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.     

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.     

The galaxy luminosity function from MR=−25 to MR=−9

Redshift surveys such as the Sloan Digital Sky Survey (SDSS) have given a very precise measurement of the galaxy luminosity function down to about   M_R =−17 (≈ M_B =−16)  . Fainter absolute magnitudes cannot be probed because of the flux limit required for spectroscopy. Wide-field surveys of nearby groups using mosaic CCDs on large telescopes are able to reach much fainter absolute magnitudes, about   M_R =−10  . These diffuse, spiral-rich groups are thought to be typical environments for galaxies, so their luminosity functions should be the same as the field luminosity function. The luminosity function of the groups at the bright end  ( M_R < −17)  is limited by Poisson statistics and is far less precise than that derived from redshift surveys. Here we combine the results of the SDSS and the surveys of nearby groups, and we supplement the results with studies of Local Group galaxies in order to determine the galaxy luminosity function over the entire range  −25 < M_R < −9  . The average logarithmic slope of the field luminosity function between   M_R =−19  and   M_R =−9  is  α=−1.26  , although a single power law is a poor fit to the data over the entire magnitude range. We also determine the luminosity function of galaxy clusters and demonstrate that it is different from the field luminosity function at a high level of significance; there are many more dwarf galaxies in clusters than in the field, due to a rise in the cluster luminosity function of  α∼−1.6  between   M_R =−17  and   M_R =−14  .     

The luminosity function and surface brightness distribution of H i selected galaxies

We measure the     B -band optical luminosity function (LF) for galaxies selected in a blind H  i survey. The total LF of the H  i selected sample is flat, with Schechter parameters     and     , in good agreement with LFs of optically selected late-type galaxies. Bivariate distribution functions of several galaxy parameters show that the H  i density in the local Universe is more widely spread over galaxies of different size, central surface brightness and luminosity than the optical luminosity density is. The number density of very low surface brightness (LSB ) (>24.0 mag arcsec⁻²) gas-rich galaxies is considerably lower than that found in optical surveys designed to detect dim galaxies. This suggests that only a part of the population of LSB galaxies is gas-rich and that the rest must be gas-poor. However, we show that this gas-poor population must be cosmologically insignificant in baryon content. The contribution of gas-rich LSB galaxies (>23.0 mag arcsec⁻²) to the local cosmological gas and luminosity density is modest     and     per cent respectively); their contribution to Ω_matter is not well-determined, but probably <11 per cent. These values are in excellent agreement with the low redshift results from the Hubble Deep Field.     

Galaxy–dark matter correlations applied to galaxy–galaxy lensing: predictions from the semi-analytic galaxy formation models

We use semi-analytic models of galaxy formation combined with high-resolution N -body simulations to make predictions for galaxy–dark matter correlations and apply them to galaxy–galaxy lensing. We analyse cross-power spectra between the dark matter and different galaxy samples selected by luminosity, colour or star formation rate. We compare the predictions with the recent detection by the Sloan Digital Sky Survey (SDSS). We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1  h ⁻¹ Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot, however, be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centres of the corresponding haloes. We compute the redshift evolution of the cross-correlation amplitude and compare it with those of galaxies and dark matter. We also compute the galaxy–dark matter correlation coefficient and show that it is close to unity on scales above 1  h ⁻¹ Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy–dark matter correlations.     

