Clustering of galaxies at 3.6 μm in the Spitzer Wide-area Infrared Extragalactic legacy survey

We investigate the clustering of galaxies selected in the 3.6 μm band of the Spitzer Wide-area Infrared Extragalactic (SWIRE) legacy survey. The angular two-point correlation function is calculated for 11 samples with flux limits of S _3.6≥ 4–400 μJy, over an 8 deg² field. The angular clustering strength is measured at >5σ significance at all flux limits, with amplitudes of A = (0.49–29) × 10⁻³ at 1°, for a power-law model, A θ^−0.8. We estimate the redshift distributions of the samples using phenomological models, simulations and photometric redshifts, and so derive the spatial correlation lengths. We compare our results with the Galaxies In Cosmological Simulations (GalICS) models of galaxy evolution and with parametrized models of clustering evolution. The GalICS simulations are consistent with our angular correlation functions, but fail to match the spatial clustering inferred from the phenomological models or the photometric redshifts. We find that the uncertainties in the redshift distributions of our samples dominate the statistical errors in our estimates of the spatial clustering. At low redshifts (median z ≤ 0.5), the comoving correlation length is approximately constant,   r ₀= 6.1 ± 0.5  h ⁻¹  Mpc, and then decreases with increasing redshift to a value of 2.9 ± 0.3  h ⁻¹ Mpc for the faintest sample, for which the median redshift is z ∼ 1. We suggest that this trend can be attributed to a decrease in the average galaxy and halo mass in the fainter flux-limited samples, corresponding to changes in the relative numbers of early- and late-type galaxies. However, we cannot rule out strong evolution of the correlation length over  0.5 < z < 1  .     

The redshift evolution of clustering in the Hubble Deep Field

We present a correlation function analysis for the catalogue of photometric redshifts obtained from the Hubble Deep Field image by Fernandez-Soto, Lanzetta & Yahil. By dividing the catalogue into redshift bins of width Δ z =0.4 we measured the angular correlation function w ( θ ) as a function of redshift up to z ∼4.8. From these measurements we derive the trend of the correlation length r ₀. We find that r ₀( z ) is roughly constant with look-back time up to z ≃2, and then increases to higher values at z ≳2.4. We estimate the values of r ₀, assuming ξ ( r , z )=[ r r ₀( z )]^{− γ} , γ =1.8 and various geometries. For Ω₀=1 we find r ₀( z =3)≃7.00±4.87  h ⁻¹ Mpc, in good agreement with the values obtained from analysis of the Lyman break galaxies.     

The clustering of K∼20 galaxies in 17 radio galaxy fields

We investigate the angular correlation function, ο(θ), of the galaxies detected in the 2.1-μm K ' band in 17 fields (101.5 arcmin² in total), each containing a z ∼1.1 radio galaxy. There is a significant detection of galaxy clustering at a limit of K ∼20, with a ο(θ) amplitude similar to that estimated by Carlberg et al. at K =21.5. The ο(θ) amplitudes of these K -limited samples are higher than expected from the faint galaxy clustering in the blue and red passbands, but consistent with a pure luminosity evolution model if clustering is stable (ε=0) and the correlation function of early-type galaxies is steeper than that of spirals.
We do not detect a significant cross-correlation between the radio galaxies and the other galaxies in these fields. The upper limits on the cross-correlation are consistent with a mean clustering environment of Abell class 0 for z ∼1.1 radio galaxies, similar to that observed for radio galaxies at z ∼0.5, but would argue against an Abell class 1 or richer environment. As Abell 0 clustering around the radio galaxies would not significantly increase the ο(θ) amplitude of galaxies in these fields, stable clustering with a steep ξ( r ) for E/S0 galaxies appears to remain the most likely interpretation of the ο(θ) amplitude.
At K ≤20, the number of galaxy–galaxy pairs of 2–3 arcsec separation exceeds the random expectation by a factor of 2.15±0.26. The excess of close pairs is comparable to that previously reported for R -band data, and consistent with a ∼(1+ z )² evolution of the galaxy merger rate.     

