APM Galaxy Survey Research Articles

Measurement of the gravitational potential evolution from the cross-correlation betweenWMAPand the APM Galaxy Survey

Models with late time cosmic acceleration, such as the Lambda-dominated CDM model, predict a freeze out for the growth of linear gravitational potential at moderate redshift z<1, what can be observed as temperature anisotropies in the CMB: the so called integrated Sachs-Wolfe (ISW) effect. We present a direct measurement of the ISW effect based on the angular cross-correlation function, w_{TG}, of CMB temperature anisotropies and dark-matter fluctuations traced by galaxies. We cross-correlate the first-year WMAP data in combination with the APM Galaxy survey. On the largest scales, theta = 4-10 deg, we detect a non-vanishing cross-correlation at 98.8 % significance level, with a 1-sigma error of w_{TG} = 0.35 +/- 0.14 microK, which favors large values of Omega_Lambda \simeq 0.8 for flat FRW models. On smaller scales, theta < 1deg, the correlations disappear. This is contrary to what would be expected from the ISW effect, but the absence of correlations may be simply explained if the ISW signal was being cancelled by anti-correlations arising from the thermal Sunyaev-Zeldovich (SZ) effect.

Evidence for an extended Sunyaev--Zel'dovich effect in WMAP data

We have cross-correlated the WMAP data with several surveys of extragalactic sources and find evidence for temperature decrements associated with galaxy clusters and groups detected in the APM Galaxy Survey and the Abell–Corwin–Olowin (ACO) catalogue. We interpret this as evidence for the thermal Sunyaev–Zel'dovich (SZ) effect from the clusters. Most interestingly, the signal may extend to ≈ 1 deg (≈5 h−1 Mpc) around both groups and clusters and we suggest that this may be due to hot ‘supercluster’ gas. We have further cross-correlated the WMAP data with clusters identified in the 2MASS galaxy catalogue and also find evidence for temperature decrements there. From the APM group data we estimate the mean Compton parameter as y(z 10 and then could seriously affect the WMAP cosmological fits.

UBR charge-coupled device photometry of Stromlo-APM galaxies

We present charge-coupled device (CCD) photometry in the Johnson-Kron-Cousins UBR bands for a sample of 320 galaxies selected from the Stromlo-APM Redshift Survey. We use these CCD data to estimate the galaxy luminosity function in the U, B, R and b J bands, finding consistent results with earlier work. Fainter galaxies serendipitously observed on our CCD frames allow a check of the photometric calibration of the APM Galaxy Survey. We find no evidence of any significant scale error in the APM magnitudes.

The power spectrum of galaxy clustering in the APM Survey

We measure the power spectrum of galaxy clustering in real space from the APM Galaxy Survey. We present an improved technique for the numerical inversion of Limber's equation that relates the angular clustering of galaxies to an integral over the power spectrum in three dimensions. Our approach is underpinned by a large ensemble of mock galaxy catalogues constructed from the Hubble volume N-body simulations. Mock catalogues are used to test for systematic effects in the inversion algorithm and to estimate the errors on our measurement. We find that we can recover the power spectrum to an accuracy of better than 15 per cent over three decades in wavenumber. A key advantage of the use of mock catalogues to infer errors is that we can apply our technique on scales for which the density fluctuations are not Gaussian, thus probing the regime that offers the best constraints on models of galaxy formation. On large scales, our measurement of the power spectrum is consistent with the shape of the mass power spectrum in the popular ‘concordance’ cold dark matter model. The galaxy power spectrum on small scales is strongly affected by non-linear evolution of density fluctuations, and, to a lesser degree, by galaxy bias. The rms variance in the galaxy distribution, when smoothed in spheres of radius 8 h−1 Mpc, is σg8= 0.96+0.17−0.20 and the shape of the power spectrum on large scales is described by a simple fitting formula with parameter Γ= 0.19+0.13−0.04 (these errors are the 1σ ranges for a two-parameter fit). We use our measurement of the power spectrum to estimate the galaxy two-point correlation function; the results are well described by a power law with correlation length r0= 5.9 ± 0.7 h−1 Mpc and slope γ= 1.61 ± 0.06 for pair separations in the range 0.1 < r/(h−1 Mpc) < 20.

