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This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society © 2011 RAS © 2011 The authors Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved, 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 are greatly indebted to the ASTROSIM network of the European Science Foundation (Science Meeting 2910) for financially supporting the workshop ‘Haloes going MAD’ held in Miraflores de la Sierra near Madrid in 2010 May where all of this work was initiated.AK is supported by the Spanish Ministerio de Ciencia e Innovación (MICINN) in Spain through the Ramón y Cajal programme as well as the grants AYA 2009-13875-C03-02, AYA2009- 12792-C03-03, CSD2009-00064 and CAM S2009/ESP-1496. SRK acknowledges the support by the MICINN under the Consolider-Ingenio, SyeC project CSD-2007-00050. SP and VQ have also been supported by the MICINN (grants AYA2010-21322-C03-01 and CONSOLIDER2007-00050) and the Generalitat Valenciana (grant PROMETEO-2009-103). MZ is supported by NSF grant AST-0708087. GY acknowledges financial support from MICINN (Spain) under project AYA 2009-13875-C03-02 and the ASTROMADRID project S2009/ESP-1496 financed by Comunidad de Madrid

We resolve the inner region of a massive cluster forming in a cosmological LCDM simulation with a mass resolution of 2*10^6 Msun and before z=4.4 even 3*10^5 Msun. This is a billion times less than the clusters final virial mass and a substantial increase over current LCDM simulations. We achieve this resolution using a new multi-mass refinement procedure and are now able to probe a dark matter halo density profile down to 0.1 percent of the virial radius. The inner density profile of this cluster halo is well fitted by a power-law rho ~ r^-gamma down to the smallest resolved scale. An inner region with roughly constant logarithmic slope is now resolved, which suggests that cuspy profiles describe the inner profile better than recently proposed profiles with a core. The cluster studied here is one out of a sample of six high resolution cluster simulations of Diemand et al. (2004) and it's inner slope of gamma = 1.2 lies close to the sample average., Comment: 10 pages,10 figures. Matches version in press. Added Figure 7 and section 3.3. about upper limits of inner slopes, text (incl, title and abstract) revised, conclusions unchanged

We present a statistical study of substructure within a sample of LCDM clusters and galaxies simulated with up to 25 million particles. With thousands of subhalos per object we can accurately measure their spatial clustering and velocity distribution functions and compare these with observational data. The substructure properties of galactic halos closely resembles those of galaxy clusters with a small scatter in the mass and circular velocity functions. The velocity distribution function is non-Maxwellian and flat topped with a negative kurtosis of about -0.7. Within the virial radius the velocity bias $b=\sigma_{\rm sub}/\sigma_{\rm DM}\sim 1.12 \pm 0.04$, increasing to b > 1.3 within the halo centers. Slow subhalos are much less common, due to physical disruption by gravitational tides early in the merging history. This leads to a spatially anti-biased subhalo distribution that is well fitted by a cored isothermal. Observations of cluster galaxies do not show such biases which we interpret as a limitation of pure dark matter simulations - we estimate that we are missing half of the halo population which has been destroyed by physical overmerging. High resolution hydrodynamical simulations are required to study these issues further. If CDM is correct then the cluster galaxies must survive the tidal field, perhaps due to baryonic inflow during elliptical galaxy formation. Spirals can never exist near the cluster centers and the elliptical galaxies there will have little remaining dark matter. This implies that the morphology-density relation is set {\it before} the cluster forms, rather than a subsequent transformation of disks to S0's by virtue of the cluster environment., Comment: MNRAS accepted version. Due to an error in the initial conditions these simulations have a lower sigma_8 than the published value, 0.7 instead of 0.9. We thank Mike Kuhlen who helped us finding this mistake. See the erratum at http://www-theorie.physik.unizh.ch/~diemand/suberr.pdf . Images and movies available at http://www-theorie.physik.unizh.ch/~diemand/clusters/

