Two-point Angular Correlation Function Research Articles

Evolution and Color Dependence of the Galaxy Angular Correlation Function: 350,000 Galaxies in 5 Square Degrees

When applied to deep photometric catalogs, the two-point angular correlation function, w(theta), is a sensitive probe of the evolution of galaxy clustering properties. Here we present measurements of w(theta) as a function of I_AB magnitude and (R-I) color to a depth of I_AB=24, using a sample of ~350,000 galaxies covering 5 degrees^2 in total over 5 separate fields. Using redshifts of 3319 galaxies in early DEEP2 Galaxy Redshift Survey data, we construct robust galaxy redshift distributions as a function of I_AB and R_AB magnitude and (R-I) color for galaxies between 0 1 to z=0. A model in which the comoving scale-length, x_0, evolves linearly with redshift, x_0(z)=x_0(0)(1-Bz), fits the data better than the 'epsilon' model proposed by Groth and Peebles (1977). The clustering properties depend strongly on observed (R-I) color, with both the reddest and bluest galaxies exhibiting large clustering amplitudes and steeper slopes. Different observed (R-I) color ranges are sensitive to very disparate redshift regimes. Red galaxies with (R-I)~1.5 lie in a narrow redshift range centered at z~0.85 and have a comoving scale length of clustering at z=0.85 of x_0=5.0 +/-0.3 Mpc/h. These galaxies have early-type spectra and are likely progenitors of massive local ellipticals. The bluest galaxies with (R-I)~0 appear to be a mix of star-forming galaxies, both relatively local (z~0.3-0.6) dwarfs and bright z>1.4 galaxies, and broad-line AGN. We find that local blue dwarfs are relatively unclustered, with x_0=1.6 +/-0.2 Mpc/h. The z>1.4 blue galaxies have a larger clustering scale-length, x_0>5 Mpc/h.

The Digitized Second Palomar Observatory Sky Survey (DPOSS). III. Star-Galaxy Separation

We discuss object classification for a multicolor survey of high-latitude fields from the Digitized Second Palomar Observatory Sky Survey (DPOSS) and the resulting Palomar-Norris Sky Catalog. Two methods are used to perform automated image classification for star-galaxy separation in DPOSS. As a source of classifier training/testing data, we employ an unprecedented 500 field collection of CCD photometry in the Thuan & Gunn gri system obtained with the Palomar 60 inch (1.5 m) telescope. We have trained artificial neural network (ANN) and decision tree (DT) image classifiers using images of ≈4000 galaxies and ≈3000 stars classified with FOCAS on 52 deep CCD images. We assess the systematic errors in our classifiers as a function of apparent magnitude. To model the loss of galaxies through misclassification and the contamination of our galaxy samples by misclassified stars, we compare the DPOSS ANN+DT image classifications with image data from 46 CCD fields on 21 POSS-II fields not used in the initial training/testing process. We assess these same functions in a more stringent manner by comparing classifications of DPOSS images common with different fields via the plate overlaps. These tests are combined to derive analytic descriptions of sample incompleteness and contamination for future use in our assessment of multicolor galaxy number counts and the two-point angular correlation function. Finally, we derive star and galaxy number counts from 341 DPOSS fields covering a total of 7756 deg2 in both the north and south Galactic hemispheres. These data are used to establish a final correction for stellar contamination in our galaxy samples and to demonstrate the level of classification homogeneity in the DPOSS g and r catalogs drawn from a wide range of Galactic latitudes.

Predictions of the Angular Power Spectrum of Clustered Extragalactic Point Sources at Cosmic Microwave Background Frequencies from Flat and All‐Sky Two‐dimensional Simulations

We present predictions of the angular power spectrum of cosmic microwave background (CMB) fluctuations due to extragalactic point sources (EPSs) by using a method for simulating realistic two-dimensional distributions of clustered EPSs. Both radio- and far-IR-selected source populations are taken into account. To analyze different clustering scenarios, we exploit the angular power spectra of EPSs, P(k), estimated either by data coming from currently available surveys or by means of theoretical predictions. By adopting the source number counts predicted by the Toffolatti et al. evolution model, capable of accounting well for the available data at radio (centimeter) wavelengths, we are able to reproduce current data on the two-point angular correlation functions, w(?), of radio sources. We can confirm that the detection of primordial CMB anisotropies is not hampered by undetected clustered sources at frequencies ?150-200 GHz. On the other hand, our current findings show that at higher frequencies the clustering signal could severely reduce the detectability of intrinsic CMB anisotropies, thus confirming previous theoretical predictions. We also show that unsubtracted EPSs can account for the excess signal at high multipoles detected by recent CMB anisotropy experiments. Moreover, the additional power due to the clustering of sources gives rise to a small but nonnegligible contribution to the same excess signal. As a final result, we also present an example of a currently feasible realistic map of EPSs at 70 GHz, by taking into account data on bright detected sources, as well as the previously quoted model for number counts. Eventually, these simulated sky maps could prove very useful for testing the efficiency of component separation techniques, the capability of new algorithms for the detection of EPSs, and the appearance of non-Gaussian signatures in residue CMB maps, in the presence of sources that are not Poisson-distributed in the sky.