The projected 2-point correlation function of the galaxy density field

We present formulas relating the angular 2-point correlation function of the galaxy density field to the spatial one. Our solution was obtained for arbitrary angles. We argue that it is particularly well applicable for middle angular scales (up to 30 – 40°), where the small angle approximation may be not valid any more but the large angle result using series of spherical harmonics (quite good for numerical purposes) is too sophisticated. We check the applicability of our result for the power law power spectrum and for a realistic model, based on the APM galaxy survey. We discuss the accuracy of our results compared to the cosmic error and find that for the middle angular scales the corrections introduced by our solution are worth to take into account.

Galaxy clustering in the Sloan Digital Sky Survey (SDSS): a first comparison with the APM Galaxy Survey

We compare the large-scale galaxy clustering in the new Sloan Digital Sky Survey (SDSS) early data release (EDR) with the clustering in the APM Galaxy Survey. We cut out pixel maps (identical in size and shape) from the SDSS and APM data to allow a direct comparison of the clustering. Here we concentrate our analysis on an equatorial SDSS strip in the South Galactic Cap (EDR/SGC) of 166 deg 2 , 2°.5 wide and 65° long. Only galaxies with Petrosian magnitudes 16.8 < g' < 19.8 are included to match the surface density of the 17 < b J < 20 APM pixel maps (median depth of ∼400 h - 1 Mpc). Both the amplitude and the shape of the angular two-point function and variance turn out to be in very good agreement with the APM on scales smaller than 2° (or ≤ 15 h - 1 Mpc). The three-point function and skewness are also in excellent agreement within a 90 per cent confidence level. On the one hand these results illustrate that the EDR data and SDSS software pipelines work well and are suitable to carry out analysis of large-scale clustering. On the other hand they confirm that large-scale clustering analysis is becoming 'repeatable' and therefore that our conclusions for structure formation models seem to stand on solid scientific grounds.

Maximum likelihood estimates of the two- and three-dimensional power spectra of the APM Galaxy Survey

We estimate the two- and three-dimensional power spectra, P2(K) and P3(k), of the galaxy distribution by applying a maximum likelihood estimator to pixel maps of the APM Galaxy Survey. The analysis provides optimal estimates of the power spectra and of their covariance matrices if the fluctuations are assumed to be Gaussian. Our estimates of P2(K) and P3(k) are in good agreement with previous work, but we find that the errors at low wavenumbers have been underestimated in some earlier studies. If the galaxy power spectrum is assumed to have the same shape as the mass power spectrum, then the APM maximum likelihood P3(k) estimates at k≤0.19 h Mpc−1 constrain the amplitude and shape parameter of a scale-invariant CDM model to lie within the 2σ ranges 0.74≤(σ8)g≤1.28 and 0.06≤Γ≤0.46. Using the Galactic extinction estimates of Schlegel, Finkbeiner & Davis, we show that Galactic obscuration has a negligible effect on galaxy clustering over most of the area of the APM Galaxy Survey.

Gravity’s Smoking Gun?

We present a new constraint on the biased galaxy formation picture. Gravitational instability theory predicts that the two-point mass density correlation function, \xi(r), has an inflection point at the separation r=r_0, corresponding to the boundary between the linear and nonlinear regime of clustering, \xi = 1. We show how this feature can be used to constrain the square of the biasing parameter, b^2 = \xi_g / \xi on scales r = r_0, where \xi_g is the galaxy-galaxy correlation function, allowed to differ from \xi. We apply our method to real data: the \xi_g(r), estimated from the APM galaxy survey. Our results suggest that the APM galaxies trace the mass at separations r > 5 Mpc/h, where h is the Hubble constant in units of 100 km/s Mpc. The present results agree with earlier studies, based on comparing higher order correlations in the APM with weakly non-linear perturbation theory. Both approaches constrain the b factor to be within 20% of unity. If the existence of the feature we identified in the APM \xi_g(r) -- the inflection point near \xi_g = 1 -- is confirmed by more accurate surveys, we may have discovered gravity's smoking gun: the long awaited ``shoulder'' in \xi, predicted by Gott and Rees 25 years ago.

