The three dimensional skeleton: tracing the filamentary structure of the universe

TL;DR

This paper extends the skeleton formalism to 3D density fields to effectively trace the universe's filamentary structure, providing a numerical method validated on Gaussian fields and applicable to cosmological simulations.

Contribution

It introduces a new 3D skeleton tracing method, analyzes its properties, and demonstrates its potential for constraining cosmological parameters and understanding galaxy formation.

Findings

The differential length scales with the density contrast PDF and spectral parameters.

Total skeleton length scales inversely with the square of the smoothing length.

Dark halo spins are orthogonal to flow directions near filaments.

Abstract

The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated here on Gaussian random fields. This method manages to trace well the filamentary structure in 3D fields such as given by numerical simulations of the dark matter distribution on large scales and is insensitive to monotonic biasing. Two of its characteristics, namely its length and differential length, are analyzed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the PDF of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length scales like the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+ n) where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology. Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark halos and the orientation of the flow near the skeleton is computed for dark matter simulations. The flow is laminar along the filaments, while spins of dark halos within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25%.