Non-perturbative effects of geometry in wide-angle redshift distortions

We use the formalism of Szapudi to derive full explicit expressions for the linear two-point correlation function, including redshift-space distortions and large angle effects. We take into account a non-perturbative geometric term in the Jacobian, which is still linear in terms of the dynamics. This term had been identified previously, but has been neglected in all subsequent explicit calculations of the linear redshift-space two-point correlation function. Our results represent a significant correction to previous explicit expressions and are in excellent agreement with our measurements in the Hubble volume simulation.     

Incorporating photometric redshift probability density information into real-space clustering measurements

The use of photometric redshifts in cosmology is increasing. Often, however these photo- z are treated like spectroscopic observations, in that the peak of the photometric redshift, rather than the full probability density function (PDF), is used. This overlooks useful information inherent in the full PDF. We introduce a new real-space estimator for one of the most used cosmological statistics, the two-point correlation function, that weights by the PDF of individual photometric objects in a manner that is optimal when Poisson statistics dominate. As our estimator does not bin based on the PDF peak, it substantially enhances the clustering signal by usefully incorporating information from all photometric objects that overlap the redshift bin of interest. As a real-world application, we measure quasi-stellar object (QSO) clustering in the Sloan Digital Sky Survey (SDSS). We find that our simplest binned estimator improves the clustering signal by a factor equivalent to increasing the survey size by a factor of 2–3. We also introduce a new implementation that fully weights between pairs of objects in constructing the cross-correlation and find that this pair-weighted estimator improves clustering signal in a manner equivalent to increasing the survey size by a factor of 4–5. Our technique uses spectroscopic data to anchor the distance scale and it will be particularly useful where spectroscopic data (e.g. from BOSS) overlap deeper photometry (e.g. from Pan-STARRS, DES or the LSST). We additionally provide simple, informative expressions to determine when our estimator will be competitive with the autocorrelation of spectroscopic objects. Although we use QSOs as an example population, our estimator can and should be applied to any clustering estimate that uses photometric objects.     

The 2dF Galaxy Redshift Survey: the dependence of galaxy clustering on luminosity and spectral type

We investigate the dependence of galaxy clustering on luminosity and spectral type using the 2dF Galaxy Redshift Survey (2dFGRS). Spectral types are assigned using the principal-component analysis of Madgwick et al. We divide the sample into two broad spectral classes: galaxies with strong emission lines ('late types') and more quiescent galaxies ('early types'). We measure the clustering in real space, free from any distortion of the clustering pattern owing to peculiar velocities, for a series of volume-limited samples. The projected correlation functions of both spectral types are well described by a power law for transverse separations in the range  2<( σ / h ^-1 Mpc)<15  , with a marginally steeper slope for early types than late types. Both early and late types have approximately the same dependence of clustering strength on luminosity, with the clustering amplitude increasing by a factor of ∼2.5 between L * and 4 L *. At all luminosities, however, the correlation function amplitude for the early types is ∼50 per cent higher than that of the late types. These results support the view that luminosity, and not type, is the dominant factor in determining how the clustering strength of the whole galaxy population varies with luminosity.     

The DEEP2 galaxy redshift survey: evolution of the colour–density relation at 0.4 < z < 1.35

Using a sample of 19 464 galaxies drawn from the DEEP2 Galaxy Redshift Survey, we study the relationship between galaxy colour and environment at  0.4 < z < 1.35  . We find that the fraction of galaxies on the red sequence depends strongly on local environment out to   z > 1  , being larger in regions of greater galaxy density. At all epochs probed, we also find a small population of red, morphologically early-type galaxies residing in regions of low measured overdensity. The observed correlations between the red fraction and local overdensity are highly significant, with the trend at   z > 1  detected at a greater than 5σ level. Over the entire redshift regime studied, we find that the colour–density relation evolves continuously, with red galaxies more strongly favouring overdense regions at low z relative to their red-sequence counterparts at high redshift. At   z ≳ 1.3  , the red fraction only weakly correlates with overdensity, implying that any colour dependence to the clustering of  ∼ L *  galaxies at that epoch must be small. Our findings add weight to existing evidence that the build-up of galaxies on the red sequence has occurred preferentially in overdense environments (i.e. galaxy groups) at   z ≲ 1.5  . Furthermore, we identify the epoch  ( z ∼ 2)  at which typical  ∼ L *  galaxies began quenching and moved on to the red sequence in significant number. The strength of the observed evolutionary trends at  0 < z < 1.35  suggests that the correlations observed locally, such as the morphology–density and colour–density relations, are the result of environment-driven mechanisms (i.e. 'nurture') and do not appear to have been imprinted (by 'nature') upon the galaxy population during their epoch of formation.     

