Carlos S. Frenk

A Universal density profile from hierarchical clustering

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 the halo mass, the initial density fluctuation spectrum, and the values of the cosmological parameters. Spherically averaged equilibrium profiles are well fitted 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 that 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 with 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, that allows accurate equilibrium profiles to be calculated as a function of mass in any hierarchical model.

The Structure of cold dark matter halos

High resolution N-body simulations show that the density profiles of dark matter halos formed in the standard CDM cosmogony can be fit accurately by scaling a simple “universal” profile. Regardless of their mass, halos are nearly isothermal over a large range in radius, but significantly shallower than r -2 near the center and steeper than r -2 in the outer regions. The characteristic overdensity of a halo correlates strongly with halo mass in a manner consistent with the mass dependence of the epoch of halo formation. Matching the shape of the rotation curves of disk galaxies with this halo structure requires (i) disk mass-to-light ratios to increase systematically with luminosity, (ii) halo circular velocities to be systematically lower than the disk rotation speed, and (iii) that the masses of halos surrounding bright galaxies depend only weakly on galaxy luminosity. This offers an attractive explanation for the puzzling lack of correlation between luminosity and dynamics in observed samples of binary galaxies and of satellite companions of bright spiral galaxies, suggesting that the structure of dark matter halos surrounding bright spirals is similar to that of cold dark matter halos.

Simulations of the formation, evolution and clustering of galaxies and quasars

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 2,1603 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.Numerical simulations are a primary theoretical tool to study the nonlinear gravitational growth of structure in the Universe, and to link the initial conditions of cold dark matter (CDM) cosmogonies to observations of galaxies at the present day. Without direct numerical simulation, the hierarchical build-up of structure with its threedimensional dynamics would be largely inaccessible. Since the dominant mass component, the dark matter, is assumed to consist of weakly interacting elementary particles that interact only gravitationally, such simulations use a set of discrete point particles to represent the collisionless dark matter fluid. This representation as an N-body system is obviously only a coarse approximation, and im-

Breaking the hierarchy of galaxy formation

Recent observations of the distant Universe suggest that much of the stellar mass of bright galaxies was already in place at z > 1. This presents a challenge for models of galaxy formation because massive halos are assembled late in the hierarchical clustering process intrinsic to the cold dark matter (CDM) cosmology. In this paper, we discuss a new implementation of the Durham semi-analytic model of galaxy formation in which feedback due to active galactic nuclei (AGN) is assumed to quench cooling flows in massive halos. This mechanism naturally creates a break in the local galaxy luminosity function at bright magnitudes. The model is implemented within the Millennium N-body simulation. The accurate dark matter merger trees and large number of realisations of the galaxy formation process enabled by this simulation result in highly accurate statistics. After adjusting the values of the physical parameters in the model by reference to the properties of the local galaxy population, we investigate the evolution of the K-band luminosity and galaxy stellar mass functions. We calculate the volume-averaged star formation rate density of the Universe as a function of redshift and the way in which this is apportioned amongst galaxies of different mass. The model robustly predicts a substantial population of massive galaxies out to redshift z � 5 and a star formation rate density which rises at least out to z � 2 in objects of all masses. Although observational data on these properties have been cited as evidence for “anti-hierarchical” galaxy formation, we find that when AGN feedback is taken into account, the fundamentally hierarchical CDM model provides a very good match to these observations.

The 2dF Galaxy Redshift Survey: Spectra and redshifts

The 2dF Galaxy Redshift Survey (2dFGRS) is designed to measure redshifts for approximately 250 000 galaxies. This paper describes the survey design, the spectroscopic observations, the redshift measurements and the survey data base. The 2dFGRS uses the 2dF multifibre spectrograph on the Anglo-Australian Telescope, which is capable of observing 400 objects simultaneously over a 2° diameter field. The source catalogue for the survey is a revised and extended version of the APM galaxy catalogue, and the targets are galaxies with extinction-corrected magnitudes brighter than b J = 19.45. The main survey regions are two declination strips, one in the southern Galactic hemisphere spanning 80° × 15° around the SGP, and the other in the northern Galactic hemisphere spanning 75° × 10° along the celestial equator; in addition, there are 99 fields spread over the southern Galactic cap. The survey covers 2000 deg 2 and has a median depth of z = 0.11. Adaptive tiling is used to give a highly uniform sampling rate of 93 per cent over the whole survey region. Redshifts are measured from spectra covering 3600-8000 A at a two-pixel resolution of 9.0 A and a median S/N of 13 pixel - 1 . All redshift identifications are visually checked and assigned a quality parameter Q in the range 1-5; Q ≥ 3 redshifts are 98.4 per cent reliable and have an rms uncertainty of 85 km s - 1 . The overall redshift completeness for Q ≥ 3 redshifts is 91.8 per cent, but this varies with magnitude from 99 per cent for the brightest galaxies to 90 per cent for objects at the survey limit. The 2dFGRS data base is available on the World Wide Web at http://www. mso.anu.edu.au/2dFGRS.

Galaxy formation through hierarchical clustering

Analytic methods for studying the formation of galaxies by gas condensation within massive dark halos are presented. The present scheme applies to cosmogonies where structure grows through hierarchical clustering of a mixture of gas and dissipationless dark matter. The simplest models consistent with the current understanding of N-body work on dissipationless clustering, and that of numerical and analytic work on gas evolution and cooling are adopted. Standard models for the evolution of the stellar population are also employed, and new models for the way star formation heats and enriches the surrounding gas are constructed. Detailed results are presented for a cold dark matter universe with Omega = 1 and H(0) = 50 km/s/Mpc, but the present methods are applicable to other models. The present luminosity functions contain significantly more faint galaxies than are observed.

Hierarchical galaxy formation

We describe the GALFORM semi-analytic model for calculating the formation and evolution of galaxies in hierarchical clustering cosmologies. It improves upon, and extends, the earlier scheme developed by Cole et al. (1994). The model employs a new Monte-Carlo algorithm to follow the merging evolution of dark matter halos with arbitrary mass resolution. It incorporates realistic descriptions of the density profiles of dark matter halos and the gas they contain; it follows the chemical evolution of gas and stars, and the associated production of dust; and it includes a detailed calculation of the sizes of disks and spheroids. Wherever possible, our prescriptions for modelling individual physical processes are based on results of numerical simulations. They require a number of adjustable parameters which we fix by reference to a small subset of local galaxy data. This results in a fully specified model of galaxy formation which can be �

Stable clustering, the halo model and non-linear cosmological power spectra

We present the results of a large library of cosmological N-body simulations, using power-law initial spectra.

The Aquarius project: the subhaloes of galactic haloes

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 halos 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 similar to 2.6 times larger and increases with decreasing distance from halo centre.

The 2dF Galaxy Redshift Survey: power-spectrum analysis of the final data set and cosmological implications

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