We study dark matter halo density profiles in a high‐resolution N‐body simulation of a ΛCDM cosmology. Our statistical sample contains ∼5000 haloes in the range 1011–1014 h−1 M⊙, and the resolution allows a study of subhaloes inside host haloes. The profiles are parametrized by an NFW form with two parameters, an inner radius rs and a virial radius Rvir, and we define the halo concentration cvir≡Rvirrs. First, we find that, for a given halo mass, the redshift dependence of the median concentration is cvir∝(1+z)−1. This corresponds to rs(z)∼constant, and is contrary to earlier suspicions that cvir does not vary much with redshift. The implications are that high‐redshift galaxies are predicted to be more extended and dimmer than expected before. Secondly, we find that the scatter in halo profiles is large, with a 1σΔ(log cvir)=0.18 at a given mass, corresponding to a scatter in maximum rotation velocities of ΔVmaxVmax=0.12. We discuss implications for modelling the Tully–Fisher relation, which has a smaller reported intrinsic scatter. Thirdly, subhaloes and haloes in dense environments tend to be more concentrated than isolated haloes, and show a larger scatter. These results suggest that cvir is an essential parameter for the theory of galaxy modelling, and we briefly discuss implications for the universality of the Tully–Fisher relation, the formation of low surface brightness galaxies, and the origin of the Hubble sequence. We present an improved analytic treatment of halo formation that fits the measured relations between halo parameters and their redshift dependence, and can thus serve semi‐analytic studies of galaxy formation.

According to the hierarchical clustering scenario, galaxies are assembled by merging and accretion of numerous satellites of di †erent sizes and masses. This ongoing process is not 100% efficient in destroying all of the accreted satellites, as evidenced by the satellites of our Galaxy and of M31. Using published data, we have compiled the circular velocity distribution function (VDF) of galaxy satellites in the (V circ ) Local Group. We Ðnd that within the volumes of radius of 570 kpc (400 h~1 kpc assuming the Hubble constant1 h \ 0.7) centered on the Milky Way and Andromeda, the average VDF is roughly approximated as km s~1)~1.4B0.4 h3 Mpc~3 for in the range B10È70 km s~1.The observed VDF is compared with results of high-resolution cosmological simulations. We Ðnd that the VDF in models is very di †erent from the observed one :Mpc~3. Cosmological models thus predict that a halo the size of our Galaxy should have about 50 dark matter satellites with circular velocity greater than 20 km s~1 and mass greater than 3 ] 108 within M _ a 570 kpc radius. This number is signiÐcantly higher than the approximately dozen satellites actually observed around our Galaxy. The di †erence is even larger if we consider the abundance of satellites in simulated galaxy groups similar to the Local Group. The models predict D300 satellites inside a 1.5 Mpc radius, while only D40 satellites are observed in the Local Group. The observed and predicted VDFs cross at B50 km s~1, indicating that the predicted abundance of satellites with km s~1 V circ Z 50 is in reasonably good agreement with observations. We conclude, therefore, that unless a large fraction of the Local Group satellites has been missed in observations, there is a dramatic discrepancy between observations and hierarchical models, regardless of the model parameters. We discuss several possible explanations for this discrepancy including identiÐcation of some satellites with the high-velocity clouds observed in the Local Group and the existence of dark satellites that failed to accrete gas and form stars either because of the expulsion of gas in the supernovae-driven winds or because of gas heating by the intergalactic ionizing background.

We present gas and total mass profiles for 13 low-redshift, relaxed clusters spanning a temperature range 0.7-9 keV, derived from all available Chandra data of sufficient quality. In all clusters, gas-temperature profiles are measured to large radii (Vikhlinin et al.) so that direct hydrostatic mass estimates are possible to nearly r 500 or beyond. The gas density was accurately traced to larger radii; its profile is not described well by a beta model, showing continuous steepening with radius. The derived tot profiles and their scaling with mass generally follow the Navarro-Frenk-White model with concentration expected for dark matter halos in ÃCDM cosmology. However, in three cool clusters, we detect a central mass component in excess of the Navarro-Frenk-White profile, apparently associated with their cD galaxies. In the inner region (r < 0:1r 500 ), the gas density and temperature profiles exhibit significant scatter and trends with mass, but they become nearly self-similar at larger radii. Correspondingly, we find that the slope of the masstemperature relation for these relaxed clusters is in good agreement with the simple self-similar behavior, M 500 / T , where ¼ (1:5 1:6) AE 0:1, if the gas temperatures are measured excluding the central cool cores. The normalization of this M-T relation is significantly, by %30%, higher than most previous X-ray determinations. We derive accurate gas mass fraction profiles, which show an increase with both radius and cluster mass. The enclosed f gas profiles within r 2500 ' 0:4r 500 have not yet reached any asymptotic value and are still far (by a factor of 1.5À2) from the universal baryon fraction according to the cosmic microwave background (CMB) observations. The f gas trends become weaker and its values closer to universal at larger radii, in particular, in spherical shells r 2500 < r < r 500 .