The Durham/UKST Galaxy Redshift Survey -- VII. Redshift-space distortions in the power spectrum

m =b: Geometrical distortions also occur if the wrong cosmology is assumed, although these would be relatively small given the low redshift of the survey. To quantify these effects, we assume the real-space power spectrum of the APM Galaxy Survey, and fit a simple model for the redshift-space and geometrical distortions. Assuming a flat Vma 1 universe, we find values for the one-dimensional pairwise velocity dispersion of spa 410 ^ 170 km s 21 ; and ba 0:38 ^ 0:17: An open Vma 0:3; and a flat Vma 0:3; VLa 0:7 universe yield spa 420 km s 21 ; ba 0:40; and spa 440 km s 21 ; ba 0:45; respectively, with comparable errors. These results are consistent with estimates using the two-point galaxy correlation function, j(s ,p), and favour either a low-density universe with Vm , 0:3 if galaxies trace the underlying mass distribution, or a bias factor of b , 2: 5i fVma 1:

The Angular Three‐Point Correlation Function in the Quasi‐linear Regime

We calculate the normalized angular three-point correlation function (3PCF), q, as well as the normalized angular skewness, s{sub 3}, assuming the small-angle approximation, for a biased mass distribution in flat and open cold dark matter (CDM) models with Gaussian initial conditions. The leading-order perturbative results incorporate the explicit dependence on the cosmological parameters, the shape of the CDM transfer function, the linear evolution of the power spectrum, the form of the assumed redshift distribution function, and linear and nonlinear biasing, which may be evolving. Results are presented for different redshift distributions, including that appropriate for the APM Galaxy Survey, as well as for a survey with a mean redshift of z{approx_equal}1 (such as the VLA FIRST Survey). Qualitatively, many of the results found for s{sub 3} and q are similar to those obtained in a related treatment of the spatial skewness and 3PCF, such as a leading-order correction to the standard result for s{sub 3} in the case of nonlinear bias (as defined for unsmoothed density fields), and the sensitivity of the configuration dependence of q to both cosmological and biasing models. We show that since angular correlation functions (CFs) are sensitive to clustering over a range of redshifts, themore » various evolutionary dependences included in our predictions imply that measurements of q in a deep survey might better discriminate between models with different histories, such as evolving versus nonevolving bias, that can have similar spatial CFs at low redshift. Our calculations employ a derived equation, valid for open, closed, and flat models, to obtain the angular bispectrum from the spatial bispectrum in the small-angle approximation. (c) (c) 2000. The American Astronomical Society.« less

The Durham/UKST Galaxy Redshift Survey -- VI. Power spectrum analysis of clustering

