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.

We present a detailed comparison of the substructure properties of a single Milky Way sized dark matter halo from the Aquarius suite at five different resolutions, as identified by a variety of different (sub)halo finders for simulations of cosmic structure formation. These finders span a wide range of techniques and methodologies to extract and quantify substructures within a larger non‐homogeneous background density (e.g. a host halo). This includes real‐space‐, phase‐space‐, velocity‐space‐ and time‐space‐based finders, as well as finders employing a Voronoi tessellation, Friends‐of‐Friends techniques or refined meshes as the starting point for locating substructure. A common post‐processing pipeline was used to uniformly analyse the particle lists provided by each finder. We extract quantitative and comparable measures for the subhaloes, primarily focusing on mass and the peak of the rotation curve for this particular study. We find that all of the finders agree extremely well in the presence and location of substructure and even for properties relating to the inner part of the subhalo (e.g. the maximum value of the rotation curve). For properties that rely on particles near the outer edge of the subhalo the agreement is at around the 20 per cent level. We find that the basic properties (mass and maximum circular velocity) of a subhalo can be reliably recovered if the subhalo contains more than 100 particles although its presence can be reliably inferred for a lower particle number limit of 20. We finally note that the logarithmic slope of the subhalo cumulative number count is remarkably consistent and <1 for all the finders that reached high resolution. If correct, this would indicate that the larger and more massive, respectively, substructures are the most dynamically interesting and that higher levels of the (sub)subhalo hierarchy become progressively less important.

The ever increasing size and complexity of data coming from simulations of cosmic structure formation demands equally sophisticated tools for their analysis. During the past decade, the art of object finding in these simulations has hence developed into an important discipline itself. A multitude of codes based upon a huge variety of methods and techniques have been spawned yet the question remained as to whether or not they will provide the same (physical) information about the structures of interest. Here we summarize and extent previous work of the "halo finder comparison project": we investigate in detail the (possible) origin of any deviations across finders. To this extent we decipher and discuss differences in halo finding methods, clearly separating them from the disparity in definitions of halo properties. We observe that different codes not only find different numbers of objects leading to a scatter of up to 20 per cent in the halo mass and V max function, but also that the particulars of those objects that are identified by all finders differ. The strength of the variation, however, depends on the property studied, e.g. the scatter in position, bulk velocity, mass, and the peak value of the rotation curve is practically below a few per cent, whereas derived quantities such as spin and shape show larger deviations. Our study indicates that the prime contribution to differences in halo properties across codes stems from the distinct particle collection methods and -to a minor extent -the particular aspects of how the procedure for removing unbound particles is implemented. We close with a discussion of the relevance and implications of the scatter across different codes for other fields such as semi-analytical galaxy formation models, gravitational lensing, and observables in general.

A new multidimensional Hierarchical Structure Finder (hsf) to study the phase‐space structure of dark matter in N‐body cosmological simulations is presented. The algorithm depends mainly on two parameters, which control the level of connectivity of the detected structures and their significance compared to Poisson noise. By working in six‐dimensional phase space, where contrasts are much more pronounced than in three‐dimensional (3D) position space, our hsf algorithm is capable of detecting subhaloes including their tidal tails, and can recognize other phase‐space structures such as pure streams and candidate caustics. If an additional unbinding criterion is added, the algorithm can be used as a self‐consistent halo and subhalo finder. As a test, we apply it to a large halo of the Millennium Simulation, where 19 per cent of the halo mass is found to belong to bound substructures, which is more than what is detected with conventional 3D substructure finders, and an additional 23–36 per cent of the total mass belongs to unbound hsf structures. The distribution of identified phase‐space density peaks is clearly bimodal: high peaks are dominated by the bound structures and show a small spread in their height distribution; low peaks belong mostly to tidal streams, as expected. However, the projected (3D) density distribution of the structures shows that some of the streams can have comparable density to the bound structures in position space. In order to better understand what hsf provides, we examine the time evolution of structures, based on the merger tree history. Given the resolution limit of the Millennium Simulation, bound structures typically make only up to six orbits inside the main halo. The number of orbits scales approximately linearly with the redshift corresponding to the moment of merging of the structures with the halo. At fixed redshift, the larger the initial mass of the structure which enters the main halo, the faster it loses mass. The difference in the mass loss rate between the largest structures and the smallest ones can reach up to 20 per cent. Still, hsf can identify at the present time at least 80 per cent of the original content of structures with a redshift of infall as high as z≤ 0.3, which illustrates the significant power of this tool to perform dynamical analyses in phase space.