The 3D skeleton of the SDSS

TL;DR

This paper measures the length of 3D filaments in the SDSS galaxy survey using the local skeleton method, finding results consistent with DM cosmology and demonstrating the method's robustness against observational biases.

Contribution

It introduces a novel application of the local skeleton method to quantify filament lengths in galaxy surveys, providing a new tool for analyzing cosmic filamentary structures.

Findings

Filament length per unit volume follows a power-law with smoothing length.

Results agree with DM cosmology within certain matter density ranges.

Method is robust against observational biases.

Abstract

The length of the three-dimensional filaments observed in the fourth public data-release of the SDSS is measured using the {\em local skeleton} method. It consists in defining the set of points where the gradient of the smoothed density field is extremal along its isocontours, with some additional constraints on local curvature to probe actual ridges in the galaxy distribution. A good fit to the mean filament length per unit volume, $\cal{L}$, in the SDSS survey is found to be ${\cal{L}}=(52500\pm6500) (L/{\rm Mpc})^{-1.75\pm0.06}\rm{Mpc}/(100 \rm{Mpc})^{3}$ for $8.2 \leq L \leq 16.4$ Mpc, where $L$ is the smoothing length in Mpc. This result, which deviates only slightly, as expected, from the trivial behavior ${\cal{L}} \propto L^{-2}$, is in excellent agreement with a $\Lambda$CDM cosmology, as long as the matter density parameter remains in the range $0.25 < \Omega_{\rm matter} < 0.4$ at one sigma confidence level, considering the universe is flat. These measurements, which are in fact dominated by linear dynamics, are not significantly sensitive to observational biases such as redshift distortion, edge effects, incompleteness, and biasing between the galaxy distribution and the dark matter distribution. Hence it is argued that the local skeleton is a rather promising and discriminating tool for the analysis of filamentary structures in three-dimensional galaxy surveys.