We have performed the largest ever particle simulation of a Milky Way sized dark matter halo, and present the most comprehensive convergence study for an individual dark matter halo carried out thus far. We have also simulated a sample of six ultrahighly resolved Milky Way sized haloes, allowing us to estimate the halo-to-halo scatter in substructure statistics. In our largest simulation, we resolve nearly 300 000 gravitationally bound subhaloes within the virialized region of the halo. Simulations of the same object differing in mass resolution by factors of up to 1800 accurately reproduce the largest subhaloes with the same mass, maximum circular velocity and position, and yield good convergence for the abundance and internal properties of dark matter substructures. We detect up to four generations of subhaloes within subhaloes, but contrary to recent claims, we find less substructure in subhaloes than in the main halo when regions of equal mean overdensity are compared. The overall substructure mass fraction is much lower in subhaloes than in the main halo. Extrapolating the main halo's subhalo mass spectrum down to an Earth mass, we predict the mass fraction in substructure to be well below 3 per cent within 100 kpc, and to be below 0.1 per cent within the solar circle. The inner density profiles of subhaloes show no sign of converging to a fixed asymptotic slope and are well fitted by gently curving profiles of Einasto form. The mean concentrations of isolated haloes are accurately described by the fitting formula of Neto et al. down to maximum circular velocities of 1.5 km s −1 , an extrapolation over some five orders of magnitude in mass. However, at equal maximum circular velocity, subhaloes are more concentrated than field haloes, with a characteristic density that is typically ∼2.6 times larger and increases with decreasing distance from halo centre.

We study the mass, velocity dispersion and anisotropy profiles of Λ cold dark matter (ΛCDM) haloes using a suite of N‐body simulations of unprecedented numerical resolution. The Aquarius Project follows the formation of six different galaxy‐sized haloes simulated several times at varying numerical resolution, allowing numerical convergence to be assessed directly. The highest resolution simulation represents a single dark matter halo using 4.4 billion particles, of which 1.1 billion end up within the virial radius. Our analysis confirms a number of results claimed by earlier work, and clarifies a few issues where conflicting claims may be found in the recent literature. The mass profile of ΛCDM haloes deviates slightly but systematically from the form proposed by Navarro, Frenk & White. The spherically averaged density profile becomes progressively shallower inwards and, at the innermost resolved radius, the logarithmic slope is γ≡− d ln  ρ/d ln  r≲ 1. Asymptotic inner slopes as steep as the recently claimed ρ∝r−1.2 are clearly ruled out. The radial dependence of γ is well approximated by a power law, γ∝rα (the Einasto profile). The shape parameter, α, varies slightly but significantly from halo to halo, implying that the mass profiles of ΛCDM haloes are not strictly universal: different haloes cannot, in general, be rescaled to look identical. Departures from similarity are also seen in velocity dispersion profiles and correlate with those in density profiles so as to preserve a power‐law form for the spherically averaged pseudo‐phase‐space density, ρ/σ3∝r−1.875. The index here is identical to that of Bertschinger's similarity solution for self‐similar infall on to a point mass from an otherwise uniform Einstein–de Sitter universe. The origin of this striking behaviour is unclear, but its robustness suggests that it reflects a fundamental structural property of ΛCDM haloes. Our conclusions are reliable down to radii below 0.4 per cent of the virial radius, providing well‐defined predictions for halo structure when baryonic effects are neglected, and thus an instructive theoretical template against which the modifications induced by the baryonic components of real galaxies can be judged.

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Dark matter is the dominant form of matter in the universe, but its nature is unknown. It is plausibly an elementary particle, perhaps the lightest supersymmetric partner of known particle species 1 . In this case, annihilation of dark matter in the halo of the Milky Way should produce γ-rays at a level which may soon be observable 2, 3 .Previous work has argued that the annihilation signal will be dominated by emission from very small clumps 4, 5 (perhaps smaller even than the Earth) which would be most easily detected where they cluster together in the dark matter halos of dwarf satellite galaxies 6 . Here we show, using the largest ever simulation of the formation of a galactic halo, that such small-scale structure will, in fact, have a negligible impact on dark matter detectability. Rather, the dominant and likely most easily detectable signal will be produced by diffuse dark matter in the main halo of the Milky Way 7, 8 . If the main halo is strongly detected, then small dark matter clumps should also be visible, but may well contain no stars, thereby confirming a key prediction of the Cold Dark Matter (CDM) model.

