The Size of the Longest Filaments in the Universe

We analyze the filamentarity in the Las Campanas redshift survey (LCRS) and determine the length scale at which filaments are statistically significant. The largest length-scale at which filaments are statistically significant, real objects, is between 70 to $80 h^{-1}$Mpc, for the LCRS $-3^o$ slice. Filamentary features longer than $80 h^{-1}$Mpc, though identified, are not statistically significant; they arise from chance alignments. For the five other LCRS slices, filaments of lengths $50 h^{-1}$Mpc to $70 h^{-1}$Mpc are statistically significant, but not beyond. These results indicate that while individual filaments up to $80 h^{-1}$Mpc are statistically significant, the impression of structure on larger scales is a visual effect. On scales larger than $80 h^{-1}$Mpc the filaments interconnect by statistical chance to form the filament-void network. The reality of the $80 h^{-1}$Mpc features in the $-3^o$ slice make them the longest coherent features in the LCRS. While filaments are a natural outcome of gravitational instability, any numerical model attempting to describe the formation of large scale structure in the universe must produce coherent structures on scales that match these observations.Comment: 16 preprint pages, 4 figures, Replaced with accepted version in ApJ. Improved discussion and added reference