N-body simulations of the hierarchical formation of cosmic structures suffer from the problem that the first objects to form always contain just a few particles. Although relaxation is not an issue for virialised objects containing millions of particles, collisional processes will always dominate within the first structures that collapse. First we quantify how the relaxation varies with resolution, softening, and radius within isolated equilibrium and non-equilibrium cuspy haloes. We then attempt to determine how this numerical effect propagates through a merging hierarchy by measuring the local relaxation rates of each particle throughout the hierarchical formation of a dark matter halo. The central few percent of the final structures - a region which one might naively think is well resolved at the final time since the haloes contains about 10^6 particles - suffer from high degrees of relaxation. It is not clear how to interpret the effects of the accumulated relaxation rate, but we argue that it describes a region within which one should be careful about trusting the numerical results. Substructure haloes are most affected by relaxation since they contain few particles at a constant energy for the entire simulation. We show that relaxation will flatten a cusp in just a few mean relaxation times of a halo. We explore the effect of resolution on the degree of relaxation and we find that increasing N slowly reduces the degree of relaxation proportional to N^{-0.25} rather than proportional to N. Simulated with the same relative mass resolution (i.e. equal numbers of particles) cluster mass objects suffer significantly more relaxation than galaxy mass objects since they form relatively late and therefore more of the particles spend more time in small N haloes., Comment: 11 pages, 14 figures. Accepted for publication in MNRAS. Movies available at http://www-theorie.physik.unizh.ch/~diemand/tbr

There is a vast menagerie of plausible candidates for the constituents of dark matter, both within and beyond extensions of the Standard Model of particle physics. Each of these candidates may have scattering (and other) cross section properties that are consistent with the dark matter abundance, BBN, and the most scales in the matter power spectrum; but which may have vastly different behavior at sub-galactic "cutoff" scales, below which dark matter density fluctuations are smoothed out. The only way to quantitatively measure the power spectrum behavior at sub-galactic scales at distances beyond the local universe, and indeed over cosmic time, is through probes available in multiply imaged strong gravitational lenses. Gravitational potential perturbations by dark matter substructure encode information in the observed relative magnifications, positions, and time delays in a strong lens. Each of these is sensitive to a different moment of the substructure mass function and to different effective mass ranges of the substructure. The time delay perturbations, in particular, are proving to be largely immune to the degeneracies and systematic uncertainties that have impacted exploitation of strong lenses for such studies. There is great potential for a coordinated theoretical and observational effort to enable a sophisticated exploitation of strong gravitational lenses as direct probes of dark matter properties. This opportunity motivates this white paper, and drives the need for: a) strong support of the theoretical work necessary to understand all astrophysical consequences for different dark matter candidates; and b) tailored observational campaigns, and even a fully dedicated mission, to obtain the requisite data., Science white paper submitted to the Astro2010 Decadal Cosmology & Fundamental Physics Science Frontier Panel

N-body simulations of the hierarchical formation of cosmic structures suffer from the problem that the first objects to form always contain just a few particles. Although relaxation is not an issue for virialized objects containing millions of particles, collisional processes will always dominate within the first structures that collapse. First we quantify how the relaxation varies with resolution, softening and radius within isolated equilibrium and non-equilibrium cuspy haloes. We then attempt to determine how this numerical effect propagates through a merging hierarchy by measuring the local relaxation rates of each particle throughout the hierarchical formation of a dark matter halo. The central few per cent of the final structures - a region that one might naively think is well resolved at the final time since the haloes contain ≈106 particles - suffer from high degrees of relaxation. It is not clear how to interpret the effects of the accumulated relaxation rate, but we argue that it describes a region within which one should be careful about trusting the numerical results. Substructure haloes are most affected by relaxation since they contain few particles at a constant energy for the entire simulation. We show that relaxation will flatten a cusp in just a few mean relaxation times of a halo. We explore the effect of resolution on the degree of relaxation, and we find that increasing N slowly reduces the degree of relaxation ∝N−0.25 rather than proportional to N as expected from the collisionless Boltzmann equation. Simulated with the same relative mass resolution (i.e. equal numbers of particles), cluster mass objects suffer significantly more relaxation than galaxy mass objects since they form relatively late and therefore more of the particles spend more time in small-N haloes