the gravitational theory, such as the class of f (R) theories (Starobinsky 2007;Hu & Sawicki 2007).…”

Tidal virialization of dark matter haloes with clustering dark energy

“…In this work, we build upon the extended formalism outlined in [1] and study the effects of shear and rotation in clustering dark-energy models. Our work differs from previous works in the literature on the same subject [17][18][19] as in this case deviations from spherical symmetry are the cause of virialization, while before virialization was achieved by considering the virial theorem.…”

A high precision semi-analytic mass function

“…As smaller scales statistically hold larger shear and angular momentum, collapse of structures at those scales require a higher density contrast. Those results have been extended more recently by [83][84][85][86][87][88][89] for models with dark matter and dark energy.…”

“…3)] 11. For an alternative description of the effects of tidal shear and angular momentum for the ΛCDM and dark energy models, we refer to[87][88][89].…”