The Three-dimensional Skeleton of the SDSS

The length of the three-dimensional filaments observed in the fourth public data release of the SDSS is measured using the "local skeleton" method. This consists of defining a 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, \mathstrutL} , in the SDSS survey is found to be \mathstrutL} =(52500+/- 6500) (L/{Mpc} ) ^{-1.75+/- 0.06}{Mpc} /(100 {Mpc} ) ³ for 8.2 Mpc <= L <= 16.4 Mpc, where L is the smoothing length in Mpc. This result, which deviates only slightly, as expected, from the trivial behavior \mathstrutL} \propto L^-2, is in excellent agreement with a ΛCDM cosmology, as long as the matter density parameter remains in the range 0.25 < Ω_matter < 0.4 at the 1 σ confidence level, considering the universe is flat. These measurements, which are in fact dominated by linear dynamics, are not significantly sensitive to observational artifacts such as redshift distortion, edge effects, incompleteness, and biasing. 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.