Carlton M. Baugh

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 �

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

The 2dF galaxy redshift survey: near-infrared galaxy luminosity functions

We combine the Two Micron All Sky Survey (2MASS) Extended Source Catalogue and the 2dF Galaxy Redshift Survey to produce an infrared selected galaxy catalogue with 17 173 measured redshifts. We use this extensive data set to estimate the galaxy luminosity functions in the J- and K-S-bands. The luminosity functions are fairly well fitted by Schechter functions with parameters M-J(*) - 5 log h = -22.36 +/-0.02, alpha (J) = -0.93 +/-0.04, Phi (*)(J)= 0.0104 +/-0.0016 h(3) Mpc(-3) in the J-band and M-K s(*) - 5 log h = -23.44 +/-0.03, alphaK(S) = -0.96 +/-0.05, PhiK(S)(*) = 0.0108 +/-0.0016 h(3) Mpc(-3) in the K-S-band (2MASS Kron magnitudes). These parameters are derived assuming a cosmological model with Omega (0) = 0.3 and Lambda (0) = 0.7. With data sets of this size, systematic rather than random errors are the dominant source of uncertainty in the determination of the luminosity function. We carry out a careful investigation of possible systematic effects in our data. The surface brightness distribution of the sample shows no evidence that significant numbers of low surface brightness or compact galaxies are missed by the survey. We estimate the present-day distributions of b(J) - Ks and J- Ks colours as a function of the absolute magnitude and use models of the galaxy stellar populations, constrained by the observed optical and infrared colours, to infer the galaxy stellar mass function. Integrated over all galaxy masses, this yields a total mass fraction in stars (in units of the critical mass density) of Omega (stars)h = (1.6 +/-0.24) x 10(-3) for a Kennicutt initial mass function (IMF) and Omega (stars)h = (2.9 +/-0.43) x 10(-3) for a Salpeter IMF. These values are consistent with those inferred from observational estimates of the total star formation history of the Universe provided that dust extinction corrections are modest.

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.

The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe

We present a detailed analysis of the two-point correlation function, xi(sigma, pi), from the 2dF Galaxy Redshift Survey (2dFGRS). The large size of the catalogue, which contains similar to220 000 redshifts, allows us to make high-precision measurements of various properties of the galaxy clustering pattern. The effective redshift at which our estimates are made is z(s) approximate to 0.15, and similarly the effective luminosity, L-s approximate to 1.4L*. We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s(o) = 6.82 +/- 0.28 h(-1) Mpc. We also estimate the projected correlation function, Xi(sigma), and the real-space correlation function, xi(r), which can be fit by a power law (r/r(o))(-gamma), with r(o) = 5.05 +/- 0.26 h(-1) Mpc, gamma(r) = 1.67 +/- 0.03. For r greater than or similar to 20 h(-1) Mpc, xi drops below a power law as, for instance, is expected in the popular Lambda cold dark matter model. The ratio of amplitudes of the real- and redshift-space correlation functions on scales of 8-30 h(-1) Mpc gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi(sigma, pi) on scales 30-40 h(-1) Mpc provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f (nu), including rigorously the significant effect due to the infall velocities, and we find that the distribution is well fit by an exponential form. The accuracy of our xi(sigma, pi) measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of xi(r) and the two redshift-space distortion effects parametrized by beta and velocity dispersion, a. We find beta = 0.49 +/- 0.09 and a = 506 +/- 52 km s(-1), although the best-fitting values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(or), and find that the shape is consistent with models and simulations. This is the first time that beta and f (v) have been estimated from a self-consistent model of galaxy velocities. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that beta(L = L*, z = 0) = 0.47 +/- 0.08, and that the present-day matter density of the Universe, Omega(m) approximate to 0.3, consistent with other 2dFGRS estimates and independent analyses.

