Cosmic web reconstruction through density ridges: Catalogue

We construct a catalogue for filaments using a novel approach called SCMS (subspace constrainedmean shift). SCMS is a gradient-based method that detects filaments through densityridges (smooth curves tracing high-density regions). A great advantage of SCMS is its uncertaintymeasure, which allows an evaluation of the errors for the detected filaments. Todetect filaments, we use data from the Sloan Digital Sky Survey, which consist of three galaxysamples: the NYU main galaxy sample (MGS), the LOWZ sample and the CMASS sample.Each of the three data set covers different redshift regions so that the combined sample allowsdetection of filaments up to z = 0.7. Our filament catalogue consists of a sequence of twodimensionalfilament maps at different redshifts that provide several useful statistics on theevolution cosmic web. To construct the maps, we select spectroscopically confirmed galaxieswithin 0.050 < z < 0.700 and partition them into 130 bins. For each bin, we ignore the redshift,treating the galaxy observations as a 2-D data and detect filaments using SCMS. The filamentcatalogue consists of 130 individual 2-D filament maps, and each map comprises points onthe detected filaments that describe the filamentary structures at a particular redshift. We alsoapply our filament catalogue to investigate galaxy luminosity and its relation with distance tofilament. Using a volume-limited sample, we find strong evidence (6.1σ-12.3σ) that galaxiesclose to filaments are generally brighter than those at significant distance from filaments.