Two-point Spatial Correlation Function Research Articles

Quasar-Cluster Associations and Gravitational Lensing by Large-Scale Matter Clumps

Motivated by the significant overdensity of background bright quasars recently detected behind the foreground clusters of galaxies on a scale of 10', we have investigated the possibility of attributing the quasar-cluster associations to gravitational lensing by large-scale matter inhomogeneities. Based on the conventional lensing models, we have shown that the reported quasar overdensity is unlikely to be generated by cluster matter alone. The situation does not change even if all of the clusters of galaxies that follow their spatial two-point correlation function are taken into account, while matter clumps on scales of greater than 20 Mpc are also found to be unable to provide the required mass surface density, since their density contrast is strictly limited by the anisotropy measurements of the cosmic background radiation. Moreover, we have pointed out that the influence of a nonzero cosmological constant on the quasar-cluster associations is very minor. We conclude that either the observed quasar number counts have been seriously contaminated by the magnification bias of matter inhomogeneities of the universe or there should exist some intercluster matter on a scale of less than ~20 Mpc, e.g., from cluster-galaxy correlation, whose mean cosmic density is about an order of magnitude higher than that of clusters of galaxies.

Two-Point Velocity and Spatial Correlation Functions of the C IV Absorption Systems toward the Tololo Quasar Group: Evidence for Superclustering at Z 2

view Abstract Citations (38) References (40) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Two-Point Velocity and Spatial Correlation Functions of the C IV Absorption Systems toward the Tololo Quasar Group: Evidence for Superclustering at Z ≃21 Dinshaw, Nadine ; Impey, Chris D. Abstract The large number of apparently correlated C IV absorption systems observed in the lines of sight to the wide QSO pair Tol 1037-2704 (zem = 2.193) and Tol 1038-2712 (zem = 2.331) between the redshifts 1.88 ≤ z ≤ 2.15 is thought to be produced by an intervening supercluster. We present high-resolution echelle spectra of Tol 1037-2704 and Tol 1038-2712, as well as two neighboring QSOs with the aim of searching for absorption associated with the putative supercluster. The lines of sight toward the original pair are separated by 17'.9 corresponding to a proper separation of D⊥ ≃ 4.4 h-1 Mpc (h = H0/100 km s-1 Mpc-1; q0 = 0.5) at z = 2. We confirm the existence of the C IV absorption complexes already reported, and find additional complexes. At a resolution of ∼30 km s-1 FWHM, many of the C IV complexes break up into multiple discrete components with a velocity spread of Δυ ≃ 50-1000 km s-1. This brings the total number of C IV absorption systems with secure identifications to 22 in Tol 1037-2704 and 11 in Tol 1038-2712 in the redshift range 1.48 ≤ z ≤ 2 15 well above the expectation from Poisson statistics. The two neighboring QSOs, Tol 1035-2737 (zem = 2.159) and Tol 1029-2654 (zem = 2.586), are located roughly 40' (D⊥ ≃ 10 h-1 Mpc) southwest and 115'(D⊥ ≃30 h-1 Mpc) northwest of the Tololo pair, respectively. We found five C IV systems in the line of sight to Tol 1035-2737, and six toward Tol 1029-2654. Most of these systems appear to match systems in the original QSO pair within a velocity separation of less than 5000 km s-1, though the significance of the matches is not strong. We find a marginal excess of C IV absorption systems in the line of sight to Tol 1029-2654, whereas the number of systems in the line of sight to Tol 1035-2737 agrees with expectation. The inferred proper dimensions of the proposed supercluster are at least 30 h-1 Mpc on the plane of the sky and approximately 80 h-1 Mpc along the line of sight. We examined the clustering properties of the absorbers toward the Tololo QSOs using the two-point velocity and spatial correlation functions. The velocity correlation function of the complete sample of 44 C IV systems shows strong clustering for velocity separations less than 1000 km s-1, which probe clouds in galactic halos as well as individual galaxies in clusters, and significant clustering signal out to scales of 7000 km s-1. In a subsample of 16 systems (W0 > 0.15 Å), where the power associated with virialized clusters on scales less than 1000 km s-1 has been removed, significant correlation signal persists for velocity separations of 4000- 7000 km s-1, which correspond to comoving spatial scales of ∼30-40 h-1 Mpc. The spatial correlation function of the same subsample, derived by pairing absorbers between different lines of sight, shows a marginally significant peak on comoving scales of less than 18 Mpc. The clustering amplitude on these scales is larger than predicted by current theories of the formation of large-scale structure. Publication: The Astrophysical Journal Pub Date: February 1996 DOI: 10.1086/176794 Bibcode: 1996ApJ...458...73D Keywords: GALAXIES: CLUSTERS: GENERAL; GALAXIES: QUASARS: ABSORPTION LINES; GALAXIES: QUASARS: GENERAL full text sources ADS | data products NED (56) SIMBAD (6)

