We use high-resolution N-body simulations to study the equilibrium density profiles of dark matter halos in hierarchically clustering universes. We find that all such profiles have the same shape, independent of halo mass, of initial density fluctuation spectrum, and of the values of the cosmological parameters. Spherically averaged equilibrium profiles are well fit over two decades in radius by a simple formula originally proposed to describe the structure of galaxy clusters in a cold dark matter universe. In any particular cosmology the two scale parameters of the fit, the halo mass and its characteristic density, are strongly correlated. Low-mass halos are significantly denser than more massive systems, a correlation which reflects the higher collapse redshift of small halos. The characteristic density of an equilibrium halo is proportional to the density of the universe at the time it was assembled. A suitable definition of this assembly time allows the same proportionality constant to be used for all the cosmologies that we have tested. We compare our results to previous work on halo density profiles and show that there is good agreement. We also provide a step-by-step analytic procedure, based on the Press-Schechter formalism, which allows accurate equilibrium profiles to be calculated as a function of mass in any hierarchical model.Comment: typos in eqs A5 and A14 corrected. In press in the ApJ, Dec 1, 1997. Full PS file with figures can be obtained from http://penedes.as.arizona.edu/~jfn/preprints/dprof.ps.g

We use N-body simulations to investigate the structure of dark halos in the standard Cold Dark Matter cosmogony. Halos are excised from simulations of cosmologically representative regions and are resimulated individually at high resolution. We study objects with masses ranging from those of dwarf galaxy halos to those of rich galaxy clusters. The spherically averaged density profiles of all our halos can be fit over two decades in radius by scaling a simple ``universal'' profile. The characteristic overdensity of a halo, or equivalently its concentration, correlates strongly with halo mass in a way which reflects the mass dependence of the epoch of halo formation. Halo profiles are approximately isothermal over a large range in radii, but are significantly shallower than $r^{-2}$ near the center and steeper than $r^{-2}$ near the virial radius. Matching the observed rotation curves of disk galaxies requires disk mass-to-light ratios to increase systematically with luminosity. Further, it suggests that the halos of bright galaxies depend only weakly on galaxy luminosity and have circular velocities significantly lower than the disk rotation speed. This may explain why luminosity and dynamics are uncorrelated in observed samples of binary galaxies and of satellite/spiral systems. For galaxy clusters, our halo models are consistent both with the presence of giant arcs and with the observed structure of the intracluster medium, and they suggest a simple explanation for the disparate estimates of cluster core radii found by previous authors. Our results also highlight two shortcomings of the CDM model. CDM halos are too concentrated to be consistent with the halo parameters inferred for dwarf irregulars, and the predicted abundance of galaxy halos is larger than the observed abundance of galaxies.Comment: compressed and uuencoded PS file. 22 pages including 14 figures. 447875 bytes. Submitted to ApJ on August 1, 199

The cold dark matter model has become the leading theoretical picture for the formation of structure in the Universe. This model, together with the theory of cosmic inflation, makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a simulation of the growth of dark matter structure using 2,160(3) particles, following them from redshift z = 127 to the present in a cube-shaped region 2.230 billion lightyears on a side. In postprocessing, we also follow the formation and evolution of the galaxies and quasars. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with future generations of observational surveys of galaxies.

We introduce the Virgo Consortium's EAGLE project, a suite of hydrodynamical simulations that follow the formation of galaxies and supermassive black holes in cosmologically representative volumes of a standard ΛCDM universe. We discuss the limitations of such simulations in light of their finite resolution and poorly constrained subgrid physics, and how these affect their predictive power. One major improvement is our treatment of feedback from massive stars and AGN in which thermal energy is injected into the gas without the need to turn off cooling or decouple hydrodynamical forces, allowing winds to develop without predetermined speed or mass loading factors. Because the feedback efficiencies cannot be predicted from first principles, we calibrate them to the present-day galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy stellar mass function is reproduced to < ∼ 0.2 dex over the full resolved mass range, 10 8 < M * /M < ∼ 10 11 , a level of agreement close to that attained by semi-analytic models, and unprecedented for hydrodynamical simulations. We compare our results to a representative set of low-redshift observables not considered in the calibration, and find good agreement with the observed galaxy specific star formation rates, passive fractions, Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic C iv and O vi. While the mass-metallicity relations for gas and stars are consistent with observations for M * > ∼ 10 9 M (M * > ∼ 10 10 M at intermediate resolution), they are insufficiently steep at lower masses. For the reference model the gas fractions and temperatures are too high for clusters of galaxies, but for galaxy groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. The EAGLE simulation suite, which also includes physics variations and higher-resolution zoomed-in volumes described elsewhere, constitutes a valuable new resource for studies of galaxy formation.