We present the power spectrum analysis of clustering in the Durham/UKST Galaxy Redshift Survey. The Survey covers 1450 square degrees and consists of 2501 galaxy redshifts. The galaxies are sampled at a rate of 1 in 3 down to a magnitude limit of bJ � 17 from COSMOS scanned UK-Schmidt plates. Our measurement of the power spectrum is robust for wavenumbers in the range 0.04 hMpc 1 � k � 0.6hMpc 1 . The slope of the power spectrum for k > 0.1hMpc 1 is close to k 2 . The fluctuations in the galaxy distribution can be expressed as the rms variance in the number of galaxies in spheres of radius 8 h 1 Mpc as �8 = 1.01±0.17. We find remarkably good agreement between the power spectrum measured for the Durham/UKST Survey and those obtained from other optical studies on scales up to � = 2�/k � 80h 1 Mpc. On scales larger than this we find good agreement with the power measured from the Stromlo-APM Survey (Tadros & Efstathiou), but find more power than estimated from the Las Campanas Redshift Survey (Lin et al). The Durham/UKST Survey power spectrum has a higher amplitude than the power spectrum of IRAS galaxies on large scales, implying a relative bias between optically and infra-red selected samples of brel = 1.3. We apply a simple model for the distortion of the pattern of clustering caused by the peculiar motions of galaxies to the APM Galaxy Survey power spectrum, which is free from such effects, and find a shape and amplitude that is in very good agreement with the power spectrum of the Durham/UKST Survey. This implies � = 0.6 /b = 0.60 ± 0.35, where b is the bias between fluctuations in the galaxy and mass distributions, and also suggests a one dimensional velocity dispersion of � = 320 ± 140kms 1 . We compare the Durham/UKST power spectrum with Cold Dark Matter models of structure formation, including the effects of nonlinear growth of the density fluctuations and redshift-space distortions on the theoretical power spectra. We find that for any choice of normalisation, the standard CDM model has a shape that cannot be reconciled with the Durham/UKST Survey power spectrum, unless either unacceptably high values of the one dimensional velocity dispersion are adopted or the assumption that bias is constant is invalid on scales greater than 20h 1 Mpc. Over the range of wavenumbers for which we have a robust measurement of the power spectrum, we find the best agreement is obtained for a critical density CDM model in which the shape of the power spectrum is modified.

On the CCD calibration of Zwicky galaxy magnitudes and the properties of nearby field galaxies

We present CCD (charge-coupled device) photometry for galaxies around 204 bright (mZ<15.5) Zwicky galaxies in the equatorial extension of the APM Galaxy Survey, sampling an area over 400 deg2, which extends 6 h in right ascension. We fit a best linear relation between the Zwicky magnitude system, mZ, and the CCD photometry, BCCD, by doing a likelihood analysis that corrects for Malmquist bias. This fit yields a mean scale error in Zwicky of 0.38 mag mag−1: i.e. ΔmZ≃(0.62±0.05)ΔBCCD and a mean zero-point of 〈BCCD−mZ〉=−0.35±0.15 mag. The scatter around this fit is about 0.4 mag. Correcting the Zwicky magnitude system with the best-fitting model results in a 60 per cent lower normalization and 0.35-mag brighter M* in the luminosity function. This brings the CfA2 luminosity function closer to the other low-redshift estimations (e.g. Stromlo-APM or LCRS). We find a significant positive angular correlation of magnitudes and position in the sky at scales smaller than about 5 arcmin, which corresponds to a mean separation of 120 h−1 kpc. We also present colours, sizes and ellipticities for galaxies in our fields, which provides a good local reference for the studies of galaxy evolution.

The power spectrum of rich clusters of galaxies on large spatial scales

We present an analysis of the redshift-space power spectrum, $P(k)$, of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that $P(k)$ can be approximated by a power law, $P(k)\proptok^{n}$, with $n\approx-1.6$ over the wavenumber range $0.04\hr<k<0.1\hr$. Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale $k \sim 0.03\hmpcrev$. We compare the power spectra estimated from simulated APM cluster catalogues to those estimated directly from cubical N-body simulation volumes and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers $k \simgt 0.02\hmpcrev$. These results suggest that the observed turn-over in the power spectrum may be a real feature of the cluster distribution and that we have detected the transition to a near scale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turn-over in the cluster power spectrum is in good agreement with the scale of the turn-over observed in the power spectrum of APM galaxies.

