Spherical collapse of dark matter haloes in tidal gravitational fields

Abstract

We study the spherical collapse model in the presence of external gravitational tidal shear fields for different dark energy scenarios and investigate the impact on the mass function and cluster number counts. While previous studies of the influence of shear and rotation on δ c have been performed with heuristically motivated models, we try to avoid this model dependence and sample the external tidal shear values directly from the statistics of the underlying linearly evolved density field based on first order Lagrangian perturbation theory. Within this selfconsistent approach, in the sense that we restrict our treatment to scales where linear theory is still applicable, only fluctuations larger than the scale of the considered objects are included into the sampling process which naturally introduces a mass dependence of δ c . We find that shear effects are predominant for smaller objects and at lower redshifts, i. e. the effect on δ c is at or below the percent level for the ΛCDM model. For dark energy models we also find small but noticeable differences, similar to ΛCDM. The virial overdensity ∆ V is nearly unaffected by the external shear. The now mass dependent δ c is used to evaluate the mass function for different dark energy scenarios and afterwards to predict cluster number counts, which indicate that ignoring the shear contribution can lead to biases of the order of 1σ in the estimation of cosmological parameters like Ω m , σ 8 or w.

Halo collapse: virialization by shear and rotation in dynamical dark-energy models. Effects on weak-lensing peaks

“…The works by [10] and [11] achieved the virialization with σ 2 − ω 2 ∝ 1/δ. Instead, with σ 2 − ω 2 ∝ δ though, including virialization a posteriori, [13][14][15] obtained a delayed collapse but a virial overdensity substantially increased, while using the Zel'dovich approximation [27][28][29] found a negligible effect on ∆ vir and a one percent variation for δ c .…”

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].…”

On the implementation of the spherical collapse model for dark energy models

“…In the following we will present numerical results only for the linearly evolved overdensity δ c and show results for the virial overdensity ∆ V only for the optimised code, since this quantity is totally unaffected by numerical problems or the exact value of the initial conditions. For a more detailed analysis of why this is the case, we refer the reader to [123] in the more general analysis of the effect of the shear and rotation invariants. Figure 1.…”