Modelling angular-momentum history in dark-matter haloes

We model the acquisition of spin by dark-matter haloes in semi-analytic merger trees. We explore two different algorithms: one in which halo spin is acquired from the orbital angular momentum of merging satellites, and another in which halo spin is gained via tidal torquing on shells of material while still in the linear regime. We find that both scenarios produce the characteristic spin distribution of haloes found in N -body simulations, namely, a log-normal distribution with mean ≈ 0.04 and standard deviation ≈ 0.5 in the log. A perfect match requires fine-tuning of two free parameters. Both algorithms also reproduce the general insensitivity of the spin distribution to halo mass, redshift and cosmology seen in N -body simulations. The spin distribution can be made strictly constant by physically motivated scalings of the free parameters. In addition, both schemes predict that haloes that have had recent major mergers have systematically larger spin values. These algorithms can be implemented within semi-analytic models of galaxy formation based on merger trees. They yield detailed predictions of galaxy properties that strongly depend on angular momentum (such as size and surface brightness) as a function of merger history and environment.     

Evolution of the mass function of dark matter haloes

We use a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15, in a  50 h ⁻¹ Mpc  volume containing 80 million particles. Our low-redshift results allow us to probe low-σ density fluctuations significantly beyond the range of previous cosmological simulations. The Sheth & Tormen mass function provides an excellent match to all of our data except for redshifts of 10 and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 per cent for the  10¹⁰–10¹¹ M_⊙  haloes sampled at redshift 15. Our results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. We provide an empirical fit to our data that corrects for the overprediction of extremely rare objects by the Sheth & Tormen mass function. This overprediction has implications for studies that use the number densities of similarly rare objects as cosmological probes. For example, the number density of high-redshift  ( z ≃ 6) QSOs  , which are thought to be hosted by haloes at 5σ peaks in the fluctuation field, are likely to be overpredicted by at least a factor of 50 per cent. We test the sensitivity of our results to force accuracy, starting redshift and halo-finding algorithm.     

Evaluating approximations for halo merging histories

We study the merging history of dark matter haloes in N -body simulations and semi-analytical 'merger trees' based on the extended Press–Schechter (EPS) formalism. The main focus of our study is the joint distribution of progenitor number and mass as a function of redshift and parent halo mass. We begin by investigating the mean quantities predicted directly by the Press–Schechter (PS) and EPS formalism, such as the halo mass and conditional mass functions, and compare these predictions with the results of the simulations. The higher moments of this distribution are not predicted by the EPS formalism alone and must be obtained from the merger trees. We find that the Press–Schechter model deviates from the simulations at the level of 30–50 per cent on certain mass scales, and that the sense of the discrepancy changes as a function of redshift. We show that this discrepancy is reflected in the higher moments of the distribution of progenitor mass and number. We investigate some related statistics such as the accretion rate and the mass ratio of the largest two progenitors. For galaxy sized haloes ( M ∼10¹² M_⊙), we find that the merging history of haloes, as represented by these statistics, is well reproduced in the merger trees compared with the simulations. The agreement deteriorates for larger mass haloes. We conclude that merger trees based on the extended Press–Schechter formalism provide a reasonably reliable framework for semi-analytical models of galaxy formation.     

Effects of merging histories on angular momentum distribution of dark matter haloes

The effects of merging histories of proto-objects on the angular momentum distributions of the present-time dark matter haloes are analysed. An analytical approach to the analysis of the angular momentum distributions assumes that the haloes are initially homogeneous ellipsoids and that the growth of the angular momentum of the haloes halts at their maximum expansion time. However, the maximum expansion time cannot be determined uniquely, because in the hierarchical clustering scenario each progenitor, or subunit, of the halo has its own maximum expansion time. Therefore the merging history of the halo may be important in estimating its angular momentum. Using the merger tree model by Rodrigues &38; Thomas, which takes into account the spatial correlations of the density fluctuations, we have investigated the effects of the merging histories on the angular momentum distributions of dark matter haloes. It was found that the merger effects, that is, the effects of the inhomogeneity of the maximum expansion times of the progenitors which finally merge together into a halo, do not strongly affect the final angular momentum distributions, so that the homogeneous ellipsoid approximation happens to be good for the estimation of the angular momentum distribution of dark matter haloes. This is because the effect of the different directions of the angular momenta of the progenitors cancels out the effect of the inhomogeneity of the maximum expansion times of the progenitors.   The contribution of the orbital angular momentum to the total angular momentum when two or more pre-existing haloes merge together was also investigated. It is shown that this contribution is more important than that of the angular momentum of diffuse accreting matter to the total angular momentum, especially when the mergers occur many times.     