Testing deprojection algorithms on mock angular catalogues: evidence for a break in the power spectrum

We produce mock angular catalogues from simulations with different initial power spectra to test methods that recover measures of clustering in three dimensions, such as the power spectrum, variance and higher order cumulants. We find that the statistical properties derived from the angular mock catalogues are in good agreement with the intrinsic clustering in the simulations. In particular, we concentrate on the detailed predictions for the shape of the power spectrum, $P(k)$. We find that there is good evidence for a break in the galaxy $P(k)$ at scales between $ 0.02 < k < 0.06 ~\impc$ using an inversion technique applied to the angular correlation function measured from the APM Galaxy Survey. For variants on the standard Cold Dark Matter model, a fit at the location of the break implies $\Omega h= 0.45 \pm 0.10$, where $\Omega$ is the ratio of the total matter density to the critical density and Hubble's constant is parameterised as $H_{0}= 100~hkm ~s^{-1}Mpc^{-1}$. On slightly smaller, though still quasi-linear scales, there is a feature in the APM power spectrum where the local slope changes appreciably, with the best match to CDM models obtained for $\Omega h \simeq 0.2$. Hence the location and narrowness of the break in the APM power spectrum combined with the rapid change in its slope on quasi-linear scales cannot be matched by any variant of CDM, including models that have a non-zero cosmological constant or a tilt to the slope of the primordial $P(k)$. These results are independent of the overall normalization of the CDM models or any simple bias that exists between the galaxy and mass distributions.

Testing deprojection algorithms on mock angular catalogues: evidence for a break in the power spectrum

We produce mock angular catalogues from simulations with different initial power spectra to test methods that recover measures of clustering in three dimensions, such as the power spectrum, variance and higher order cumulants. We find that the statistical properties derived from the angular mock catalogues are in good agreement with the intrinsic clustering in the simulations. In particular, we concentrate on the detailed predictions for the shape of the power spectrum, P(k). We find that there is good evidence for a break in the galaxy P(k) at scales in the range 0.02<k<0.06 h Mpc-1, using an inversion technique applied to the angular correlation function measured from the APM Galaxy Survey. For variants on the standard cold dark matter (CDM) model, a fit at the location of the break implies Ωh=0.45±0.10, where Ω is the ratio of the total matter density to the critical density, and Hubble's constant is parametrized as H0=100 h km s-1 Mpc-1. On slightly smaller, though still quasi-linear scales, there is a feature in the APM power spectrum where the local slope changes appreciably, with the best match to CDM models obtained for Ωh≃0.2. Hence the location and narrowness of the break in the APM power spectrum combined with the rapid change in its slope on quasi-linear scales cannot be matched by any variant of CDM, including models that have a non-zero cosmological constant or a tilt to the slope of the primordial P(k). These results are independent of the overall normalization of the CDM models or any simple bias that exists betwen the galaxy and mass distributions.

The APM Galaxy Survey -- V. Catalogues of galaxy clusters

We describe the construction of catalogues of galaxy clusters from the APM Galaxy survey using an automated algorithm based on Abell-like selection criteria. We investigate the effects of varying several parameters in our selection algorithm, including the magnitude range, and radius from the cluster centre used to estimate the cluster richnesses. We quantify the accuracy of the photometric distance estimates by comparing with measured redshifts, and we investigate the stability and completeness of the resulting catalogues. We find that the angular correlation functions for different cluster catalogues are in good agreement with one another, and are also consistent with the observed amplitude of the spatial correlation function of rich clusters.

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 2-point galaxy correlation function from the Durham/UKST Galaxy Redshift Survey. This survey is magnitude limited to bj = 17, contains 2500 galaxies sampled at a rate of one in three and surveys a 4 \times 10^6 (h^-1Mpc)^3 volume of space. We have empirically determined the optimal method of estimating the 2-point correlation function from just such a magnitude limited survey. Using this method, our correlation function results confirm the previously claimed detections of large scale power out to 40h^-1 Mpc scales. We compare with two common models of cosmological structure formation and find that our 2-point correlation function has power significantly in excess of the standard cold dark matter model in the 10-30h^-1 Mpc region, supporting the observational results of the APM galaxy survey.

