We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends‐of‐friends, spherical‐overdensity and phase‐space‐based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allow halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large‐scale structure of the universe. All the halo‐finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo, and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Through a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30–40 particles. However, also here the phase‐space finders excelled by resolving substructure down to 10–20 particles. By comparing the halo finders using a high‐resolution cosmological volume, we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity and peak of the rotation curve). We further suggest to utilize the peak of the rotation curve, vmax, as a proxy for mass, given the arbitrariness in defining a proper halo edge.

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Aims. We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures. Methods. Our Multiscale Morphology Filter (MMF) method has been developed on the basis of visualization and feature extraction techniques in computer vision and medical research. The density or intensity field of the sample is smoothed over a range of scales. The smoothed signals are processed through a morphology response filter whose form is dictated by the particular morphological feature it seeks to extract, and depends on the local shape and spatial coherence of the intensity field. The morphology signal at each location is then defined to be the one with the maximum response across the full range of smoothing scales. The success of our method in identifying anisotropic features such as filaments and walls depends critically on the use of an optimally defined intensity field. This is accomplished by applying the DTFE reconstruction methodology to the sample particle or galaxy distribution. Results. We have tested our MMF Filter against a set of heuristic models of weblike patterns such as are seen in the Megaparsec cosmic matter distribution. To test its effectiveness in the context of more realistic configurations we also present preliminary results from the MMF analysis of an N-body model. Comparison with alternative prescriptions for feature extraction shows that MMF is a remarkably strong structure finder

We analyse the structure and connectivity of the distinct morphologies that define the cosmic web. With the help of our multiscale morphology filter (MMF), we dissect the matter distribution of a cosmological λ cold dark matter N‐body computer simulation into cluster, filaments and walls. The MMF is ideally suited to address both the anisotropic morphological character of filaments and sheets, and the multiscale nature of the hierarchically evolved cosmic matter distribution. The results of our study may be summarized as follows. (i) While all morphologies occupy a roughly well‐defined range in density, this alone is not sufficient to differentiate between them given their overlap. Environment defined only in terms of density fails to incorporate the intrinsic dynamics of each morphology. This plays an important role in both linear and non‐linear interactions between haloes. (ii) Most of the mass in the Universe is concentrated in filaments, narrowly followed by clusters. In terms of volume, clusters only represent a minute fraction and filaments not more than 9 per cent. Walls are relatively inconspicuous in terms of mass and volume. (iii) On average, massive clusters are connected to more filaments than low‐mass clusters. Clusters with M∼ 1014 M⊙ h−1 have on average two connecting filaments, while clusters with M≥ 1015 M⊙ h−1 have on average five connecting filaments. (iv) Density profiles indicate that the typical width of filaments is 2 h−1 Mpc. Walls have less well‐defined boundaries with widths between 5 and 8 Mpc h−1. In their interior, filaments have a power‐law density profile with slope γ≈−1, corresponding to an isothermal density profile.