The statistical properties of Λ cold dark matter halo formation

We present a comparison of the statistical properties of dark matter halo merger trees extracted from the Millennium Simulation with Extended Press–Schechter (EPS) formalism and the related galform Monte Carlo method for generating ensembles of merger trees. The volume, mass resolution and output frequency make the Millennium Simulation a unique resource for the study of the hierarchical growth of structure. We construct the merger trees of present-day friends-of-friends groups and calculate a variety of statistics that quantify the masses of their progenitors as a function of redshift, accretion rates, and the redshift distribution of their most recent major merger. We also look in the forward direction and quantify the present-day mass distribution of haloes into which high-redshift progenitors of a specific mass become incorporated. We find that the EPS formalism and its Monte Carlo extension capture the qualitative behaviour of all these statistics, but as redshift increases they systematically underestimate the masses of the most massive progenitors. This shortcoming is worst for the Monte Carlo algorithm. We present a fitting function to a scaled version of the progenitor mass distribution and show how it can be used to make more accurate predictions of both progenitor and final halo mass distributions.     

Optical and near-infrared colours as a discriminant of the age and metallicity of stellar populations

We present a comprehensive analysis of the ability of current stellar population models to reproduce the optical ( ugriz ) and near-infrared ( JHK ) colours of a small sample of well-studied nearby elliptical and S0 galaxies. We find broad agreement between the ages and metallicities derived using different population models, although different models show different systematic deviations from the measured broad-band fluxes. Although it is possible to constrain simple stellar population models to a well-defined area in age–metallicity space, there is a clear degeneracy between these parameters even with such a full range of precise colours. The precision to which age and metallicity can be determined independently, using only broad-band photometry with realistic errors, is  Δ[Fe/H]≃ 0.18  and  Δlog Age ≃ 0.25  . To constrain the populations and therefore the star formation history further, it will be necessary to combine broad-band optical–IR photometry with either spectral line indices, or else photometry at wavelengths outside this range.     

The build-up of haloes within Press–Schechter theory

Modelling the build-up of haloes is important for linking the formation of galaxies with cosmological models. A simple model of halo growth is provided by Press–Schechter (PS) theory, where the initial field of density fluctuations is smoothed using spherically symmetric filters centred on a given position to obtain information about the likelihood of later collapse on varying scales. In this paper the predicted halo mass growth is compared for three filter shapes: Gaussian, top-hat and sharp k -space. Preliminary work is also presented analysing the build-up of haloes within numerical simulations using a friends-of-friends group finder. The best-fit to the simulation mass function was obtained using PS theory with a top-hat filter. By comparing both the backwards conditional mass function, which gives the distribution of halo progenitors, and the distribution of halo mergers in time, the build-up of haloes in the simulations is shown to be better fitted by PS theory with a sharp k -space filter. This strengthens previous work, which also found the build-up of haloes in simulations to be well matched to PS theory with a sharp k -space filter by providing a direct comparison of different filters and by extending the statistical tools used to analyse halo mass growth. The usefulness of this work is illustrated by showing that the cosmological evolution in the proportion of haloes that have undergone recent merger is predicted to be independent of mass and power spectrum and to only depend upon cosmology. Recent results from observations of field galaxies are shown to match the evolution expected, but are not sufficiently accurate to distinguish usefully between cosmological parameters.     