The local far-infrared galaxy colour–luminosity distribution: a reference for BLAST and Herschel/SPIRE submillimetre surveys

We measure the local galaxy far-infrared (FIR) 60 to 100 μm colour–luminosity distribution using an all-sky IRAS survey. This distribution is an important reference for the next generation of FIR–submillimetre surveys that have and will conduct deep extragalactic surveys at 250–500 μm. With the peak in dust-obscured star-forming activity leading to present-day giant ellipticals now believed to occur in submillimetre galaxies near   z ∼ 2.5  , these new FIR–submillimetre surveys will directly sample the spectral energy distributions of these distant objects at rest-frame FIR wavelengths similar to those at which local galaxies were observed by IRAS . We have taken care to correct for the temperature bias and the evolution effects in our IRAS 60-μm-selected sample. We verify that our colour–luminosity distribution is consistent with the measurements of the local FIR luminosity function, before applying it to the higher redshift Universe. We compare our colour–luminosity correlation with recent dust–temperature measurements of submillimetre galaxies and find evidence for pure luminosity evolution of the form  (1 + z )³  . This distribution will be useful for the development of evolutionary models for Balloon-borne Large Aperture Submillimeter Telescope (BLAST) and Spectral and Photometric Imaging Receiver (SPIRE) surveys as it provides a statistical distribution of the rest-frame dust temperatures for galaxies as a function of luminosity.     

The 2dF Galaxy Redshift Survey: luminosity functions by density environment and galaxy type

We use the 2dF Galaxy Redshift Survey to measure the dependence of the b _J-band galaxy luminosity function on large-scale environment, defined by density contrast in spheres of radius  8  h ⁻¹ Mpc  , and on spectral type, determined from principal component analysis. We find that the galaxy populations at both extremes of density differ significantly from that at the mean density. The population in voids is dominated by late types and shows, relative to the mean, a deficit of galaxies that becomes increasingly pronounced at magnitudes brighter than   M _{b J}−5log₁₀ h ≲−18.5  . In contrast, cluster regions have a relative excess of very bright early-type galaxies with   M _{b J}−5log₁₀ h ≲−21  . Differences in the mid- to faint-end population between environments are significant: at   M _{b J}−5log₁₀ h =−18  early- and late-type cluster galaxies show comparable abundances, whereas in voids the late types dominate by almost an order of magnitude. We find that the luminosity functions measured in all density environments, from voids to clusters, can be approximated by Schechter functions with parameters that vary smoothly with local density, but in a fashion that differs strikingly for early- and late-type galaxies. These observed variations, combined with our finding that the faint-end slope of the overall luminosity function depends at most weakly on density environment, may prove to be a significant challenge for models of galaxy formation.     

The clustering evolution of the galaxy distribution

We follow the evolution of the galaxy population in a ΛCDM cosmology by means of high-resolution N -body simulations in which the formation of galaxies and their observable properties are calculated using a semi-analytic model. We display images of the spatial distribution of galaxies in the simulations that illustrate its evolution and provide a qualitative understanding of the processes responsible for the various biases that develop. We consider three specific statistical measures of clustering at     and     : the correlation length (in both real and redshift space) of galaxies of different luminosity, the morphology–density relation and the genus curve of the topology of galaxy isodensity surfaces. For galaxies with luminosity below L ∗, the     correlation length depends very little on the luminosity of the sample, but for brighter galaxies it increases very rapidly, reaching values in excess of 10  h ⁻¹ Mpc. The 'accelerated' dynamical evolution experienced by galaxies in rich clusters, which is partly responsible for this effect, also results in a strong morphology–density relation. Remarkably, this relation is already well-established at     . The genus curves of the galaxies are significantly different from the genus curves of the dark matter, however this is not a result of genuine topological differences but rather of the sparse sampling of the density field provided by galaxies. The predictions of our model at     will be tested by forthcoming data from the 2dF and Sloan galaxy surveys, and those at     by the DEEP and VIRMOS surveys.     