We study predictions for dark matter (DM) phase‐space structure near the Sun based on high‐resolution simulations of six galaxy haloes taken from the Aquarius project. The local DM density distribution is predicted to be remarkably smooth; the density at the Sun differs from the mean over a best‐fitting ellipsoidal equidensity contour by less than 15 per cent at the 99.9 per cent confidence level. The local velocity distribution is also very smooth, but it differs systematically from a (multivariate) Gaussian distribution. This is not due to the presence of individual clumps or streams, but to broad features in the velocity modulus and energy distributions that are stable in both space and time and reflect the detailed assembly history of each halo. These features have a significant impact on the signals predicted for weakly interacting massive particle and axion searches. For example, weakly interacting massive particles recoil rates can deviate by ∼10 per cent from those expected from the best‐fitting multivariate Gaussian models. The axion spectra in our simulations typically peak at lower frequencies than in the case of multivariate Gaussian velocity distributions. Also in this case, the spectra show significant imprints of the formation of the halo. This implies that once direct DM detection has become routine, features in the detector signal will allow us to study the DM assembly history of the Milky Way. A new field, ‘DM astronomy’, will then emerge.

We use the Millennium Simulation series to investigate the mass and redshift dependence of the concentration of equilibrium cold dark matter (CDM) halos. We extend earlier work on the relation between halo mass profiles and assembly histories to show how the latter may be used to predict concentrations for halos of all masses and at any redshift. Our results clarify the link between concentration and the "collapse redshift" of a halo as well as why concentration depends on mass and redshift solely through the dimensionless "peak height" mass parameter, ν(M, z) = δ crit (z)/σ(M, z). We combine these results with analytic mass accretion histories to extrapolate the c(M, z) relations to mass regimes difficult to reach through direct simulation. Our model predicts that, at given z, c(M ) should deviate systematically from a simple power law at high masses, where concentrations approach a constant value, and at low masses, where concentrations are substantially lower than expected from extrapolating published empirical fits. This correction may reduce the expected self-annihilation boost factor from substructure by about one order of magnitude. The model also reproduces the c(M, z) dependence on cosmological parameters reported in earlier work, and thus provides a simple and robust account of the relation between cosmology and the massconcentration-redshift relation of CDM halos.

We explore similarities in the luminosity distribution of early type galaxies and the mass profiles of LCDM halos. The spatial structure of these systems may be accurately described by a simple law where the logarithmic slope of the projected density is a power law of radius; the Sersic law. We show that this law provides a significantly better fit than a three-parameter generalization of the NFW profile and derive the best-fitting Sersic parameters for a set of high-resolution LCDM halos spanning a wide range in mass. The mean Sersic n values are 3.0 for dwarf- and galaxy-sized halos and 2.4 for cluster-sized halos, similar to the values that characterize luminous elliptical galaxies. We discuss possible reasons why the same law should describe dark and luminous systems that span a range of over seven decades in mass.Comment: 4 page

We use the Millennium Simulation series to investigate the relation between the accretion history and mass profile of cold dark matter halos. We find that the mean inner density within the scale radius, r −2 (where the halo density profile has isothermal slope), is directly proportional to the critical density of the Universe at the time when the virial mass of the main progenitor equals the mass enclosed within r −2 . Scaled to these characteristic values of mass and density, the average mass accretion history, expressed in terms of the critical density of the Universe, M (ρ crit (z)), resembles that of the enclosed density profile, M ( ρ ), at z = 0. Both follow closely the NFW profile, which suggests that the similarity of halo mass profiles originates from the mass-independence of halo accretion histories. Support for this interpretation is provided by outlier halos whose accretion histories deviate from the NFW shape; their mass profiles show correlated deviations from NFW and are better approximated by Einasto profiles. Fitting both M ( ρ ) and M (ρ crit ) with either NFW or Einasto profiles yield concentration and shape parameters that are correlated, confirming and extending earlier work that has linked the concentration of a halo with its accretion history. These correlations also confirm that halo structure is insensitive to initial conditions: only halos whose accretion histories differ greatly from the NFW shape show noticeable deviations from NFW in their mass profiles. As a result, the NFW profile provides acceptable fits to hot dark matter halos, which do not form hierarchically, and for fluctuation power spectra other than CDM. Our findings, however, predict a subtle but systematic dependence of mass profile shape on accretion history which, if confirmed, would provide strong support for the link between accretion history and halo structure we propose here.