A measurement of the faint source correlation function in the GOODS and UDF surveys

We present a stable procedure for defining and measuring the two point angular autocorrelation function,   w (θ) =[θ/θ₀( V )]^−Γ  , of faint  (25 < V < 29)  , barely resolved and unresolved sources in the Hubble Space Telescope Great Observatories Origins Deep Survey and Ultra Deep Field data sets. We construct catalogues that include close pairs and faint detections. We show, for the first time, that, on subarcsec scales, the correlation function exceeds unity. This correlation function is well fit by a power law with index  Γ≈ 2.5  and a  θ₀= 10^{−0.1( V −25.8)} arcsec  . This is very different from the values of  Γ≈ 0.7  and  θ₀( r ) = 10^{−0.4( r −21.5)} arcsec  associated with the gravitational clustering of brighter galaxies. This observed clustering probably reflects the presence of giant star-forming regions within galactic-scale potential wells. Its measurement enables a new approach to measuring the redshift distribution of the faintest sources in the sky.     

The effect of weak lensing on the angular correlation function of faint galaxies

The angular correlation function ο(θ) of faint galaxies is affected both by non-linear gravitational evolution and by magnification bias resulting from gravitational lensing. We compute the resulting ο(θ) for different cosmological models and show how its shape and redshift evolution depend on Ω and Λ. For galaxies at redshift greater than 1 ( R magnitude fainter than about 24), magnification bias can significantly enhance or suppress ο(θ), depending on the slope of the number–magnitude relation. We show, for example, how it changes the ratio of ο(θ) for two galaxy samples with different number count slopes.     

The redshift distribution of FIRST radio sources at 1 mJy

We present spectra for a sample of radio sources from the FIRST survey, and use them to define the form of the redshift distribution of radio sources at mJy levels. We targeted 365 sources and obtained 46 redshifts (13 per cent of the sample). We find that our sample is complete in redshift measurement to R ∼18.6, corresponding to z ∼0.2. Galaxies were assigned spectral types based on emission-line strengths. Early-type galaxies represent the largest subset (45 per cent) of the sample and have redshifts 0.15≲ z ≲0.5; late-type galaxies make up 15 per cent of the sample and have redshifts 0.05≲ z ≲0.2; starbursting galaxies are a small fraction (∼6 per cent), and are very nearby ( z ≲0.05). Some 9 per cent of the population have Seyfert 1/quasar-type spectra, all at z ≳0.8, and 4 per cent are Seyfert 2 type galaxies at intermediate redshifts ( z ∼0.2).
Using our measurements and data from the Phoenix survey (Hopkins et al.), we obtain an estimate for N ( z ) at S _1.4 GHz≥1 mJy and compare this with model predictions. At variance with previous conclusions, we find that the population of starbursting objects makes up ≲5 per cent of the radio population at S ∼1 mJy.     

The clustering of colour-selected galaxies

We present measurements of the angular correlation function of galaxies selected from a B _J ∼23.5 multicolour survey of two 5°×5° fields located at high galactic latitudes. The galaxy catalogue of ∼4×10⁵ galaxies is comparable in size to catalogues used to determine the galaxy correlation function at low redshift. Measurements of the z ∼0.4 correlation function at large angular scales show no evidence for a break from a power law, although our results are not inconsistent with a break at ≳15 h⁻¹ Mpc. Despite the large fields-of-view, there are large discrepancies between the measurements of the correlation function in each field, possibly caused by dwarf galaxies within z ∼0.11 clusters near the South Galactic Pole.
Colour selection is used to study the clustering of galaxies from z ∼0 to z ∼0.4. The galaxy correlation function is found to depend strongly on colour, with red galaxies more strongly clustered than blue galaxies by a factor of ≳5 at small scales. The slope of the correlation function is also found to vary with colour, with γ∼1.8 for red galaxies and γ∼1.5 for blue galaxies. The clustering of red galaxies is consistently strong over the entire magnitude range studied, although there are large variations between the two fields. The clustering of blue galaxies is extremely weak over the observed magnitude range, with clustering consistent with r ₀∼2 h⁻¹ Mpc. This is weaker than the clustering of late-type galaxies in the local Universe, and suggests that galaxy clustering is more strongly correlated with colour than morphology. This may also be the first detection of a substantial low-redshift galaxy population with clustering properties similar to faint blue galaxies.     