Correlations between theWilkinson Microwave Anisotropy Probeand MAXIMA Cosmic Microwave Background Anisotropy Maps

We cross-correlate the cosmic microwave background (CMB) temperature anisotropy maps from the Wilkinson Microwave Anisotropy Probe (WMAP), MAXIMA-1, and MAXIMA-2 experiments. We use the cross spectrum, which is the spherical harmonic transform of the angular two-point correlation function, to quantify the correlation as a function of angular scale. We find that the three possible pairs of cross spectra are in close agreement with each other and with the power spectra of the individual maps. The probability that there is no correlation between the maps is smaller than 1 × 10-8. We also calculate power spectra for maps made of differences between pairs of maps and show that they are consistent with no signal. The results conclusively show that the three experiments not only display the same statistical properties of the CMB anisotropy, but also detect the same features wherever the observed sky areas overlap. We conclude that the contribution of systematic errors to these maps is negligible and that MAXIMA and WMAP have accurately mapped the CMB anisotropy.

Fluctuations ofK-band galaxy counts

We measure the variance in the distribution of off-plane (|b|>20 deg.) galaxies with m_K<13.5 from the 2MASS K-band survey in circles of diameter between 0.344 deg. and 57.2 deg. The use of a near-infrared survey makes negligible the contribution of Galactic extinction to these fluctuations. We calculate these variances within the standard Lambda-CDM model assuming that the sources are distributed like halos of the corresponding mass, and it reproduces qualitatively the galaxy counts variance. Therefore, we test that the counts can be basically explained in terms only of the large scale structure. A second result of this paper is a new method to determine the two point correlation function obtained by forcing agreement between model and data. This method does not need the knowledge of the two-point angular correlation function, allows an estimation of the errors (which are low with this method), and can be used even with incomplete surveys. Using this method we get xi(z=0, r<10 h^{-1}Mpc)=(29.8+/-0.3) (r/h^{-1}Mpc)^{-1.79+/-0.02}, which is the first measure of the amplitude of xi in the local Universe for the K-band. It is more or less in agreement with those obtained through red optical filters selected samples, but it is larger than the amplitude obtained for blue optical filters selected samples.

Large-scale structure in the ELAIS S1 Survey

We present an analysis of the two-point angular correlation function of The European Large-Area Infrared Space Observatory (ELAIS) S1 survey. The survey covers 4 deg2 and contains 462 sources detected at 15 mum to a 5sigma flux limit of 0.45 mJy. Using the 329 extragalactic sources not repeated in different observations, we detect a significant clustering signal; the resulting angular correlation function can be fitted by a power law w(theta) =Atheta1-gamma with A= 0.014 +/- 0.005 and gamma= 2.04 +/- 0.18. Using the observed redshift distribution of the objects (from spectroscopic and photometric redshifts), we invert Limber's equation and deduce a spatial correlation length r0= 4.3+0.4-0.7h-1 Mpc. This is smaller than that obtained from optical surveys but it is in agreement with results from IRAS. This extends to higher redshift the observational evidence that infrared selected surveys show smaller correlation lengths (i.e. reduced clustering amplitudes) than optical surveys.

Evidence for anisotropy in the distribution of short-lived gamma-ray bursts

Measurements of the two-point angular correlation function w(\theta) for 407 short gamma-ray bursts collected in the Current BATSE Catalogue reveal a ~2 \sigma deviation from isotropy on angular scales \theta ~ 2-4 degrees. Such an anisotropy is not observed in the distribution of long gamma-ray bursts and hints to the presence of repeated bursts for up to ~13% of the sources under exam. However, the available data cannot exclude the signal as due to the presence of large-scale structure. Under this assumption, the amplitude of the observed w(\theta) is compatible with those derived for different populations of galaxies up to redshifts ~0.5, result that suggests short gamma-ray bursts to be relatively local sources.

