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.

The influence of a galaxy’s environment on its evolution has been studied and compared extensively in the literature, although differing techniques are often used to define environment. Most methods fall into two broad groups: those that use nearest neighbours to probe the underlying density field and those that use fixed apertures. The differences between the two inhibit a clean comparison between analyses and leave open the possibility that, even with the same data, different properties are actually being measured. In this work, we apply 20 published environment definitions to a common mock galaxy catalogue constrained to look like the local Universe. We find that nearest‐neighbour‐based measures best probe the internal densities of high‐mass haloes, while at low masses the interhalo separation dominates and acts to smooth out local density variations. The resulting correlation also shows that nearest‐neighbour galaxy environment is largely independent of dark matter halo mass. Conversely, aperture‐based methods that probe superhalo scales accurately identify high‐density regions corresponding to high‐mass haloes. Both methods show how galaxies in dense environments tend to be redder, with the exception of the largest apertures, but these are the strongest at recovering the background dark matter environment. We also warn against using photometric redshifts to define environment in all but the densest regions. When considering environment, there are two regimes: the ‘local environment’ internal to a halo best measured with nearest neighbour and ‘large‐scale environment’ external to a halo best measured with apertures. This leads to the conclusion that there is no universal environment measure and the most suitable method depends on the scale being probed.

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.

We explore the structures of protoclusters and their relationship with high redshift clusters using the Millennium Simulation combined with a semi-analytic model. We find that protoclusters are very extended, with 90 per cent of their mass spread across ∼ 35 h −1 Mpc comoving at z = 2 (∼ 30 arcmin). The 'main halo', which can manifest as a high redshift cluster or group, is only a minor feature of the protocluster, containing less than 20 per cent of all protocluster galaxies at z = 2. Furthermore, many protoclusters do not contain a main halo that is massive enough to be identified as a high redshift cluster. Protoclusters exist in a range of evolutionary states at high redshift, independent of the mass they will evolve to at z = 0. We show that the evolutionary state of a protocluster can be approximated by the mass ratio of the first and second most massive haloes within the protocluster, and the z = 0 mass of a protocluster can be estimated to within 0.2 dex accuracy if both the mass of the main halo and the evolutionary state is known. We also investigate the biases introduced by only observing star-forming protocluster members within small fields. The star formation rate required for line-emitting galaxies to be detected is typically high, which leads to the artificial loss of low mass galaxies from the protocluster sample. This effect is stronger for observations of the centre of the protocluster, where the quenched galaxy fraction is higher. This loss of low mass galaxies, relative to the field, distorts the size of the galaxy overdensity, which in turn can contribute to errors in predicting the z = 0 evolved mass.

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.