Merger rates of dark matter haloes

We derive analytic merger rates for dark matter haloes within the framework of the extended Press–Schechter (EPS) formalism. These rates become self-consistent within EPS once we realize that the typical merger in the limit of a small time-step involves more than two progenitors, contrary to the assumption of binary mergers adopted in earlier studies. We present a general method for computing merger rates that span the range of solutions permitted by the EPS conditional mass function, and focus on a specific solution that attempts to match the merger rates in N -body simulations. The corrected EPS merger rates are more accurate than the earlier estimates of Lacey & Cole by ∼20 per cent for major mergers and by up to a factor of ∼3 for minor mergers of mass ratio 1:10⁴. Based on the revised merger rates, we provide a new algorithm for constructing Monte Carlo EPS merger trees, which could be useful in semi-analytic modelling. We provide analytic expressions and plot numerical results for several quantities that are very useful in studies of galaxy formation. This includes (i) the rate of mergers of a given mass ratio per given final halo, (ii) the fraction of mass added by mergers to a halo and (iii) the rate of mergers per given main progenitor. The creation and destruction rates of haloes serve for a self-consistency check. Our method for computing merger rates can be applied to conditional mass functions beyond EPS, such as those obtained by the ellipsoidal collapse model or extracted from N -body simulations.     

On the galaxy stellar mass function, the mass–metallicity relation and the implied baryonic mass function

A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ω_b= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α₂≃−1.6  . At masses below  ∼10^8.5 M_⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α₂≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼10¹¹ M_⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.     

Globular cluster systems in nearby dwarf galaxies – I. HST/ACS observations and dynamical properties of globular clusters at low environmental density

We investigate the old globular cluster (GC) population of 68 faint  ( M _V > −16 mag)  dwarf galaxies located in the halo regions of nearby (≲12 Mpc) loose galaxy groups and in the field environment based on archival Hubble Space Telescope ( HST )/Advanced Camera for Surveys (ACS) images in F606W and F814W filters. The combined colour distribution of 175 GC candidates peaks at  ( V − I ) = 0.96 ± 0.07 mag  and the GC luminosity function turnover for the entire sample is found at   M _{V ,TO}=−7.6 ± 0.11 mag  , similar to the old metal-poor Large Magellanic Cloud (LMC) GC population. Our data reveal a tentative trend of   M _{V ,TO}  becoming fainter from late- to early-type galaxies. The luminosity and colour distributions of GCs in dIrrs show a lack of faint blue GCs (bGCs). Our analysis reveals that this might reflect a relatively younger GC system than typically found in luminous early-type galaxies. If verified by spectroscopy, this would suggest a later formation epoch of the first metal-poor star clusters in dwarf galaxies. We find several bright (massive) GCs which reside in the nuclear regions of their host galaxies. These nuclear clusters have similar luminosities and structural parameters as the peculiar Galactic clusters suspected of being the remnant nuclei of accreted dwarf galaxies, such as M54 and ωCen. Except for these nuclear clusters, the distribution of GCs in dIrrs in the half-light radius versus cluster mass plane is very similar to that of Galactic young halo clusters, which suggests comparable formation and dynamical evolution histories. A comparison with theoretical models of cluster disruption indicates that GCs in low-mass galaxies evolve dynamically as self-gravitating systems in a benign tidal environment.     

Testing the modified Press–Schechter model against N-body simulations

A modified version of the extended Press–Schechter model for the growth of dark-matter haloes was introduced in two previous papers, with the aim of explaining the mass–density relation shown by haloes in high-resolution cosmological simulations. In this model, major mergers are well separated from accretion, thereby allowing a natural definition of halo formation and destruction. This makes it possible to derive analytic expressions for halo formation and destruction rates, the mass accretion rate and the probability distribution functions of halo formation times and progenitor masses. The stochastic merger histories of haloes can be readily derived and easily incorporated into semi-analytical models of galaxy formation, thus avoiding the usual problems encountered in the construction of Monte Carlo merger trees from the original extended Press–Schechter formalism. Here we show that the predictions of the modified Press–Schechter model are in good agreement with the results of N -body simulations for several scale-free cosmologies.     

