The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web -depending on the data at hand, be it numerical simulations, large sky surveys or other. In this paper we bring twelve of these methods together and apply them to the same data set in order to understand how they compare. In general these cosmic web classifiers have been designed with different cosmological goals in mind, and to study different questions. Therefore one would not a priori expect agreement between different techniques however, many of these methods do converge on the identification of specific features. In this paper we study the agreements and disparities of the different methods. For example, each method finds that knots inhabit higher density regions than filaments, etc. and that voids have the lowest densities. For a given web environment, we find substantial overlap in the density range assigned by each web classification scheme. We also compare classifications on a halo-by-halo basis; for example, we find that 9 of 12 methods classify around a third of group-mass haloes (i.e. M halo ∼ 10 13.5 h −1 M ⊙ ) as being in filaments. Lastly, so that any future cosmic web classification scheme can be compared to the 12 methods used here, we have made all the data used in this paper public.

We describe the observations and resultant galaxy cluster catalog from the 2770 deg 2 SPTpolExtended Cluster Survey (SPT-ECS). Clusters are identified via the Sunyaev-Zel'dovich (SZ) effect and confirmed with a combination of archival and targeted follow-up data, making particular use of data from the Dark Energy Survey (DES). With incomplete follow-up we have confirmed as clusters 244 of 266 candidates at a detection significance ξ5 and an additional 204systems at 4<ξ<5. The confirmed sample has a median mass of~´-M Mh 4.4 10 c 500 14 70 1  and a median redshift of z=0.49, and we have identified 44strong gravitational lenses in the sample thus far. Radio data are used to characterize contamination to the SZ signal; the median contamination for confirmed clusters is predicted to be ∼1% of the SZ signal at the ξ>4 threshold, and <4% of clusters have a predicted contamination >10% of their measured SZ flux. We associate SZ-selected clusters, from both SPT-ECS and the SPT-SZ survey, with clusters from the DES redMaPPer sample, and we find an offset distribution between the SZ center and central galaxy in general agreement with previous work, though with a larger fraction of clusters with significant offsets. Adopting a fixed Planck-like cosmology, we measure the optical richness-SZ mass (l-M) relation and find it to be 28% shallower than that from a weak-lensing analysis of the DES data-a difference significant at the 4σ level-with the relations intersecting at λ=60. The SPT-ECS cluster sample will be particularly useful for studying the evolution of massive clusters and, in combination with DES lensing observations and the SPT-SZ cluster sample, will be an important component of future cosmological analyses.

We report the results of the first study of the multi-stream environment of dark matter haloes in cosmological N-body simulations in the ΛCDM cosmology. The full dynamical state of dark matter can be described as a three-dimensional sub-manifold in six-dimensional phase space -the dark matter sheet. In our study we use a Lagrangian sub-manifold x = x(q, t) (where x and q are co-moving Eulerian and Lagrangian coordinates respectively), which is dynamically equivalent to the dark matter sheet but is more convenient for numerical analysis. Our major results can be summarized as follows. At the resolution of the simulation i.e. without additional smoothing, the cosmic web represents a hierarchical structure: each halo is embedded in the filamentary framework of the web predominantly at the filament crossings, and each filament is embedded in the wall like fabric of the web at the wall crossings. Locally, each halo or sub-halo is a peak in the number of streams field. The number of streams in the neighbouring filaments is higher than in the neighbouring walls. The walls are regions where number of streams is equal to three or a few. Voids are uniquely defined by the local condition requiring to be a single-stream flow region. The shells of streams around haloes are quite thin and the closest void region is typically within one and a half FOF radius from the center of the halo.

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