The DEEP2 Galaxy Redshift Survey: the red sequence AGN fraction and its environment and redshift dependence

We measure the dependence of the active galactic nuclei (AGN) fraction on local environment at   z ∼ 1  , using spectroscopic data taken from the DEEP2 Galaxy Redshift Survey, and Chandra X-ray data from the All-Wavelength Extended Groth Strip International Survey (AEGIS). To provide a clean sample of AGN, we restrict our analysis to the red sequence population; this also reduces additional colour–environment correlations. We find evidence that high-redshift LINERs in DEEP2 tend to favour higher density environments relative to the red population from which they are drawn. In contrast, Seyferts and X-ray selected AGN at   z ∼ 1  show little (or no) environmental dependencies within the same underlying population. We compare these results with a sample of local AGN drawn from the Sloan Digital Sky Survey (SDSS). Contrary to the high-redshift behaviour, we find that both LINERs and Seyferts in the SDSS show a slowly declining red sequence AGN fraction towards high-density environments. Interestingly, at   z ∼ 1  red sequence Seyferts and LINERs are approximately equally abundant. By   z ∼ 0  , however, the red Seyfert population has declined relative to the LINER population by over a factor of ∼4.5. We speculate on possible interpretations of our results.     

The distance–redshift equation in quintessence cosmology and the estimation of H0 through time delays

We calculate analytically and numerically the distance–redshift equation in perfect fluid quintessence models and give an accurate fit to the numerical solutions for all the values of the density parameter and the quintessence equation of state. Then we apply our solutions to the estimation of H ₀ from multiple image time delays and find that the inclusion of quintessence modifies significantly the likelihood distribution of H ₀, generally reducing the best estimate with respect to a pure cosmological constant. Marginalizing over the other parameters (Ω _m and the quintessence equation of state) we obtain H ₀=71±6 km s⁻¹ Mpc⁻¹ for an empty beam and H ₀=64±4 km s⁻¹ Mpc⁻¹ for a filled beam. These errors, however, do not take into account the uncertainty on the modelling of the lens. We also discuss the future prospects for distinguishing quintessence from a cosmological constant with time delays.     

Power spectrum analysis of the ESO Slice Project galaxy redshift survey

We measure the power spectrum of the galaxy distribution in the ESO Slice Project (ESP) galaxy redshift survey. We develop a technique to describe the survey window function analytically, and then deconvolve it from the measured power spectrum using a variant of the Lucy method. We test the whole deconvolution procedure on ESP mock catalogues drawn from large N -body simulations, and find that it is reliable for recovering the correct amplitude and shape of P ( k ) at k >0.065  h  Mpc⁻¹. In general, the technique is applicable to any survey composed of a collection of circular fields with an arbitrary pattern on the sky, as typical of surveys based on fibre spectrographs. The estimated power spectrum has a well-defined power-law shape k ⁿ with n ≃−2.2 for k ≥0.2  h  Mpc⁻¹, and a smooth bend to a flatter shape ( n ≃−1.6) for smaller k . The smallest wavenumber where a meaningful reconstruction can be performed ( k ∼0.06  h  Mpc⁻¹) does not allow us to explore the range of scales where other power spectra seem to show a flattening and hint at a turnover. We also find, by a direct comparison of the Fourier transforms, that the estimate of the two-point correlation function ξ ( s ) is much less sensitive to the effect of a problematic window function, such as that of the ESP, than the power spectrum. Comparison with other surveys shows an excellent agreement with estimates from blue-selected surveys. In particular, the ESP power spectrum is virtually indistinguishable from that of the Durham–UKST survey over the common range of k , an indirect confirmation of the quality of the deconvolution technique applied.     

Recovering the real-space correlation function from photometric redshift surveys

Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real-space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated with the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large-scale distribution of galaxies.     

Variance and skewness in the FIRST survey

We investigate the large-scale clustering of radio sources in the FIRST 1.4-GHz survey by analysing the distribution function ( counts in cells ). We select a reliable sample from the the FIRST catalogue, paying particular attention to the problem of how to define single radio sources from the multiple components listed. We also consider the incompleteness of the catalogue. We estimate the angular two-point correlation function w (θ), the variance Ψ₂ and skewness Ψ₃ of the distribution for the various subsamples chosen on different criteria. Both w (θ) and Ψ₂ show power-law behaviour with an amplitude corresponding to a spatial correlation length of r ₀ ∼ 10  h ⁻¹Mpc. We detect significant skewness in the distribution, the first such detection in radio surveys. This skewness is found to be related to the variance through Ψ₃ =  S ₃(Ψ₂)^α, with α = 1.9 ± 0.1, consistent with the non-linear gravitational growth of perturbations from primordial Gaussian initial conditions. We show that the amplitude of variance and the skewness are consistent with realistic models of galaxy clustering.