The Angular Correlation Function of Galaxies from Early Sloan Digital Sky Survey Data

The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local universe. In this paper we present some of the initial results on the angular two-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18 < r* < 22, is shown to be consistent with results from existing wide-field, photographic-based surveys and narrower CCD galaxy surveys. On scales between 1' and 1° the correlation function is well described by a power law with an exponent of ≈-0.7. The amplitude of the correlation function, within this angular interval, decreases with fainter magnitudes in good agreement with analysis from existing galaxy surveys. There is a characteristic break in the correlation function on scales of approximately 1°-2°. On small scales, θ < 1', the SDSS correlation function does not appear to be consistent with the power-law form fitted to the 1' < θ < 05 data. With a data set that is less than 2% of the full SDSS survey area, we have obtained high-precision measurements of the power-law angular correlation function on angular scales 1' < θ < 1°, which are robust to systematic uncertainties. Because of the limited area and the highly correlated nature of the error covariance matrix, these initial results do not yet provide a definitive characterization of departures from the power-law form at smaller and larger angles. In the near future, however, the area of the SDSS imaging survey will be sufficient to allow detailed analysis of the small- and large-scale regimes, measurements of higher order correlations, and studies of angular clustering as a function of redshift and galaxy type.

The Clustering Properties of Lyman Break Galaxies at Redshiftz ∼ 3

We present a new measure of the angular two-point correlation function of Lyman break galaxies (LBGs) at z ~ 3, obtained from the variance of galaxy counts in two-dimensional cells. By avoiding binning of the angular separations, this method is significantly less affected by shot noise than traditional measures and allows for a more accurate determination of the correlation function. We used a sample of about 1000 galaxies with ≤ 25.5 extracted from the survey by Steidel and collaborators and found the following results. At scales in the range 30'' ≲ θ ≲ 100'', the angular correlation function w(θ) can be accurately described as a power law with slope β = 0.50 (1 σ random)-0.10 (systematic), shallower than the measure presented by Giavalisco and collaborators. However, the spatial correlation length, derived by Limber deprojection, is in very good agreement with the previous measures, confirming the strong spatial clustering of these sources. We discuss in detail the effects of both random and systematic errors, in particular of the so-called integral constraint bias, to which we set a lower limit using numerical simulations. This suggests that the current samples do not yet provide a "fair representation" of the large-scale distribution of LBGs at z ~ 3. An intriguing result of our analysis is that at angular separations smaller than θ ≲ 30'' the correlation function seems to depart from the power law fitted at larger scales and become smaller. This feature is detected at the ~90% confidence level and, if real, can provide information on the number density and spatial distribution of LBGs within their host halos as well as the size and the mass of the halos.

Probing Large Scale Structures in HI with GMRT

The redshifted 1420 MHz emission from the HI in unresolved Lyman-α clouds (DLA) at high z will appear as a background radiation in low frequency radio observations. We calculate the brightness temperature and the angular two-point correlation function of the fluctuations of this radiation. This can be an important probe of the large-scale structure at high z.

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, γ = 1.8, with a 3D correlation length r 0 ∼ 6 h - 1 Mpc (under certain assumptions). Calibration problems in the survey prevent clustering analysis below S 1 . 4 GHz = 10 mJy. 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.

Determining Cosmic Microwave Background Structure from Its Peak Distribution

We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic describing their angular clustering analogously to galaxies, the two-point angular correlation function, ξν(θ). We show that for increasing peak threshold ν, ξν(θ) is strongly amplified and becomes measurable for ν 1 on angular scales ≤10°. Its amplitude at every scale depends uniquely on the CMB temperature correlation function, C(θ), and thus the measured ξν can be uniquely inverted to obtain C(θ) and its Legendre transform, the power spectrum of the CMB field. Because in this method the CMB power spectrum is deduced from high peaks/troughs of the CMB field, the procedure takes only [f(ν)]2N2 operations, where f(ν) is the fraction of pixels with |δT| ≥ ν standard deviations in the map of N pixels and is, e.g., 0.045 and 0.01 for ν = 2 and 2.5, respectively. We develop theoretical formalism for the method and show with detailed simulations, using the Microwave Anisotropy Probe mission parameters, that this method allows us to determine very accurately the CMB power spectrum from the upcoming CMB maps in only ~(10-4 to 10-3) N2 operations.

