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We present a power-spectrum analysis of the final 2dF Galaxy Redshift Survey (2dFGRS), employing a direct Fourier method. The sample used comprises 221 414 galaxies with measured redshifts. We investigate in detail the modelling of the sample selection, improving on previous treatments in a number of respects. A new angular mask is derived, based on revisions to the photometric calibration. The redshift selection function is determined by dividing the survey according to rest-frame colour, and deducing a self-consistent treatment of k-corrections and evolution for each population. The covariance matrix for the power-spectrum estimates is determined using two different approaches to the construction of mock surveys, which are used to demonstrate that the input cosmological model can be correctly recovered. We discuss in detail the possible differences between the galaxy and mass power spectra, and treat these using simulations, analytic models and a hybrid empirical approach. Based on these investigations, we are confident that the 2dFGRS power spectrum can be used to infer the matter content of the universe. On large scales, our estimated power spectrum shows evidence for the 'baryon oscillations' that are predicted in cold dark matter (CDM) models. Fitting to a CDM model, assuming a primordial n s = 1 spectrum, h = 0.72 and negligible neutrino mass, the preferred parameters are m h = 0.168 ± 0.016 and a baryon fraction b / m = 0.185 ± 0.046 (1σ errors). The value of m h is 1σ lower than the 0.20 ± 0.03 in our 2001 analysis of the partially E-mail: shaun.cole@durham.ac.uk C 2005 RAS 506 S. Cole et al.complete 2dFGRS. This shift is largely due to the signal from the newly sampled regions of space, rather than the refinements in the treatment of observational selection. This analysis therefore implies a density significantly below the standard m = 0.3: in combination with cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP), we infer m = 0.231 ± 0.021.

We present a detailed analysis of the dynamical properties of a simulated disk galaxy assembled hierarchically in the ΛCDM cosmogony. At z = 0, two distinct dynamical components are easily identified solely on the basis of the orbital parameters of stars in the galaxy: a slowly rotating, centrally concentrated spheroid and a disk-like component largely supported by rotation. These components are also clearly recognized in the surface brightness profile of the galaxy, which can be very well approximated by the superposition of an R 1/4 spheroid and an exponential disk. However, neither does the dynamicallyidentified spheroid follow de Vaucouleurs' law nor is the disk purely exponential, a result which calls for caution when estimating the importance of the disk from traditional photometric decomposition techniques. The disk may be further decomposed into a thin, dynamically cold component with stars on nearly circular orbits and a hotter, thicker component with orbital parameters transitional between the thin disk and the spheroid. Supporting evidence for the presence of distinct thick and thin disk components is found, as in the Milky Way, in the double-exponential vertical structure of the disk and in abrupt changes in the vertical velocity distribution as a function of age. The dynamical origin of these components offers intriguing clues to the assembly of spheroids and disks in the Milky Way and other spirals. The spheroid is old, and has essentially no stars younger than the time elapsed since the last major accretion event; ∼ 8 Gyr ago for the system we consider here. The majority of thin disk stars, on the other hand, form after the merging activity is over, although a significant fraction (∼ 15%) of thin-disk stars are old enough to predate the last major merger event. This unexpected population of old disk stars consists mainly of the tidal debris of satellites whose orbital plane was coincident with the disk and whose orbits were circularized by dynamical friction prior to full disruption. More than half of the stars in the thick disk share this origin, part of a trend that becomes more pronounced with age: nine out of ten stars presently in the old (τ ∼ > 10 Gyr) disk component were actually brought into the disk by satellites. By contrast, only one in two stars belonging to the old spheroid are tidal debris; the rest may be traced to a major merger event that dispersed the luminous progenitor at z ∼ 1.5 and seeded the formation of the spheroid. Our results highlight the role of satellite accretion events in shaping the disk-as well as the spheroidal-component and reveal some of the clues to the assembly process of a galaxy preserved in the detailed dynamics of old stellar populations.

We investigate the spins and shapes of over a million dark matter haloes identified at z = 0 in the Millennium simulation. Our sample spans halo masses ranging from dwarf galaxies to rich galaxy clusters. The very large dynamic range of this cold dark matter cosmological simulation enables the distribution of spins and shapes and their variation with halo mass and environment to be characterized with unprecedented precision. We compare results for haloes identified using three different algorithms, and investigate (and remove) biases in the estimate of angular momentum introduced both by the algorithm itself and by numerical effects. We introduce a novel halo definition called the TREE halo, based on the branches of the halo merger trees, which is more appropriate for comparison with real astronomical objects than the traditional 'friends-of-friends' and 'spherical overdensity' (SO) algorithms. We find that for this many objects, the traditional lognormal function is no longer an adequate description of the distribution, P(λ), of the dimensionless spin parameter λ, and we provide a different function that gives a better fit for TREE and SO haloes. The variation in spin with halo mass is weak but detectable, although the trend depends strongly on the halo definition used. For the entire population of haloes, we find median values of λ med = 0.0367-0.0429, depending on the definition of a halo. The haloes exhibit a range of shapes, with a preference for prolateness over oblateness. More-massive haloes tend to be less spherical and more prolate. We find that the more-spherical haloes have less coherent rotation in the median, and those closest to being spherical have a spin independent of mass (λ med ≈ 0.033). The most-massive haloes have a spin independent of shape (λ med ≈ 0.032). The majority of haloes have their angular momentum vector aligned with their minor axis and perpendicular to their major axis. We find a general trend for higher spin haloes to be more clustered, with a stronger effect for more-massive haloes. For galaxy cluster haloes, this can be larger than a factor of ∼2.