The richness dependence of galaxy cluster correlations: results from a redshift survey of rich APM clusters

We analyse the spatial clustering properties of a new catalogue of very rich galaxy clusters selected from the APM Galaxy Survey. These clusters are of comparable richness and space density to Abell Richness Class $\geq 1$ clusters, but selected using an objective algorithm from a catalogue demonstrably free of artificial inhomogeneities. Evaluation of the two-point correlation function $\xi_{cc}(r)$ for the full sample and for richer subsamples reveals that the correlation amplitude is consistent with that measured for lower richness APM clusters and X-ray selected clusters. We apply a maxmimum likelihood estimator to find the best fitting slope and amplitude of a power law fit to $\xi_{cc}(r)$, and to estimate the correlation length $r_{0}$ (the value of $r$ at which $\xi_{cc}(r)$ is equal to unity). For clusters with a mean space density of $1.6\times 10^{-6}\hmpccc$ (equivalent to the space density of Abell Richness $\geq 2$ clusters), we find $r_{0}=21.3^{+11.1}_{-9.3} \hmpc$ (95% confidence limits). This is consistent with the weak richness dependence of $\xi_{cc}(r)$ expected in Gaussian models of structure formation. In particular, the amplitude of $\xi_{cc}(r)$ at all richnesses matches that of $\xi_{cc}(r)$ for clusters selected in N-Body simulations of a low density Cold Dark Matter model.

The correlation function of clusters of galaxies and the amplitude of mass fluctuations in the Universe

We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by the spectrum of linear density fluctuations. Thus if the shape of the initial fluctuation spectrum is known, its amplitude $\sigma_8$ can be estimated directly from the correlation length of a cluster sample in a way which is independent of the value of $\Omega_0$. If the cluster mass corresponding to the sample threshold is also known, it provides an independent estimate of the quantity $\sigma_8\Omega_0^{0.6}$. Thus cluster data should allow both $\sigma_8$ and $\Omega_0$ to be determined observationally. We explore these questions using N-body simulations together with a simple but accurate analytical model based on extensions of Press-Schechter theory. Applying our results to currently available data we find that if the linear fluctuation spectrum has a shape similar to that suggested by the APM galaxy survey, then a correlation length $r_0$ in excess of $20\mpch$ for Abell clusters would require $\sigma_8>1$, while $r_0<15\mpch$ would require $\sigma_8<0.5$. With conventional estimates of the relevant mass threshold these imply $\Omega_0\la 0.3$ and $\Omega_0\ga 1$ respectively.

Power spectrum analysis of the Stromlo—APM redshift survey

We test estimators of the galaxy power spectrum $P(k)$ against simulated galaxy catalogues constructed from N-body simulations and we derive formulae to correct for biases. These estimators are then applied to compute the power spectrum of galaxies in the Stromlo-APM redshift survey. We test whether the amplitude of $P(k)$ depends on galaxy luminosity, but find no significant luminosity dependence except at absolute magnitudes brighter than $M_{\bj} = -20.3$, ($H_{0} = 100 \kms$) where there is some evidence for a rise in the amplitude of $P(k)$. By comparing the redshift space power spectrum of the Stromlo-APM survey with the real space power spectrum determined from the parent APM Galaxy Survey, we attempt to measure the distortion in the shape of $P(k)$ caused by galaxy peculiar motions. We find some evidence for an effect, but the errors are large and do not exclude a value of $\beta = \Omega^{0.6}/b = 1$, where $\Omega$ is the cosmological density parameter and $b$ is the linear biasing parameter relating galaxy fluctuations to those in the mass, $\left(\delta \rho/\rho\right)_{gal} = b \left(\delta \rho/\rho\right)_{m}$. The shape of the Stromlo-APM power spectrum is consistent with that determined from the CfA-2 survey, but has a slightly higher amplitude by a factor of about 1.4 than the power spectrum of IRAS galaxies.