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.

We study the angular-momentum profiles of a statistical sample of halos drawn from a high-resolution N -body simulation of the ΛCDM cosmology. We find that the cumulative mass distribution of specific angular momentum j in a halo of mass M v is well fit by a universal function, M (< j) = M v µj/(j 0 + j). This profile is defined by one shape parameter (µ or j 0 ) in addition to the global spin parameter λ. It follows a power-law M (< j) ∝ j over most of the mass, and flattens at large j, with the flattening more pronounced for small values of µ (or large j 0 at a fixed λ). Compared to a uniform sphere in solid-body rotation, most halos have a higher fraction of their mass in the low-and high-j tails of the distribution. High-λ halos tend to have high µ values, corresponding to a narrower, more uniform j distribution. The spatial distribution of angular momentum in halos tends to be cylindrical and is well-aligned within each halo for ∼ 80% of the halos. The more misaligned halos tend to have low-µ values. When averaged over spherical shells encompassing mass M , the halo j profiles are fit by j(M ) ∝ M s with s = 1.3 ± 0.3. We investigate two ideas for the origin of this profile. The first is based on a revised version of linear tidal-torque theory combined with extended Press-Schechter mass accretion, and the second focuses on j transport in minor mergers.Finally, we briefly explore implications of the M (< j) profile on the formation of galactic disks assuming that j is conserved during an adiabatic baryonic infall. The implied gas density profile deviates from an exponential disk, with a higher density at small radii and a tail extending to large radii. The steep central density profiles may imply disk scale lengths that are smaller than observed. This is reminiscent of the "angular-momentum problem" seen in hydrodynamic simulations, even though we have assumed perfect j conservation. A possible solution is to associate the central excesses with bulge components and the outer regions with extended gaseous disks.

A B S T R A C TWe investigate several approaches for constructing Monte Carlo realizations of the merging history of virialized dark matter haloes (`merger trees') using the extended Press±Schechter formalism. We describe several unsuccessful methods in order to illustrate some of the dif®cult aspects of this problem. We develop a practical method that leads to the reconstruction of the mean quantities that can be derived from the Press±Schechter model. This method is convenient, computationally ef®cient, and works for any power spectrum or background cosmology. In addition, we investigate statistics that describe the distribution of the number of progenitors and their masses as a function of redshift.

We compare Tully-Fisher (TF) data for 838 galaxies within cz = 3000 km s −1 from the Mark III catalog to the peculiar velocity and density fields predicted from the 1.2 Jy IRAS redshift survey. Our goal is to test the relation between the galaxy density and velocity fields predicted by gravitational instability theory and linear biasing, and thereby to estimate β I ≡ Ω 0.6 /b I , where b I is the linear bias parameter for IRAS galaxies on a 300 km s −1 scale. Adopting the IRAS velocity and density fields as a prior model, we maximize the likelihood of the raw TF observables, taking into account the full range of selection effects and properly treating triple-valued zones in the redshiftdistance relation. Extensive tests with realistic simulated galaxy catalogs demonstrate that the method produces unbiased estimates of β I and its error. When we apply the method to the real data, we model the presence of a small but significant velocity quadrupole residual (∼ 3.3% of Hubble flow), which we argue is due to density fluctuations incompletely sampled by IRAS. The method then yields a maximum likelihood estimate β I = 0.49 ± 0.07 (1 σ error). We discuss the constraints on Ω and biasing that follow from this estimate of β I if we assume a COBE-normalized CDM power spectrum. Our model also yields the one dimensional noise in the velocity field, including IRAS prediction errors, which we find to be 125 ± 20 km s −1 .We define a χ 2 -like statistic, χ 2 ξ , that measures the coherence of residuals between the TF data and the IRAS model. In contrast with maximum likelihood, this statistic can identify poor fits, but is relatively insensitive to the best β I . As measured by χ 2 ξ , the IRAS model does not fit the data well without accounting for the residual quadrupole; when the quadrupole is added the fit is acceptable for 0.3 ≤ β I ≤ 0.9. We discuss this in view of the Davis, Nusser, & Willick analysis that questions the consistency of the TF and IRAS data.