The formation of CDM haloes – I. Collapse thresholds and the ellipsoidal collapse model

Abstract

In the excursion set approach to structure formation initially spherical regions of the linear density field collapse to form haloes of mass M at redshift z id if their linearly extrapolated density contrast, averaged on that scale, exceeds some critical threshold, δ c (z id ). The value of δ c (z id ) is often calculated from the spherical or ellipsoidal collapse model, which provide well-defined predictions given auxiliary properties of the tidal field at a given location. We use two cosmological simulations of structure growth in a Λ cold dark matter scenario to quantify δ c (z id ), its dependence on the surrounding tidal field, as well as on the shapes of the Lagrangian regions that collapse to form haloes at z id . Our results indicate that the ellipsoidal collapse model provides an accurate description of the mean dependence of δ c (z id ) on both the strength of the tidal field and on halo mass. However, for a given z id , δ c (z id ) depends strongly on the halo's characteristic formation redshift: the earlier a halo forms, the higher its initial density contrast. Surprisingly, the majority of haloes forming today fall below the ellipsoidal collapse barrier, contradicting the model predictions. We trace the origin of this effect to the non-spherical shapes of Lagrangian haloes, which arise naturally due to the asymmetry of the linear tidal field. We show that a modified collapse model, that accounts for the triaxial shape of protohaloes, provides a more accurate description of the measured minimum overdensities of recently collapsed objects.

Concentration, ellipsoidal collapse, and the densest dark matter haloes

“…This was subsequently corroborated by later studies, e.g., Ludlow, Borzyszkowski & Porciani (2014), who investigated the protohaloes of collapsed haloes in simulations. Equation 45 is extremely useful since it allows us to incorporate the effect of ellipsoidal collapse into our concentration-mass relation.…”

The Hunt for Primordial Interactions in the Large-Scale Structures of the Universe

“…The first line is leading order in δ and the non-Gaussian correction ψ, where we have considered the leading order in Eq. (155), while the second line is second order. We do not include terms which are second order in ψ given that from current CMB observations we expect PNG corrections to be small [6].…”

Galaxies flowing in the oriented saddle frame of the cosmic web

“…Haloes that are close to more massive structures are on the other hand expected to be stalled and their growth may stop earlier, as their mass inflow is dynamically quenched by anisotropic tides generated in their vicinity (e.g. Dalal et al 2008;Hahn et al 2009;Ludlow et al 2014;Borzyszkowski et al 2017;Paranjape et al 2018a). Individual properties of dark matter haloes, such as their mass, formation time or accretion, are thus expected to be affected by the exact position of haloes within the large-scale anisotropic cosmic web (e.g.…”