Light curves for off-centre ignition models of Type Ia supernovae

We compare observations of the high-redshift galaxy population to the predictions of the galaxy formation model of Croton et al. and De Lucia & Blaizot. This model, implemented on the Millennium Simulation of the concordance Lambda cold dark matter cosmogony, introduces 'radio mode' feedback from the central galaxies of groups and clusters in order to obtain quantitative agreement with the luminosity, colour, morphology and clustering properties of the present-day galaxy population. Here we construct deep light cone surveys in order to compare model predictions to the observed counts and redshift distributions of distant galaxies, as well as to their inferred luminosity and mass functions out to redshift 5. With the exception of the mass functions, all these properties are sensitive to modelling of dust obscuration. A simple but plausible treatment agrees moderately well with most of the data. The predicted abundance of relatively massive  (∼ M _*)  galaxies appears systematically high at high redshift, suggesting that such galaxies assemble earlier in this model than in the real Universe. An independent galaxy formation model implemented on the same simulation matches the observed mass functions slightly better, so the discrepancy probably reflects incomplete or inaccurate galaxy formation physics rather than problems with the underlying cosmogony.     

Scale-dependent bias induced by local non-Gaussianity: a comparison to N-body simulations

We investigate the effect of primordial non-Gaussianity of the local f _NL type on the auto- and cross-power spectra of dark matter haloes using simulations of the Λ cold dark matter cosmology. We perform a series of large N -body simulations of both positive and negative f _NL, spanning the range between 10 and 100. Theoretical models predict a scale-dependent bias correction  Δ b ( k , f _NL)  that depends on the linear halo bias   b ( M )  . We measure the power spectra for a range of halo mass and redshifts covering the relevant range of existing galaxy and quasar populations. We show that auto- and cross-correlation analyses of bias are consistent with each other. We find that for low wavenumbers with   k < 0.03  h  Mpc⁻¹  the theory and the simulations agree well with each other for biased haloes with   b ( M ) > 1.5  . We show that a scale-independent bias correction improves the comparison between theory and simulations on smaller scales, where the scale-dependent effect rapidly becomes negligible. The current limits on f _NL from Slosar et al. come mostly from very large scales   k < 0.01  h  Mpc⁻¹  and, therefore, remain valid. For the halo samples with   b ( M ) < 1.5 − 2  , we find that the scale-dependent bias from non-Gaussianity actually exceeds the theoretical predictions. Our results are consistent with the bias correction scaling linearly with f _NL.     

A sample of radio-loud active galactic nuclei in the Sloan Digital Sky Survey

A sample of 2712 radio-luminous galaxies is defined from the second data release of the Sloan Digital Sky Survey (SDSS) by cross-comparing the main spectroscopic galaxy sample with two radio surveys: the National Radio Astronomy Observatories (NRAO) Very Large Array (VLA) Sky Survey (NVSS) and the Faint Images of the Radio Sky at Twenty centimeters (FIRST) survey. The comparison is carried out in a multistage process and makes optimal use of both radio surveys by exploiting the sensitivity of the NVSS to extended and multicomponent radio sources in addition to the high angular resolution of the FIRST images. A radio source sample with 95 per cent completeness and 98.9 per cent reliability is achieved, far better than would be possible for this sample if only one of the surveys was used. The radio source sample is then divided into two classes: radio-loud active galactic nuclei (AGN) and galaxies in which the radio emission is dominated by star formation. The division is based on the location of a galaxy in the plane of 4000-Å break strength versus radio luminosity per unit stellar mass and provides a sample of 2215 radio-loud AGN and 497 star-forming galaxies brighter than 5 mJy at 1.4 GHz. A full catalogue of positions and radio properties is provided for these sources. The local radio luminosity function is then derived both for radio-loud AGN and for star-forming galaxies and is found to be in agreement with previous studies. By using the radio to far-infrared (FIR) correlation, the radio luminosity function of star-forming galaxies is also compared to the luminosity function derived in the FIR. It is found to agree well at high luminosities but less so at lower luminosities, confirming that the linearity of the radio to FIR correlation breaks down below about 10²² W Hz⁻¹ at 1.4 GHz.     

