The persistent cosmic web and its filamentary structure - II. Illustrations

The recently introduced discrete persistent structure extractor (DisPerSE, Sousbie, Paper I) is implemented on realistic 3D cosmological simulations and observed redshift catalogues; it is found that DisPerSE traces very well the observed filaments, walls and voids seen both in simulations and in observations. In either setting, filaments are shown to connect on to haloes, outskirt walls, which circumvent voids, as is topologically required by the Morse theory. Indeed this algorithm returns the optimal critical set while operating directly on the particles. DisPerSE, as illustrated here, assumes nothing about the geometry of the survey or its homogeneity, and yields a natural (topologically motivated) self-consistent criterion for selecting the significance level of the identified structures. It is shown that this extraction is possible even for very sparsely sampled point processes, as a function of the persistence ratio (a measure of the significance of topological connections between critical points). Hence, astrophysicists should be in a position to trace precisely the locus of filaments, walls and voids from such samples and assess the confidence of the post-processed sets as a function of this threshold, which can be expressed relative to the expected amplitude of shot noise. In a cosmic framework, this criterion is shown to level with the friends-of-friends structure finder for the identification of peaks, while it also identifies the connected filaments and walls, and quantitatively recovers the full set of topological invariants (number of holes, etc.) directly from the particles, and at no extra cost as a function of the persistence threshold. This criterion is found to be sufficient even if one particle out of two is noise, when the persistence ratio is set to 3 sigma or more. The algorithm is also implemented on the SDSS catalogue and used to locate interesting configurations of the filamentary structure. In this context, we carried the identification of an 'optically faint' cluster at the intersection of filaments through the recent observation of its X-ray counterpart by Suzaku.