The Universal Size Distribution of the Mini-filaments in Voids

The size distribution of the 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 anisotropy in the distribution of the void halos which resulted in the presence of the mini-filaments in the void regions ad that the mini-filaments in the voids are pristine without being modified severely in the evolutionary stages. Applying the filament-finding-algorithm based on the minimal spanning technique to the Millennium voids, we identify the minifilaments connecting the void halos and measure their sizes at each redshift. Then, we calculate the comoving number density of the void mini-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 the 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 powerlaw, dN/d logS ≈ S, while in the long-size section it decreases exponentially as dN/d logS ≈ exp[−S/(2S 0)], with S0 ≈ 11 h Mpc . We expect that the universal size distribution of the void filaments may provide a useful cosmological probe without resorting to the rms density fluctuation, σ. Subject headings: cosmology:theory — large-scale structure of universe