We simulate the growth of galaxies and their central supermassive black holes by implementing a suite of semi‐analytic models on the output of the Millennium Run, a very large simulation of the concordance Λ cold dark matter cosmogony. Our procedures follow the detailed assembly history of each object and are able to track the evolution of all galaxies more massive than the Small Magellanic Cloud throughout a volume comparable to that of large modern redshift surveys. In this first paper we supplement previous treatments of the growth and activity of central black holes with a new model for ‘radio’ feedback from those active galactic nuclei that lie at the centre of a quasi‐static X‐ray‐emitting atmosphere in a galaxy group or cluster. We show that for energetically and observationally plausible parameters such a model can simultaneously explain: (i) the low observed mass drop‐out rate in cooling flows; (ii) the exponential cut‐off at the bright end of the galaxy luminosity function; and (iii) the fact that the most massive galaxies tend to be bulge‐dominated systems in clusters and to contain systematically older stars than lower mass galaxies. This success occurs because static hot atmospheres form only in the most massive structures, and radio feedback (in contrast, for example, to supernova or starburst feedback) can suppress further cooling and star formation without itself requiring star formation. We discuss possible physical models that might explain the accretion rate scalings required for our phenomenological ‘radio mode’ model to be successful.

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 investigate the mass profile of cold dark matter (ΛCDM) haloes using a suite of numerical simulations spanning five decades in halo mass, from dwarf galaxies to rich galaxy clusters. These haloes typically have a few million particles within the virial radius (r200), allowing robust mass profile estimates down to radii <1 per cent of r200. Our analysis confirms the proposal of Navarro, Frenk & White (NFW) that the shape of the ΛCDM halo mass profiles differs strongly from a power law and depends little on mass. The logarithmic slope of the spherically averaged density profile, as measured by β=−d ln ρ/d ln r, decreases monotonically towards the centre and becomes shallower than isothermal (β < 2) inside a characteristic radius, r−2. The fitting formula proposed by NFW provides a reasonably good approximation to the density and circular velocity profiles of individual haloes; circular velocities typically deviate from NFW best fits by <10 per cent over the radial range that is numerically well resolved. Alternatively, systematic deviations from the NFW best fits are also noticeable. Inside r−2, the profile of simulated haloes becomes shallower with radius more gradually than predicted and, as a result, NFW fits tend to underestimate the dark matter density in these regions. This discrepancy has been interpreted as indicating a steeply divergent cusp with asymptotic inner slope, β0≡β(r = 0) ∼ 1.5. Our results suggest a different interpretation. We use the density and enclosed mass at our innermost resolved radii to place strong constraints on β0: density cusps as steep as r−1.5 are inconsistent with most of our simulations, although β0= 1 is still consistent with our data. Our density profiles show no sign of converging to a well‐defined asymptotic inner power law. We propose a simple formula that reproduces the radial dependence of the slope better than the NFW profile, and so may minimize errors when extrapolating our results inward to radii not yet reliably probed by numerical simulations.

We use the Millennium Simulation (MS) to study the statistics of Λ cold dark matter (ΛCDM) halo concentrations at z= 0. Our results confirm that the average halo concentration declines monotonically with mass; the concentration–mass relation is well fitted by a power law over three decades in mass, up to the most massive objects that form in a ΛCDM universe (∼ 1015 h−1 M⊙). This is in clear disagreement with the predictions of the model proposed by Bullock et al. for these rare objects, and agrees better with the original predictions of Navarro, Frenk & White. The large volume surveyed, together with the unprecedented numerical resolution of the MS, allows us to estimate with confidence the distribution of concentrations and, consequently, the abundance of systems with unusual properties. About one in a hundred cluster haloes (M200≳ 3 × 1014 h−1 M⊙) have concentrations exceeding c200= 7.5, a result that may be useful in interpreting the likelihood of unusually strong massive gravitational lenses, such as Abell 1689, in the ΛCDM cosmogony. A similar fraction of about 1 per cent of galaxy‐sized haloes (M200∼ 1012 h−1 M⊙) have c200 < 4.5 and this could be relevant to models that attempt to reconcile the ΛCDM cosmology with rotation curves of low surface brightness galaxies by appealing to haloes of unexpectedly low concentration. We find that halo concentrations are independent of spin once haloes manifestly out of equilibrium have been removed from the sample. Compared to their relaxed brethren, the concentrations of out‐of‐equilibrium haloes tend to be lower and have more scatter, while their spins tend to be higher. A number of previously noted trends within the halo population are induced primarily by these properties of unrelaxed systems. Finally, we compare the result of predicting halo concentrations using the mass assembly history of the main progenitor with predictions based on simple arguments regarding the assembly time of all progenitors. The latter are typically as good or better than the former, suggesting that halo concentration depends not only on the evolutionary path of a halo's main progenitor, but on how and when all of its constituents collapsed to form non‐linear objects.