Correlation function of ultrahigh-energy cosmic rays favors point sources

We calculate the angular two-point correlation function of ultrahigh-energy cosmic rays (UHECR) observed in the AGASA and Yakutsk experiments. In both data sets, there is a strong signal at the highest energies, which is concentrated in the first bin of size equal to the angular resolution of the experiment. For the uniform distribution of sources, the probability of chance clustering is 4×10−6. Correlations are absent or insignificant at larger angles. This favors the models with compact sources of UHECR

Quasar-Galaxy Correlations: A Detection of Magnification Bias

Weak gravitational lensing by clusters and superclusters can change our perception of the distribution of bright background quasars through the phenomenon of magnification bias. It has been suggested that this lensing will lead to an association of moderate-redshift quasars (z ~ 1.0–2.0) and foreground galaxies (z ~ 0.2–0.3). We report on the analysis of a sample of 90 CCD fields centered on moderate-redshift quasars that are bright at both radio (S5 GHz > 1 Jy) and optical (V < 21.0) wavelengths, along with 12 control fields. The quasars presented here are chosen to have the highest potential for evidence of this weak lensing effect. We find no evidence for the presence of rich galaxy clusters (Abell richness class 1) in the foreground of these fields. However, using a Spearman rank-order correlation test, we detect a correlation between galaxy number density and angular distance from bright quasars on scales of ~15' with a significance of 96%. The observed correlation is unlikely the result of Galactic dust and is consistent with weak gravitational lensing of the quasars by foreground matter. We also determine the two-point angular correlation function between these background quasars and foreground galaxies. We find a correlation amplitude of 0.056 ± 0.020 over scales of ~5'. This angular correlation is consistent with the semianalytic weak gravitational lensing models of Dolag & Bartelmann (published in 1997), which incorporate nonlinear evolution of mass clustering.

Wide‐Field Imaging of the Hubble Deep Field–South Region. II. The Evolution of Galaxy Clustering atz&lt; 1

We present the galaxy-galaxy angular correlations as a function of photometric redshift in a deep, wide galaxy survey centered on the Hubble Deep Field-South (HDF-S). Images were obtained with the Big Throughput Camera on the Blanco 4 m telescope at CTIO, of square degree in broadband uBVRI, reaching ~24 mag. Approximately 40,000 galaxies are detected in the survey. We determine photometric redshifts using galaxy template fitting to the photometry. Monte Carlo simulations show that redshifts from these data should be reliable out to z ~ 1, where the 4000 A break shifts into the I band. The inferred redshift distribution, n(z), shows good agreement with the distribution of galaxies measured in the Hubble Deep Field-North (HDF-N) and the Canada-France Redshift Survey. After assigning galaxies to redshift bins with width Δz = 0.33, we determine the two-point angular correlation function in each bin. We find that the amplitude of the correlation, Aw, drops across the three bins to redshift z ~ 1. Simple models of clustering evolution fit this result, with the best agreement for = 0. Hierarchical cold dark matter models best fit in a low-density, Λ-dominated universe.

Measuring Omega/b with Weak Lensing.

A correlation between the surface density of foreground galaxies tracing the large-scale structure and the position of distant galaxies and quasars is expected from the magnification bias effect. We show that this foreground-background correlation function wfb can be used as a straightforward and almost model-free method to measure the cosmological ratio Omega/b. For samples with appropriate redshift distributions, wfb~Omegadeltag, where delta and g are respectively the foreground dark matter and galaxy surface density fluctuations. Therefore, Omega&solm0;b~wfb&solm0;w, where w identical withgg is the foreground galaxy angular two-point correlation function, b is the biasing factor, and the proportionality factor is independent of the dark matter power spectrum. Simple estimations show that the application of this method to the galaxy and quasar samples generated by the upcoming Sloan Sky Digital Survey will achieve a highly accurate and well-resolved measurement of the ratio Omega/b.

ESO Imaging Survey

This paper presents the first data evaluation of the ESO Imaging Survey (EIS), a public survey being carried out by ESO and member states, in preparation for the VLT first-light. The survey goals, organization, strategy and observations are discussed and an overview is given of the survey pipeline developed to handle EIS data and produce object catalogs. A report is presented on moderately deep I -band observations obtained in the first of four patches surveyed, covering a region of 3.2 square degrees centered at and . The products available to the community, including pixel maps (with astrometric and photometric calibrations) and the corresponding object catalogs, are also described. In order to evaluate the quality of the data, preliminary estimates are presented for the star and galaxy number counts, and for the angular two-point correlation function obtained from the available data. The present work is meant as a preview of the final release of the EIS data that will become available later this year.