Modelling the number counts of early-type galaxies by pure luminosity evolution

In this paper, we explore the plausible luminosity evolution of early-type galaxies in different cosmological models by constructing a set of pure luminosity evolution (PLE) models via the choices of the star-formation rate (SFR) parameters and formation redshift z _f of galaxies, with the observational constraints derived from the Hubble Space Telescope ( HST  ) morphological number counts for elliptical and S0 galaxies of the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF). We find that the number counts of early-type galaxies can be explained by the pure luminosity evolution models, without invoking exotic scenarios such as merging or introducing an additional population, but the evolution should be nearly passive, with a high z _f assumed. The conclusion is valid in all of the three cosmological models we adopt in this paper. We also present the redshift distributions for three bins of observed magnitudes in the F814w passband, to show the redshift at which the objects that dominate the counts at a given magnitude may be found. The predictions of the redshift distribution of 22.5 <  b _j  < 24.0 are also presented for comparison with future data.     

Constraints on cosmological and biasing models using active galactic nucleus clustering

We attempt to put constraints on different cosmological and biasing models by combining the recent clustering results of X-ray sources in the local ( z ≤0.1) and distant Universe ( z ∼1) . To this end we compare the measured angular correlation function for bright (Akylas et al.) and faint (Vikhlinin & Forman) ROSAT X-ray sources respectively with those expected in three spatially flat cosmological models. Taking into account the different functional forms of the bias evolution, we find that there are two cosmological models which match the data well. In particular, low-Ω_○ cosmological models (Ω_Λ=1−Ω_○=0.7) that contain either (i) high σ ₈^mass=1.13 value with galaxy merging bias, b ( z )∝(1+ z )^1.8 or (ii) low σ ₈^mass=0.9 with non-bias, b ( z ) ≡ 1 best reproduce the AGN clustering results, while τ CDM models with different bias behaviour are ruled out at a high significance level.     

The redshift-space two-point correlation function of ELAIS-S1 galaxies

We investigate the clustering properties of galaxies in the recently completed ELAIS-S1 redshift survey through their spatial two-point autocorrelation function. We used a subsample of the ELAIS-S1 catalogue covering approximately 4 deg² and consisting of 148 objects selected at 15 μm with a flux >0.5 mJy and a redshift   z < 0.5  . We detected a positive signal in the correlation function that in the range of separations  1–10  h ⁻¹ Mpc  is well approximated by a power law with a slope  γ= 1.4 ± 0.25  and a correlation length   s ₀= 5.4 ± 1.2  h ⁻¹ Mpc  , at the 90 per cent significance level. This result is in good agreement with the redshift-space correlation function measured in more local samples of mid-infrared-selected galaxies such as the IRAS Point Source Catalog (PSC z ) redshift survey. This suggests a lack of significant clustering evolution of infrared-selected objects out to   z = 0.5  that is further confirmed by the consistency found between the correlation functions measured in a local  ( z < 0.2)  and a distant  (0.2 < z < 0.5)  subsample of ELAIS-S1 galaxies. We also confirm that optically selected galaxies in the local redshift surveys, especially those of the SDSS sample, are significantly more clustered than infrared objects.     