Simulating subhaloes at high redshift: merger rates, counts and types

Galaxies are believed to be in one-to-one correspondence with simulated dark matter subhaloes. We use high-resolution N -body simulations of cosmological volumes to calculate the statistical properties of subhalo (galaxy) major mergers at high redshift ( z = 0.6–5). We measure the evolution of the galaxy merger rate, finding that it is much shallower than the merger rate of dark matter host haloes at   z > 2.5  , but roughly parallels that of haloes at   z < 1.6  . We also track the detailed merger histories of individual galaxies and measure the likelihood of multiple mergers per halo or subhalo. We examine satellite merger statistics in detail: 15–35 per cent of all recently merged galaxies are satellites, and satellites are twice as likely as centrals to have had a recent major merger. Finally, we show how the differing evolution of the merger rates of haloes and galaxies leads to the evolution of the average satellite occupation per halo, noting that for a fixed halo mass, the satellite halo occupation peaks at   z ∼ 2.5  .     

The LBDS Hercules sample of mJy radio sources at 1.4 GHz – I. Multicolour photometry

The results are presented of an extensive programme of optical and infrared imaging of radio sources in a complete subsample of the Leiden–Berkeley Deep Survey. The LBDS Hercules sample consists of 72 sources observed at 1.4 GHz, with flux densities S _1.41.0 mJy, in a 1.2 deg² region of Hercules. This sample is almost completely identified in the g , r , i and K bands, with some additional data available at J and H . The magnitude distributions peak at r ≃22 mag, K ≃16 mag and extend down to r ≃26 mag, K ≃21 mag. The K -band magnitude distributions for the radio galaxies and quasars are compared with those of other radio surveys. At S _1.4 GHz≲1 Jy, the K -band distribution does not change significantly with radio flux density. The sources span a broad range of colours, with several being extremely red ( r − K ≳6). Though small, this is the most optically complete sample of mJy radio sources available at 1.4 GHz, and is ideally suited for studying the evolution of the radio luminosity function out to high redshifts.     

Multifrequency observations of the jets in the radio galaxy NGC 315

We present images of the jets in the nearby radio galaxy NGC 315 made with the Very Large Array at five frequencies between 1.365 and 5 GHz with resolutions between 1.5 and 45 arcsec. Within 15 arcsec of the nucleus, the spectral index of the jets is  α= 0.61  . Further from the nucleus, the spectrum is flatter, with significant transverse structure. Between 15 and 70 arcsec from the nucleus, the spectral index varies from ≈0.55 on-axis to ≈0.44 at the edge. This spectral structure suggests a change of dominant particle acceleration mechanism with distance from the nucleus and the transverse gradient may be associated with shear in the jet velocity field. Further from the nucleus, the spectral index has a constant value of 0.47. We derive the distribution of Faraday rotation over the inner ±400 arcsec of the radio source and show that it has three components: a constant term, a linear gradient (both probably due to our Galaxy) and residual fluctuations at the level of 1–2 rad m⁻². These residual fluctuations are smaller in the brighter (approaching) jet, consistent with the idea that they are produced by magnetic fields in a halo of hot plasma that surrounds the radio source. We model this halo, deriving a core radius of ≈225 arcsec and constraining its central density and magnetic field strength. We also image the apparent magnetic field structure over the first ±200 arcsec from the nucleus.     

Old high-redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at z  ≃ 1.5 which have apparent stellar ages of ≳ 3 Gyr, based on detailed spectroscopy in the rest-frame ultraviolet. In order for galaxies to have existed at the high collapse redshifts indicated by these ages, there must be a minimum level of power in the density fluctuation spectrum on galaxy scales. This paper compares the required power with that inferred from other high-redshift populations: damped Lyα absorbers and Lyman-limit galaxies at z  ≃ 3.2. If the collapse redshifts for the old red galaxies are in the range z _c ≃ 6–8, there is general agreement between the various tracers on the required inhomogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately ν ≃ 3.0 fluctuations, implying a very large bias parameter b  ≃ 6. If the collapse redshifts of the red galaxies are indeed in the range z _c = 6–8 required for power spectrum consistency, their implied ages at z  ≃ 1.5 are between 3 and 3.8 Gyr for essentially any model universe of current age 14 Gyr. The age of these objects as deduced from gravitational collapse thus provides independent support for the ages estimated from their stellar populations. Such early-forming galaxies are rare, and their contribution to the cosmological stellar density is consistent with an extrapolation to higher redshifts of the star formation rate measured at z  < 5; there is no evidence for a general era of spheroid formation at extreme redshifts.     

