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Crawling the Cosmic Network: Identifying and Quantifying Filamentary Structure

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. The filament width distributions, which are much more sensitive to non-linear growth, are also consistent between the real and mock galaxy distributions using a standard cosmology. In SDSS, we find mean filament widths of 5.5 h^{-1} Mpc and 8.4 h^{-1} Mpc on 10 h^{-1} Mpc and 15 h^{-1} Mpc smoothing scales, with standard deviations of 1.1 h^{-1} Mpc and 1.4 h^{-1} Mpc, respectively. Finally, the spatial distribution of filamentary structure in simulations is very similar between z=3 and z=0 on smoothing scales as large as 15 h^{-1} Mpc, suggesting that the outline of filamentary structure is already in place at high redshift.