The Size Distribution of Void Filaments in a ΛCDM Cosmology

The size distribution of mini-filaments in voids has been derived from the Millennium Run halo catalogs at redshifts z = 0, 0.5, 1 and 2. It is assumed that the primordial tidal field originated the presence of filamentary substructures in voids and that the void filaments have evolved only little, keeping the initial memory of the primordial tidal field. Applying the filament-finding algorithm based on the minimal spanning tree (MST) technique to the Millennium voids, we identify the mini-filaments running through voids and measure their sizes at each redshift. Then, we calculate the comoving number density of void filaments as a function of their sizes in the logarithmic interval and determine an analytic fitting function for it. It is found that the size distribution of void mini-filaments in the logarithmic interval, dN/d logS, has an almost universal shape, insensitive to the redshift: In the short-size section it is well approximated as a power-law, dN/d logS ≈ S, while in the long-size section it decreases exponentially as dN/d logS ≈ exp(−Sα). We expect that the universal size distribution of void filaments may provide a useful cosmological probe without resorting to the rms density fluctuations.