Cedric G. Lacey

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.

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 �

What Shapes the Luminosity Function of Galaxies

We investigate the physical mechanisms that shape the luminosity function of galaxies in hierarchical clustering models. Beginning with the mass function of dark matter halos in the ΛCDM (Λ cold dark matter) cosmology, we show, in incremental steps, how gas cooling, photoionization at high redshift, feedback processes, galaxy merging, and thermal conduction affect the shape of the luminosity function. We consider three processes whereby supernovae and stellar wind energy can affect the forming galaxy: (1) the reheating of cold disk gas to the halo temperature; (2) expansion of the hot, diffuse halo gas; and (3) complete expulsion of cold disk gas from the halo. We demonstrate that while feedback of form 1 is able to flatten the faint end of the galaxy luminosity function, this process alone does not produce the sharp cutoff observed at large luminosities. Feedback of form 2 is also unable to solve the problem at the bright end of the luminosity function. The relative paucity of very bright galaxies can only be explained if cooling in massive halos is strongly suppressed. This might happen if thermal conduction near the centers of halos is very efficient, or if a substantial amount of gas is expelled from halos by process 3 above. Conduction is a promising mechanism, but an uncomfortably high efficiency is required to suppress cooling to the desired level. If, instead, superwinds are responsible for the lack of bright galaxies, then the total energy budget required to obtain a good match to the galaxy luminosity function greatly exceeds the energy available from supernova explosions. The mechanism is only viable if the formation of central supermassive black holes and the associated energy generation play a crucial role in limiting the amount of stars that form in the host galaxy. The models that best reproduce the galaxy luminosity function also give reasonable approximations to the Tully-Fisher relation and the galaxy autocorrelation function.

Merger rates in hierarchical models of galaxy formation – II. Comparison with N-body simulations

We have made a detailed comparison of the results of N-body simulations with the analytical description of the merging histories of dark matter haloes presented in Lacey & Cole, which is based on an extension of the Press-Schechter method. We find the analytical predictions for the halo mass function, merger rates and formation times to be remarkably accurate. The N-body simulations used 1283 particles and were of self- similar clustering, with Ω=1 and initial power spectra P(k)∝kn with spectral indices n =−2, −1,0. The analytical model is, however, expected to apply for arbitrary Ω and more general power spectra. Dark matter haloes were identified in the simulations using two different methods and at a range of overdensities. For haloes selected at mean overdensities ∼100-200, the analytical mass function was found to provide a good fit to the simulations with a collapse threshold close to that predicted by the spherical collapse model, with a typical error of ≲30 per cent over a range of 103 in mass, which is the full dynamical range of our N-body simulation. This was insensitive to the type of filtering used. Over a range of 102- 103 in mass, there was also good agreement with the analytical predictions for merger rates including their dependence on the masses of the two haloes involved and the time interval being considered, and for formation times, including the dependence on halo mass and formation epoch. The analytical Press-Schechter mass function and its extension to halo lifetimes and merger rates thus provide a very useful description of the growth of dark matter haloes through hierarchical clustering, and should provide a valuable tool in studies of the formation and evolution of galaxies and galaxy clusters.