The extended rotation curve and the dark matter halo of M33

We present the 21-cm rotation curve of the nearby galaxy M33 out to a galactocentric distance of 16 kpc (13 disc scalelengths). The rotation curve keeps rising out to the last measured point and implies a dark halo mass ≳5×10¹⁰ M_⊙. The stellar and gaseous discs provide virtually equal contributions to the galaxy gravitational potential at large galactocentric radii, but no obvious correlation is found between the radial distribution of dark matter and the distribution of stars or gas.
Results of the best fit to the mass distribution in M33 picture a dark halo which controls the gravitational potential from 3 kpc outward, with a matter density which decreases radially as R ^−1.3. The density profile is consistent with the theoretical predictions for structure formation in hierarchical clustering cold dark matter (CDM) models, and favours lower mass concentrations than those expected in the standard cosmogony.     

The first galaxies: assembly, cooling and the onset of turbulence

We investigate the properties of the first galaxies at   z ≳ 10  with highly resolved numerical simulations, starting from cosmological initial conditions and taking into account all relevant primordial chemistry and cooling. A first galaxy is characterized by the onset of atomic hydrogen cooling, once the virial temperature exceeds  ≃10⁴ K  , and its ability to retain photoheated gas. We follow the complex accretion and star formation history of a  ≃5 × 10⁷ M_⊙  system by means of a detailed merger tree and derive an upper limit on the number of Population III (Pop III) stars formed prior to its assembly. We investigate the thermal and chemical evolution of infalling gas and find that partial ionization at temperatures  ≳10⁴ K  catalyses the formation of  H₂  and hydrogen deuteride, allowing the gas to cool to the temperature of the cosmic microwave background. Depending on the strength of radiative and chemical feedback, primordial star formation might be dominated by intermediate-mass Pop III stars formed during the assembly of the first galaxies. Accretion on to the nascent galaxy begins with hot accretion, where gas is accreted directly from the intergalactic medium and shock heated to the virial temperature, but is quickly accompanied by a phase of cold accretion, where the gas cools in filaments before flowing into the parent halo with high velocities. The latter drives supersonic turbulence at the centre of the galaxy and could lead to very efficient chemical mixing. The onset of turbulence in the first galaxies thus likely marks the transition to Pop II star formation.     

A disc-wind model with correct crossing of all magnetohydrodynamic critical surfaces

We present CCD (charge-coupled device) photometry for galaxies around 204 bright ( m _Z<15.5) Zwicky galaxies in the equatorial extension of the APM Galaxy Survey, sampling an area over 400 deg², which extends 6 h in right ascension. We fit a best linear relation between the Zwicky magnitude system, m _Z, and the CCD photometry, B _CCD, by doing a likelihood analysis that corrects for Malmquist bias. This fit yields a mean scale error in Zwicky of 0.38 mag mag⁻¹: i.e. Δ m _Z≃(0.62±0.05)Δ B _CCD and a mean zero-point of 〈 B _CCD− m _Z〉=−0.35±0.15 mag. The scatter around this fit is about 0.4 mag. Correcting the Zwicky magnitude system with the best-fitting model results in a 60 per cent lower normalization and 0.35-mag brighter M * in the luminosity function. This brings the CfA2 luminosity function closer to the other low-redshift estimations (e.g. Stromlo-APM or LCRS). We find a significant positive angular correlation of magnitudes and position in the sky at scales smaller than about 5 arcmin, which corresponds to a mean separation of 120  h ⁻¹ kpc. We also present colours, sizes and ellipticities for galaxies in our fields, which provides a good local reference for the studies of galaxy evolution.