High-resolution N-body simulations are used to examine the power spectrum dependence of the concentration of galaxy-sized dark matter halos. It is found that dark halo concentrations depend on the amplitude of mass fluctuations as well as on the ratio of power between small and virial mass scales. This finding is consistent with the original results of Navarro, Frenk & White (NFW), and allows their model to be extended to include power spectra substantially different from Cold Dark Matter (CDM). In particular, the single-parameter model presented here fits the concentration dependence on halo mass for truncated power spectra, such as those expected in the warm dark matter scenario, and predicts a stronger redshift dependence for the concentration of CDM halos than proposed by NFW. The latter conclusion confirms recent suggestions by Bullock et al., although this new modeling differs from theirs in detail. These findings imply that observational limits on the concentration, such as those provided by estimates of the dark matter content within individual galaxies, may be used to constrain the amplitude of mass fluctuations on galactic and subgalactic scales. The constraints on $\Lambda$CDM models posed by the dark mass within the solar circle in the Milky Way and by the zero-point of the Tully-Fisher relation are revisited, with the result that neither dataset is clearly incompatible with the `concordance' ($\Omega_0=0.3$, $\Lambda_0=0.7$, $\sigma_8=0.9$) $\Lambda$CDM cosmogony. This conclusion differs from that reached recently by Navarro & Steinmetz, a disagreement that can be traced to inconsistencies in the normalization of the $\Lambda$CDM power spectrum used in that work.Comment: 12 pages including 7 figures using emulateapj, submitted to Ap

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We use N-body simulations to examine the e ects of mass out ows on the density pro les of cold dark matter (CDM) haloes surrounding dwarf galaxies. In particular, we investigate the consequences of supernova-driven winds that expel a large fraction of the baryonic component from a dwarf galaxy disk after a vigorous episode of star formation. We show that this sudden loss of mass leads to the formation of a core in the dark matter density pro le, although the original halo is modeled by a coreless (Hernquist) pro le. The core radius thus created is a sensitive function of the mass and radius of the baryonic disk being blown up. The loss of a disk with mass and size consistent with primordial nucleosynthesis constraints and angular momentum considerations imprints a core radius which is only a small fraction of the original scale-length of the halo. These small perturbations are, however, enough to reconcile the rotation curves of dwarf irregulars with the density pro les of haloes formed in the standard CDM scenario.

We present results of N-body/gasdynamical simulations designed to investigate the evolution of X-ray clusters in a flat, low-density, Λ-dominated cold dark matter (CDM) cosmogony. The simulations include self-gravity, pressure gradients and hydrodynamical shocks, but neglect radiative cooling. The density profile of the dark matter component can be fitted accurately by the simple formula originally proposed by Navarro, Frenk & White to describe the structure of clusters in a CDM universe with Ω = 1. In projection, the shape of the dark matter radial density profile and the corresponding line-of-sight velocity dispersion profile are in very good agreement with the observed profiles for galaxies in the CNOC sample of clusters. This suggests that galaxies are not strongly segregated relative to the dark matter in X-ray luminous clusters. The gas in our simulated clusters is less centrally concentrated than the dark matter, and its radial density profile is well described by the familiar β-model. As a result, the average baryon fraction within the virial radius (r vir ) is only 85-90% of the universal value and is lower nearer the center. The total mass and velocity dispersion of our clusters can be accurately inferred (with ∼ 15% uncertainty) from their X-ray emission-weighted temperature. We generalize Kaiser's scalefree scaling relations to arbitrary power spectra and low-density universes and show that simulated clusters generally follow these relations. The agreement between the simulations and the analytical results provides a convincing demonstration of the soundness of our gasdynamical numerical techniques. Although our simulated clusters resemble observed clusters in several respects, the slope of the luminosity-temperature relation implied by the scaling relations, and obeyed by the simulations, is in disagreement with observations. This suggests that non-gravitational effects such as preheating or cooling must have played an important role in determining the properties of the observed X-ray emission from galaxy clusters.