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 ∼ 10^13.5h⁻¹M_⊙) 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.

The properties of galaxies are known to be affected by their environment. One important question is how their angular momentum reflects the surrounding cosmic web. We use the Sloan Digital Sky Survey to investigate the spin axes of spiral and elliptical galaxies relative to their surrounding filament/sheet orientations. To detect filaments, a marked point process with interactions (the Bisous model) is used. Sheets are found by detecting flattened filaments. The minor axes of ellipticals are found to be preferentially perpendicular to hosting filaments. A weak correlation is found with sheets. These findings are consistent with the notion that elliptical galaxies formed via mergers, which predominantly occurred along the filaments. The spin axis of spiral galaxies is found to align with the host filament, with no correlation between spiral spin and sheet normal. When examined as a function of distance from the filament axis, a much stronger correlation is found in the outer parts, suggesting that the alignment is driven by the laminar infall of gas from sheets to filaments. When compared with numerical simulations, our results suggest that the connection between dark matter halo and galaxy spin is not straightforward. Our results provide an important input to the understanding of how galaxies acquire their angular momentum.

A new approach for the classification of the cosmic web is presented. In extension of the previous work of Hahn et al. and Forero-Romero et al., the

Available proper motion measurements of Milky Way (MW) satellite galaxies are used to calculate their orbital poles and projected uncertainties. These are compared to a set of recent cold dark-matter (CDM) simulations, tailored specifically to solve the MW satellite problem. We show that the CDM satellite orbital poles are fully consistent with being drawn from a random distribution, while the MW satellite orbital poles indicate that the disc-of-satellites of the Milky Way is rotationally supported. Furthermore, the bootstrapping analysis of the spatial distribution of theoretical CDM satellites also shows that they are consistent with being randomly drawn. The theoretical CDM satellite population thus shows a significantly different orbital and spatial distribution than the MW satellites, most probably indicating that the majority of the latter are of tidal origin rather than being DM dominated sub-structures. A statistic is presented that can be used to test a possible correlation of satellite galaxy orbits with their spatial distribution.Comment: Accepted for publication in Ap

The alignment of dark matter (DM) haloes and the surrounding large-scale structure (LSS) is examined in the context of the cosmic web. Halo spin, shape and the orbital angular momentum of subhaloes are investigated relative to the LSS using the eigenvectors of the velocity shear tensor evaluated on a grid with a scale of 1 Mpc h⁻¹, deep within the non-linear regime. Knots, filaments, sheets and voids are associated with regions that are collapsing along 3, 2, 1 or 0 principal directions simultaneously. Each halo is tagged with a web classification (i.e. knot halo, filament halo, etc.) according to the nature of the collapse at the halo position. The full distribution of shear eigenvalues is found to be substantially different from that tagged to haloes, indicating that the observed velocity shear is significantly biased. We find that larger mass haloes live in regions where the shear is more isotropic, namely the expansion or collapse is more spherical. A correlation is found between the halo shape and the eigenvectors of the shear tensor, with the longest (shortest) axis of the halo shape being aligned with the slowest (fastest) collapsing eigenvector. This correlation is web independent, suggesting that the velocity shear is a fundamental tracer of the halo alignment. A similar result is found for the alignment of halo spin with the cosmic web. It has been shown that high-mass haloes exhibit a spin flip with respect to the LSS: we find that the mass at which this spin flip occurs is web dependent and not universal as suggested previously. Although weaker than haloes, subhalo orbits too exhibit an alignment with the LSS, providing a possible insight into the highly correlated corotation of the Milky Way's satellite system. The present study suggests that the velocity shear tensor constitutes the natural framework for studying the directional properties of the non-linear LSS and those of haloes and galaxies.