Statistical analysis of galaxy surveys – III. The non-linear clustering of red and blue galaxies in the 2dFGRS

We present measurements of the higher order clustering of red and blue galaxies as a function of scale and luminosity made from the two-degree field galaxy redshift survey (2dFGRS). We use a counts-in-cells analysis to estimate the volume-averaged correlation functions,     , as a function of scale up to the order of   p = 5  , and also the reduced void probability function. Hierarchical amplitudes are constructed using the estimates of the correlation functions:     . We find that (i) red galaxies display stronger clustering than blue galaxies at all orders measured; (ii) red galaxies show values of   S _p   that are strongly dependent on luminosity whereas blue galaxies show no segregation in   S _p   within the errors; this is remarkable given the segregation in the variance; (iii) the linear relative bias shows the opposite trend to the hierarchical amplitudes, with little segregation for the red sequence and some segregation for the blue; (iv) faint red galaxies deviate significantly from the 'universal' negative binomial reduced void probabilities followed by all other galaxy populations. Our results show that the characteristic colour of a galaxy population reveals a unique signature in its spatial distribution. Such signatures will hopefully further elucidate the physics responsible for shaping the cosmological evolution of galaxies.     

Measurement of the angular correlation function of radio galaxies from the NRAO VLA Sky Survey

We quantify the angular distribution of radio sources in the NRAO VLA Sky Survey (NVSS) by measuring the two-point angular correlation function w ( θ ). By careful consideration of the resolution of radio galaxies into multiple components, we are able to determine both the galaxy angular clustering and the size distribution of giant radio galaxies. The slope of the correlation function for radio galaxies agrees with that for other classes of galaxy,     , with a 3D correlation length     (under certain assumptions). Calibration problems in the survey prevent clustering analysis below     . About 7 per cent of radio galaxies are resolved by NVSS into multiple components, with a power-law size distribution. Our work calls into question previous analyses and interpretations of w ( θ ) from radio surveys.     

The environments of intermediate-redshift QSOs: 0.3 < z < 0.7

An angular correlation of low significance (2 σ ) is observed between 0.3< z <0.5 QSOs and V 23 galaxies. Overall, the cross-correlation function between 82 intermediate-redshift (0.3< z <0.7) X-ray selected QSOs and V ≲24 galaxies is investigated, but no signal is detected for the z >0.5 QSOs. After converting to an excess of galaxies physically associated with the QSO, this lack of strong correlation is shown to be consistent with the clustering of normal galaxies at the same moderate redshifts. Combined with previous observations, these results imply that the environments of radio-quiet QSOs do not undergo significant evolution with respect to the galaxy population over a wide range of redshifts (0< z <1.5). This is in marked contrast to the rapid increase in the richness of the environments associated with radio-loud QSOs over the same redshift range.     

Hubble Space Telescope imaging of the CFRS and LDSS redshift surveys – IV. Influence of mergers in the evolution of faint field galaxies from z∼1

Hubble Space Telescope images of a sample of 285 galaxies with measured redshifts from the Canada–France Redshift Survey (CFRS) and Autofib–Low Dispersion Spectrograph Survey (LDSS) redshift surveys are analysed to derive the evolution of the merger fraction out to redshifts z ∼1. We have performed visual and machine-based merger identifications, as well as counts of bright pairs of galaxies with magnitude differences δm ≤1.5 mag. We find that the pair fraction increases with redshift, with up to ∼20 per cent of the galaxies being in physical pairs at z ∼0.75–1. We derive a merger fraction varying with redshift as ∝(1+ z )^3.2±0.6, after correction for line-of-sight contamination, in excellent agreement with the merger fraction derived from the visual classification of mergers for which m =3.4±0.6. After correcting for seeing effects on the ground-based selection of survey galaxies, we conclude that the pair fraction evolves as ∝(1+ z )^2.7±0.6. This implies that an average L * galaxy will have undergone 0.8–1.8 merger events from z =1 to z =0, with 0.5 to 1.2 merger events occuring in a 2-Gyr time-span at around z ∼0.9. This result is consistent with predictions from semi-analytical models of galaxy formation. From the simple coaddition of the observed luminosities of the galaxies in pairs, physical mergers are computed to lead to a brightening of 0.5 mag for each pair on average, and a boost in star formation rate of a factor of 2, as derived from the average [O  ii ] equivalent widths. Mergers of galaxies are therefore contributing significantly to the evolution of both the luminosity function and luminosity density of the Universe out to z ∼1.     