The 2dF Galaxy Redshift Survey: the environmental dependence of galaxy star formation rates near clusters

We have measured the equivalent width of the Hα emission line for 11 006 galaxies brighter than M_b-=-−19 (Ω_Λ = 0.7, Ω_m = 0.3, H_0 = 70 km s^(−1) Mpc^(−1)) at 0.05 < z < 0.1 in the 2dF Galaxy Redshift Survey (2dFGRS), in the fields of 17 known galaxy clusters. The limited redshift range ensures that our results are insensitive to aperture bias, and to residuals from night sky emission lines. We use these measurements to trace μ*, the star formation rate normalized to L*, as a function of distance from the cluster centre, and local projected galaxy density. We find that the distribution of μ* steadily skews toward larger values with increasing distance from the cluster centre, converging to the field distribution at distances greater than ∼3 times the virial radius. A correlation between star formation rate and local projected density is also found, which is independent of cluster velocity dispersion and disappears at projected densities below ∼1 galaxy Mpc^(−2) (brighter than M_b = −19). This characteristic scale corresponds approximately to the mean density at the cluster virial radius. The same correlation holds for galaxies more than two virial radii from the cluster centre. We conclude that environmental influences on galaxy properties are not restricted to cluster cores, but are effective in all groups where the density exceeds this critical value. The present-day abundance of such systems, and the strong evolution of this abundance, makes it likely that hierarchical growth of structure plays a significant role in decreasing the global average star formation rate. Finally, the low star formation rates well beyond the virialized cluster rule out severe physical processes, such as ram pressure stripping of disc gas, as being completely responsible for the variations in galaxy properties with environment.

The 2dF Galaxy Redshift Survey: the power spectrum and the matter content of the Universe

The 2dF Galaxy Redshift Survey has now measured in excess of 160 000 galaxy redshifts. This paper presents the power spectrum of the galaxy distribution, calculated using a direct Fourier transform based technique. We argue that, within the k-space region 0.02 less than or similar to k less than or similar to 0.15 h Mpc(-1), the shape of this spectrum should be close to that of the linear density perturbations convolved with the window function of the survey. This window function and its convolving effect on the power spectrum estimate are analysed in detail. By convolving model spectra, we are able to fit the power-spectrum data and provide a measure of the matter content of the Universe. Our results show that models containing baryon oscillations are mildly preferred over featureless power spectra. Analysis of the data yields 68 per cent confidence limits on the total matter density times the Hubble parameter Omega (m) h = 0.20 +/- 0.03, and the baryon fraction Omega (b)/Omega (m) = 0.15 +/- 0.07, assuming scale-invariant primordial fluctuations.

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.

Galaxy ecology: groups and low-density environments in the SDSS and 2dFGRS

We analyse the observed correlation between galaxy environment and Halpha emission-line strength, using volume-limited samples and group catalogues of 24 968 galaxies at 0.05 < z < 0.095, drawn from the 2dF Galaxy Redshift Survey (M-bJ < -19.5) and the Sloan Digital Sky Survey (M-r < -20.6). We characterize the environment by: (1) Sigma(5), the surface number density of galaxies determined by the projected distance to the fifth nearest neighbour; and (2) rho(1.1) and rho(5.5), three-dimensional density estimates obtained by convolving the galaxy distribution with Gaussian kernels of dispersion 1.1 and 5.5 Mpc, respectively. We find that star-forming and quiescent galaxies form two distinct populations, as characterized by their H equivalent width, W-0(Halpha). The relative numbers of star-forming and quiescent galaxies vary strongly and continuously with local density. However, the distribution of W-0(Halpha) amongst the star-forming population is independent of environment. The fraction of star-forming galaxies shows strong sensitivity to the density on large scales, rho(5.5), which is likely independent of the trend with local density, rho(1.1). We use two differently selected group catalogues to demonstrate that the correlation with galaxy density is approximately independent of group velocity dispersion, for sigma = 200-1000 km s(-1). Even in the lowest-density environments, no more than similar to70 per cent of galaxies show significant Halpha emission. Based on these results, we conclude that the present-day correlation between star formation rate and environment is a result of short-time-scale mechanisms that take place preferentially at high redshift, such as starbursts induced by galaxy-galaxy interactions.