THE STRUCTURE OF DARK MATTER HALOES IN HIERARCHICAL CLUSTERING MODELS

We use a set of large cosmological N-body simulations to study the internal structure of dark matter haloes which form in scale-free hierarchical clustering models (initial power spectra P(k) ∞ kn with n = 0, −1 and −2) in an Ω = 1 universe. We find that the radius r178 in a halo corresponding to a mean interior overdensity of 178 accurately delineates the quasi-static halo interior from the surrounding infalling material, in agreement with the simple spherical collapse model. The interior velocity dispersion correlates with mass, again in good agreement with the spherical collapse model. Interior to the virial radius r178 the spherically averaged density, circular velocity and velocity dispersion profiles are well fitted by a simple two-parameter analytical model proposed by Navarro, Frenk & White. This model has ρ ∞ r−l at small radii, steepening to ρ ∞ r−3 at large radii, and fits our haloes to the resolution limit of the simulations. The two model parameters, scalelength and mass, are tightly correlated. Lower mass haloes are more centrally concentrated, and so have scalelengths which are a smaller fraction of their virial radius than those of their higher mass counterparts. This reflects the earlier formation times of low-mass haloes. The haloes are moderately aspherical, with typical axial ratios 1 : 0.8 : 0.65 at their virial radii, becoming gradually more spherical towards their centres. The haloes are generically triaxial, but with a slight preference for prolate over oblate configurations, at least for n = −1 and 0. These shapes are maintained by an anisotropic velocity dispersion tensor. The median value of the spin parameter is λ ≈ 0.04, with a weak trend for lower λ at higher halo mass. We also investigate how the halo properties depend on the algorithm used to identify them in the simulations, using both friends-of-friends and spherical overdensity methods. We find that, for groups selected at mean overdensities ∼ 100 – 400 by either method, the properties are insensitive to how the haloes are selected, if the halo centre is taken as the position of the most bound particle.

The Epoch of Galaxy Formation

We use a semianalytic model of galaxy formation in hierarchical clustering theories to interpret recent data on galaxy formation and evolution, focusing primarily on the recently discovered population of Lyman-break galaxies at z 3. For a variety of cold dark matter (CDM) cosmologies, we construct mock galaxy catalogs subject to selection criteria identical to those applied to the real data. We find that the expected number of Lyman-break galaxies is very sensitive to the assumed stellar initial mass function and to the normalization of the primordial power spectrum. For reasonable choices of these and other model parameters, it is possible to reproduce the observed abundance of Lyman-break galaxies in CDM models with ?0 = 1 and ?0 < 1. The characteristic masses, circular velocities, and star formation rates of the model Lyman-break galaxies depend somewhat on the values of the cosmological parameters, but are broadly in agreement with available data. These galaxies generally form from rare peaks at high redshift, and as a result their spatial distribution is strongly biased, with a typical bias parameter of b 4 and a comoving correlation length of r0 4 h-1 Mpc. The typical sizes of these galaxies, ~0.5 h-1 kpc, are substantially smaller than those of present-day bright galaxies. In combination with data at lower redshifts, the Lyman-break galaxies can be used to trace the cosmic star formation history. We compare theoretical predictions for this history with a compilation of recent data. The observational data match the theoretical predictions reasonably well, both for the distribution of star formation rates at various redshifts and for the integrated star formation rate as a function of redshift. Most galaxies (in our models and in the data) never experience star formation rates in excess of a few solar masses per year. Our models predict that even at z = 5, the integrated star formation rate is similar to that measured locally, although less than 1% of all the stars have formed prior to this redshift. The weak dependence of the predicted star formation histories on cosmological parameters allows us to propose a fairly general interpretation of the significance of the Lyman-break galaxies as the first galaxy-sized objects that experience significant amounts of star formation. These galaxies mark the onset of the epoch of galaxy formation that continues into the present day. The basic ingredients of a consistent picture of galaxy formation may well now be in place.

The Herschel ATLAS

The Herschel ATLAS is the largest open-time key project that will be carried out on the Herschel Space Observatory. It will survey 570 deg2 of the extragalactic sky, 4 times larger than all the other Herschel extragalactic surveys combined, in five far-infrared and submillimeter bands. We describe the survey, the complementary multiwavelength data sets that will be combined with the Herschel data, and the six major science programs we are undertaking. Using new models based on a previous submillimeter survey of galaxies, we present predictions of the properties of the ATLAS sources in other wave bands.