A sample of 6C radio sources designed to find objects at redshift z>4– III. Imaging and the radio galaxy K–z relation

In this paper, the third and final of a series, we present complete K -band imaging and some complementary I -band imaging of the filtered 6C* sample. We find no systematic differences between the K – z relation of 6C* radio galaxies and those from complete samples, so the near-infrared properties of luminous radio galaxies are not obviously biased by the additional 6C* radio selection criteria (steep spectral index and small angular size). The 6C* K – z data significantly improve delineation of the K – z relation for radio galaxies at high redshift ( z >2) . Accounting for non-stellar contamination, and for correlations between radio luminosity and stellar mass, we find little support for previous claims that the underlying scatter in the stellar luminosity of radio galaxies increases significantly at z >2 . In a particular spatially flat universe with a cosmological constant (Ω_M=0.3 and Ω_Λ=0.7) , the most luminous radio sources appear to be associated with galaxies with a luminosity distribution with a high mean (≈5  L *), and a low dispersion ( σ ∼0.5 mag) which formed their stars at epochs corresponding to z ≳2.5 . This result is in line with recent submillimetre studies of high-redshift radio galaxies and the inferred ages of extremely red objects from faint radio samples.     

On the formation of massive galaxies: a simultaneous study of number density, size and intrinsic colour evolution in GOODS

The evolution of number density, size and intrinsic colour is determined for a volume-limited sample of visually classified early-type galaxies selected from the Hubble Space Telescope /Advanced Camera for Surveys images of the Great Observatories Origins Deep Survey (GOODS) North and South fields (version 2). The sample comprises 457 galaxies over 320 arcmin² with stellar masses above  3 × 10¹⁰ M_⊙  in the redshift range  0.4 < z < 1.2  . Our data allow a simultaneous study of number density, intrinsic colour distribution and size. We find that the most massive systems  (≳3 × 10¹¹ M_⊙)  do not show any appreciable change in comoving number density or size in our data. Furthermore, when including the results from 2dF galaxy redshift survey, we find that the number density of massive early-type galaxies is consistent with no evolution between   z = 1.2  and 0, i.e. over an epoch spanning more than half of the current age of the Universe. We find large discrepancies between the predictions of semi-analytic models. Massive galaxies show very homogeneous intrinsic colour distributions, with nearly flat radial colour gradients, but with a significant negative correlation between stellar mass and colour gradient, such that red cores appear predominantly in massive galaxies. The distribution of half-light radii – when compared to   z ∼ 0  and   z > 1  samples – is compatible with the predictions of semi-analytic models relating size evolution to the amount of dissipation during major mergers.     

SDSS galaxy clustering: luminosity and colour dependence and stochasticity

Differences in clustering properties between galaxy subpopulations complicate the cosmological interpretation of the galaxy power spectrum, but can also provide insights about the physics underlying galaxy formation. To study the nature of this relative clustering, we perform a counts-in-cells analysis of galaxies in the Sloan Digital Sky Survey in which we measure the relative bias between pairs of galaxy subsamples of different luminosities and colours. We use a generalized  χ²  test to determine if the relative bias between each pair of subsamples is consistent with the simplest deterministic linear bias model, and we also use a maximum likelihood technique to further understand the nature of the relative bias between each pair. We find that the simple, deterministic model is a good fit for the luminosity-dependent bias on scales above  ∼2  h ⁻¹ Mpc  , which is good news for using magnitude-limited surveys for cosmology. However, the colour-dependent bias shows evidence for stochasticity and/or non-linearity which increases in strength towards smaller scales, in agreement with previous studies of stochastic bias. Also, confirming hints seen in earlier work, the luminosity-dependent bias for red galaxies is significantly different from that of blue galaxies: both luminous and dim red galaxies have higher bias than moderately bright red galaxies, whereas the biasing of blue galaxies is not strongly luminosity dependent. These results can be used to constrain galaxy formation models and also to quantify how the colour and luminosity selection of a galaxy survey can impact measurements of the cosmological matter power spectrum.