Satellite kinematics – II. The halo mass–luminosity relation of central galaxies in SDSS

The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass–luminosity relation (MLR) of their corresponding central galaxies. In this paper, we select a large sample of centrals and satellites from the Sloan Digital Sky Survey and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the r -band luminosity of the central galaxies. Using the analytical framework presented in More, van den Bosch & Cacciato, we use these data to infer both the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity,  σ_{log  M}   , also increases with increasing luminosity. As we demonstrate, this is consistent with  σ_{log  L}   , which reflects the scatter in the conditional probability function   P ( L _c| M )  , being independent of halo mass. Our analysis of the satellite kinematics yields  σ_{log  L} = 0.16  ±  0.04  , in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by  σ_{log  L}   , is well constrained, independent of halo mass and in a good agreement with current models of galaxy formation.     

The luminosity function around isolated spiral galaxies

We determine the companion galaxy luminosity function (LF) for regions around isolated spiral galaxies. If we assume that any excess in the galaxy number counts in the vicinity of a spiral galaxy is due to galaxies at the same distance, then a system LF can be determined from the variation of excess numbers with apparent magnitude. By studying the excess over many field 'centre' galaxies, a good statistical accuracy can be obtained for the companion galaxy LF. Since redshift information is not required for the faint galaxies, it is possible to sample further down the LF as compared with redshift surveys. For 23 primary galaxies of known redshift, we find a dwarf satellite Schechter LF with a characteristic magnitude M _V *( D )≃−19 and a faint-end slope α=−1.7, down to M_V =−14 ( H ₀=50 km s⁻¹ Mpc⁻¹).     

A model of slingshot prominences in rapidly rotating stars

We analyse the spatial clustering properties of the ROSAT All-Sky Survey (RASS) 1 Bright Sample, an X-ray flux-limited catalogue of galaxy clusters selected from the southern part of the survey. The two-point correlation function ( r ) of the whole sample is well fitted (in an Einsteinde Sitter model) by the power law =( r r ₀) , with and (95.4 per cent confidence level with one fitting parameter). We use the RASS 1 Bright Sample as a first application of a theoretical model that aims to predict the clustering properties of X-ray clusters in flux-limited surveys for different cosmological scenarios. The model uses the theoretical and empirical relations between mass, temperature and X-ray cluster luminosity, and fully accounts for the redshift evolution of the underlying dark matter clustering and cluster bias factor. The comparison between observational results and theoretical predictions shows that the Einsteinde Sitter models display too low a correlation length, while models with a matter density parameter _0m=0.3 (with or without a cosmological constant) are successful in reproducing the observed clustering. The dependence of the correlation length r ₀ on the X-ray limiting flux and luminosity of the sample is generally consistent with the predictions of all our models. Quantitative agreement is however only reached for _0m=0.3 models. The model presented here can be reliably applied to future deeper X-ray cluster surveys: the study of the clustering properties will provide a useful complementary tool to the traditional cluster abundance analyses used to constrain the cosmological parameters.     

Constraints on σ8 from galaxy clustering in N-body simulations and semi-analytic models

We generate mock galaxy catalogues for a grid of different cosmologies, using rescaled N -body simulations in tandem with a semi-analytic model run using consistent parameters. Because we predict the galaxy bias, rather than fitting it as a nuisance parameter, we obtain an almost pure constraint on σ₈ by comparing the projected two-point correlation function we obtain to that from the Sloan Digital Sky Survey (SDSS). A systematic error arises because different semi-analytic modelling assumptions allow us to fit the r -band luminosity function equally well. Combining our estimate of the error from this source with the statistical error, we find  σ₈= 0.97 ± 0.06  . We obtain consistent results if we use galaxy samples with a different magnitude threshold, or if we select galaxies by b _J-band rather than r -band luminosity and compare to data from the 2dF Galaxy Redshift Survey (2dFGRS). Our estimate for σ₈ is higher than that obtained for other analyses of galaxy data alone, and we attempt to find the source of this difference. We note that in any case, galaxy clustering data provide a very stringent constraint on galaxy formation models.     

