Haloes gone MAD: The Halo-Finder Comparison Project

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, v_max, as a proxy for mass, given the arbitrariness in defining a proper halo edge.