The SCUBA Half-Degree Extragalactic Survey - II. Submillimetre maps, catalogue and number counts

We present maps, source catalogue and number counts of the largest, most complete and unbiased extragalactic submillimetre survey: the 850-μm SCUBA Half-Degree Extragalactic Survey (SHADES). Using the Submillimetre Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT), SHADES mapped two separate regions of sky: the Subaru/XMM–Newton Deep Field (SXDF) and the Lockman Hole East (LH). Encompassing 93 per cent of the overall acquired data (i.e. data taken up to 2004 February 1), these SCUBA maps cover 720 arcmin2 with a rms noise level of about 2 mJy and have uncovered >100 submillimetre galaxies. In order to ensure the utmost robustness of the resulting source catalogue, data reduction was independently carried out by four subgroups within the SHADES team, providing an unprecedented degree of reliability with respect to other SCUBA catalogues available from the literature. Individual source lists from the four groups were combined to produce a robust 120-object SHADES catalogue; an invaluable resource for follow-up campaigns aiming to study the properties of a complete and consistent sample of submillimetre galaxies. For the first time, we present deboosted flux densities for each submillimetre galaxy found in a large survey. Extensive simulations and tests were performed separately by each group in order to confirm the robustness of the source candidates and to evaluate the effects of false detections, completeness and flux density boosting. Corrections for these effects were then applied to the data to derive the submillimetre galaxy source counts. SHADES has a high enough number of detected sources that meaningful differential counts can be estimated, unlike most submillimetre surveys which have to consider integral counts. We present differential and integral source number counts and find that the differential counts are better fit with a broken power law or a Schechter function than with a single power law; the SHADES data alone significantly show that a break is required at several mJy, although the precise position of the break is not well constrained. We also find that a 850-μm survey complete down to 2 mJy would resolve 20–30 per cent of the far-infrared background into point sources.

The Effects of Photoionization on Galaxy Formation — I: Model and Results at z=0

We develop a coupled model for the evolution of the global properties of the intergalactic medium (IGM) and the formation of galaxies, in the presence of a photoionizing background due to stars and quasars. We use this model to predict the thermodynamic history of the IGM when photoionized by galaxies forming in a cold dark matter (CDM) universe. The evolution of the galaxies is calculated using a semi-analytical model, including a detailed treatment of the effects of tidal stripping and dynamical friction on satellite galaxies orbiting inside larger dark matter halos. We include in the model the negative feedback on galaxy formation from the photoionizing background. Photoionization inhibits galaxy formation in low-mass dark matter halos in two ways: (i) heating of the IGM and inhibition of the collapse of gas into dark halos by the IGM pressure, and (ii) reduction in the radiative cooling of gas within halos. The result of our method is a self-consistent model of galaxy formation and the IGM. The IGM is reheated twice (during reionization of Hi and Heii), and we find that the star formation rate per unit volume is slightly suppressed after each episode of reheating. We find that galaxies brighter than L⋆ are mostly unaffected by reionization, while the abundance of faint galaxies is significantly reduced, leading to present-day galaxy luminosity functions with shallow faint end slopes, in good agreement with recent observational data. Reionization also affects other properties of these faint galaxies, in a readily understandable way.

The effects of photoionization on galaxy formation – II. Satellite galaxies in the Local Group

We use a self-consistent model of galaxy formation and the evolution of the intergalactic medium to study the effects of the reionization of the Universe at high redshift on the properties of satellite galaxies like those seen around the Milky Way. Photoionization suppresses the formation of small galaxies, so that surviving satellites are preferentially those that formed before the Universe reionized. As a result, the number of satellites expected today is about an order of magnitude smaller than the number inferred by identifying satellites with subhaloes of the same circular velocity in high-resolution simulations of the dark matter. The resulting satellite population has an abundance similar to that observed in the Local Group, although the distribution of circular velocities differs somewhat from the available data. We explore many other properties of satellite galaxies, including their gas content, metallicity and star formation rate, and find generally good agreement with available data. Our model predicts the existence of many as yet undetected satellites in the Local Group. We quantify their observability in terms of their apparent magnitude and surface brightness, and also in terms of their constituent stars. A near-complete census of the Milky Ways satellites would require imaging to V≈20 and to a surface brightness fainter than 26 V-band magnitudes per square arcsecond. Satellites with integrated luminosity V=15 should contain of order 100 stars brighter than B=26, with central stellar densities of a few tens per square arcminute. Discovery of a large population of faint satellites would provide a strong test of current models of galaxy formation.