Clustering of X-ray selected active galactic nuclei

A total of 235 active galactic nuclei (AGN) from two different soft X-ray surveys [the ROSAT Deep Survey (DRS) and the ROSAT International X-ray Optical Survey (RIXOS)] with redshifts between 0 and 3.5 are used to study the clustering of X-ray selected AGN and its evolution. A 2σ significant detection of clustering of such objects is found on scales < 40–80 h ⁻¹ Mpc in the RIXOS sample, while no clustering is detected on any scales in the DRS sample. Assuming a single power-law model for the spatial correlation function (SCF), quantitative limits on the AGN clustering have been obtained: a comoving correlation length 1.5 ≲  r ₀ ≲ 3.3  h ⁻¹ Mpc is implied for comoving evolution, while 1.9 ≲  r ₀ ≲ 4.8 for stable clustering and 2.2 ≲  r ₀ ≲ 5.5 for linear evolution. These values are consistent with the correlation lengths and evolutions obtained for galaxy samples, but imply smaller amplitude or faster evolution than recent ultraviolet and optically selected AGN samples. We also constrain the ratio of bias parameters between X-ray selected AGN and IRAS galaxies to be ≲ 1.7 on scales ≲ 10  h ⁻¹ Mpc, a somewhat smaller value than is inferred from local large-scale dynamical studies.     

The Durham/UKST Galaxy Redshift Survey – III. Large-scale structure via the two-point correlation function

We have investigated the statistical clustering properties of galaxies by calculating the two-point galaxy correlation function from the optically selected Durham/UKST Galaxy Redshift Survey. This survey is magnitude-limited to b _J∼17, contains ∼2500 galaxies sampled at a rate of one-in-three and surveys a ∼4×10⁶ ( h ⁻¹ Mpc)³ volume of space. We have empirically determined the optimal method of estimating the two-point correlation function from just such a magnitude-limited survey. Applying our methods to this survey, we find that our redshift-space results agree well with those from previous optical surveys. In particular, we confirm the previously claimed detections of large-scale power out to ∼40 h ⁻¹ Mpc scales. We compare with two common models of cosmological structure formation and find that our two-point correlation function has power significantly in excess of the standard cold dark matter model in the 10–30 h ⁻¹ Mpc region. We therefore support the observational results of the APM galaxy survey. Given that only the redshift-space clustering can be measured directly, we use standard modelling methods and indirectly estimate the real-space two-point correlation function from the projected two-point correlation function. We then invert this projected correlation function to obtain an estimate of the spatial two-point correlation function in real space. This correlation function in real space has a lower amplitude than that in redshift space, but a steeper slope.     

The 2dF Galaxy Redshift Survey: luminosity dependence of galaxy clustering

We investigate the dependence of the strength of galaxy clustering on intrinsic luminosity using the Anglo-Australian two degree field galaxy redshift survey (2dFGRS). The 2dFGRS is over an order of magnitude larger than previous redshift surveys used to address this issue. We measure the projected two-point correlation function of galaxies in a series of volume-limited samples. The projected correlation function is free from any distortion of the clustering pattern induced by peculiar motions and is well described by a power law in pair separation over the range     . The clustering of     galaxies in real space is well-fitted by a correlation length     and power-law slope     . The clustering amplitude increases slowly with absolute magnitude for galaxies fainter than M *, but rises more strongly at higher luminosities. At low luminosities, our results agree with measurements from the Southern Sky Redshift Survey 2 by Benoist et al. However, we find a weaker dependence of clustering strength on luminosity at the highest luminosities. The correlation function amplitude increases by a factor of 4.0 between     and −22.5, and the most luminous galaxies are 3.0 times more strongly clustered than L * galaxies. The power-law slope of the correlation function shows remarkably little variation for samples spanning a factor of 20 in luminosity. Our measurements are in very good agreement with the predictions of the hierarchical galaxy formation models of Benson et al.