Which filaments matter: the relative scalings of anisotropic infall

TL;DR

This paper derives the characteristic scale at which anisotropic tidal fields influence dark matter halo formation, providing practical scaling laws for cosmological surveys and simulations.

Contribution

It introduces a first-principles derivation of the scale ratio where tidal effects most impact halo formation in a LambdaCDM universe.

Findings

The inflection point of the tidal compression probability occurs at Rsd/Rpk ≈ 2.2 + (nu - 2.5).

The anisotropic tidal influence extends to 2-3 times the Lagrangian patch size.

Filament scale around 2.5 sigma peaks varies with redshift as Rsd(z) = 31 /(2+(1+z)**2) Mpc/h.

Abstract

Dark-matter haloes do not form in isolation but within the surrounding cosmic web. By the time a halo begins to collapse, its larger-scale environment has typically collapsed along two axes, forming filaments that channel anisotropic infall toward the halo. In this work, we derive from first principles the characteristic Lagrangian scale ratio at which such an anisotropic tidal field most strongly influences halo formation. Specifically, we identify the inflection point of the conditional probability that the tidal field, smoothed on a scale Rsd, undergoes two-dimensional compression, given the presence of a density peak of rarity nu on a smaller scale Rpk. For a standard LambdaCDM cosmology, we find (Rsd/Rpk)infl = 2.2 + (nu-2.5) for Rpk corresponding to a tophat filter of 8Mpc/h. This result implies that the anisotropic tidal influence on a collapsing halo typically extends to 2-3 times the size of its Lagrangian patch. Recast as a function of formation redshift z, the characteristic filament scale around 2.5 sigma peaks can be approximated by Rsd(z) = 31 /(2+(1+z)**2)Mpc/h. We provide practical scaling laws for selecting dynamically relevant smoothing scales in large-scale surveys and for setting initial patch sizes in high-resolution zoom simulations.