Clustering at High Redshift: Precise Constraints from a Deep, Wide‐Area Survey

We present constraints on the evolution of large-scale structure from a catalog of 710,000 galaxies with IAB ? 24 derived from a KPNO 4 m CCD imaging survey of a contiguous 4? ? 4? region. The advantage of using large contiguous surveys for measuring clustering properties on even modest angular scales is substantial: the effects of cosmic scatter are strongly suppressed. We provide highly accurate measurements of the two-point angular correlation function, ?(?), as a function of magnitude on scales up to 15. The amplitude of ?(?) declines by a factor of ~10 over the range 16 ? I ? 20 but only by a factor of 2-3 over the range 20 20, our best-fit values shift toward lower r0 and more negative . A strong covariance between r0 and prevents us from rejecting > 0 even at faint magnitudes, but if > 1, we strongly reject r0 4 h-1 Mpc (comoving). The above expression for ?(r, z) and our data give a correlation length of r0(z = 0.5) ? 3.0 ? 0.4 h-1 Mpc, about a factor of 2 larger than the correlation length at z = 0.5 derived from the Canada-France Redshift Survey (CFRS). The small volume sampled by the CFRS and other deep redshift probes, however, makes these spatial surveys strongly susceptible to cosmic scatter and will tend to bias their derived correlation lengths toward the low end. Our results are consistent with redshift distributions in which ~30%-50% of the galaxies at I = 23 lie at z > 1. The best-fit power-law slope of the correlation function remains independent of I magnitude for I ? 22. At fainter limits, there is a suggestive trend toward flatter slopes that occurs at fluxes consistent with similar trends seen by Neuschaffer & Windhorst and Campos and coworkers. The galaxy counts span 11 magnitudes and provide an accurate calibration of the galaxy surface density. We find evidence for mild galaxy evolution: about 1 mag of brightening or a doubling of the density by I = 23 relative to an ?0 = 1 no-evolution model, about 0.5 mag of brightening or a factor of 1.5 increase in surface density relative to an open model. Our galaxy counts agree well with those from the Hubble Deep Field survey and, thus, argue against a significant inclusion of subgalactic components in the latter census for I < 24.

The Morphology Dependence of Luminosity Segregation in the Coma Cluster

We carry out CCD photometry of galaxies in the 5.25 square region centered on Coma cluster down to $M_R=-16.0$, beyond the limit of conventional morphological classification. We use the angular two-point correlation function as well as radial profiles in order to characterize the luminosity segregation. We find strong luminosity segregation for our total sample over the magnitude range of $-20 \leq M_R \leq -16$, which is not entirely accounted for in terms of the morphology-density relation that is known to exist only for bright galaxies. We use a single consistent parameter, the degree of luminosity concentration, to parameterize the morphology of galaxies over the wide magnitude range, where both giant and dwarf galaxies are included. Galaxies with high central concentration (HCC) show strong luminosity segregation, i.e. their clustering strength depends strongly on luminosity while those with low central concentration (LCC) show almost no luminosity segregation. Radial density profile shows that brighter HCC-type galaxies tend to more strongly concentrate near the cluster center while LCC-type galaxies do not show such a dependence on luminosity. We show that these results are tenable against the contamination by field galaxies and uncertainties in our method of classification.

Evolution of the Angular Correlation Function

For faint photometric surveys, our ability to quantify the clustering of galaxies has depended on interpreting the angular correlation function as a function of the limiting magnitude of the data. Because of the broad redshift distribution of galaxies at faint magnitude limits, the correlation signal has been extremely difficult to detect and interpret. Here we introduce a new technique for measuring the evolution of clustering. We utilize photometric redshifts derived from multicolor surveys to isolate redshift intervals and to calculate the evolution of the amplitude of the angular two-point correlation function. Applying these techniques to the Hubble Deep Field, we find that the shape of the correlation function at z=1 is consistent with a power law with a slope of -0.8. For z > 0.4, the best fit to the data is given by a model of clustering evolution with a comoving r -->0=2.37 h-1 Mpc and =-0.4 -->+ 0.37−0.65, which is consistent with published measures of the clustering evolution. To match the canonical value of r -->0=5.4 h-1 Mpc found for the clustering of local galaxies requires a value of =2.10 -->+ 0.43−0.64 (significantly more than linear evolution). The log likelihood of this latter fit is 4.15 times smaller than that for the r -->0=2.37 h-1 Mpc model. We, therefore, conclude that the parameterization of the clustering evolution of (1+z)-(3+) is not a particularly good fit to the data.