Crawling the Cosmic Network: Identifying and Quantifying Filamentary Structure

Understand

We present the Smoothed Hessian Major Axis Filament Finder (SHMAFF), an algorithm that uses the eigenvectors of the Hessian matrix of the smoothed galaxy distribution to identify individual filamentary structures.

• Filaments are traced along the Hessian eigenvector corresponding to the largest eigenvalue, and are stopped when the axis orientation changes more rapidly than a preset threshold.
• In both N-body simulations and the Sloan Digital Sky Survey (SDSS) main galaxy redshift survey data, the resulting filament length distributions are approximately exponential.
• In the SDSS galaxy distribution, using smoothing lengths of 10 h^{-1} Mpc and 15 h^{-1} Mpc, we find filament lengths per unit volume of 1.9x10^{-3} h^2 Mpc^{-2} and 7.6x10^{-4} h^2 Mpc^{-2}, respectively.