A possibility to reveal parent populations for objects with active nuclei comparing their spatial correlation functions

Abstract The possibility to derive conclusions about parent population comparing two-point spatial correlation functions of single objects and/or of systems of different types, including AGN, is demonstrated. Similarity of correlation function for groups of galaxies, radio-quiet QSGs, and Seyfert galaxies testify to their evolutionary connection. This method can be used for choosing FR-I-type radiogalaxies or radi-quiet QSGs as parent population of BL Lacertae-type objects.

The two-point correlation function of rich clusters of galaxies: results from an extended APM cluster redshift survey

We present new estimates of the spatial two-point correlation function of rich clusters of galaxies selected from the APM Galaxy Survey. We have measured redshifts for a sample of $364$ clusters out to a depth of $\sim 450\hmpc$. The clusters have a mean space density of $\bar{n} = 3.4\times 10^{-5}\hmpccc$. The two-point correlation function, $\xi_{cc}$, for this sample is equal to unity at a pair-separation of $r_0 = 14.3\pm1.75\hmpc$ (2$\sigma$ errors), consistent with our earlier results from a smaller sample. The new observations provide an accurate determination of the shape of $\xi_{cc}$ to pair-separations of about $50\hmpc$. Our results show that $\xi_{cc}$ has a higher amplitude than expected according to the standard $\Omega=1$ cold dark matter (CDM) model on spatial scales $2\simlt s \simlt 50\hmpc$, but are in good agreement with scale-invariant fluctuations in either a low density CDM model or a critical density universe made up of a mixture of hot and cold dark matter. Our results provide strong constraints on so called `co-operative' models of galaxy formation in which the galaxy formation process introduces large-scale structure in the galaxy distribution.

Inverse problems with quasi-homogeneous random media

Formulas are derived for determining low-pass filtered versions of the two constituent factors of the two-point spatial correlation function of a quasi-homogeneous random medium from knowledge of the cross-spectral density of the scattered field in the far zone. The results are illustrated by an example. When the scale lengths of variation of these quantities are greater than approximately half of the mean wavelength of the incident light, the reconstructions are found to be practically exact.

Stochastic analysis of mantle convection experiments using two‐point correlation functions

This paper discusses the stochastic analysis of spatially complex, time‐dependent flows in spherical and cylindrical geometries where the reference states, internal heating rates, and boundary conditions are temporally invariant and rotationally symmetric. Snapshots of the aspherical temperature anomalies δT (r,Ω,t) from a single convection run are taken to be samples of a stationary, rotationally invariant random field, and the spatial two‐point correlation function CTT(r,r′,Δ) is constructed by averaging over rotational transformations of this ensemble. Three subfunctions are extracted: the rms variation, the radial correlation function, RT(r,r′) = CTT(r,r′,0)/ σT(r)σT(r′), and the angular correlation function All three are useful in assessing the structural differences among mantle convection simulations, but the diagnostic properties of RT and its robustness with respect to low‐pass filtering recommend it as a tool for testing stratification hypotheses against whole‐mantle tomographic models.

The spatial correlation properties of galaxy halos in a cold dark matter universe

Using high-resolution N-body simulations, the two-point spatial correlation function, ξ(r), of dark galaxy halos in a cold dark matter universe is determined as a function of halo mass and local environment. A linear bias model is a good description of the formation of halos with overdensity ∼200, but not for halos with overdensities ∼2000 and ∼70

Clustering properties of galaxies: an empirical model

To study the dependence of the recently discovered twin power-law behaviour of the two-point spatial correlation function on the geometry of the large-scale distribution of galaxies, a geometrical toy model is constructed which enables us to restore all the main features of the correlation function of galaxies

Redshift and structure formation in a spatially flat inhomogeneous universe.

We study a spherically symmetric Tolman-Bondi cosmological model with globally flat spatial sections $t=\mathrm{const}$. We consider the model valid for the description of the Universe after matter starts to dominate. The redshift and cosmological observations in the model are examined and a simple scenario of the changes in the structure formation when compared to the standard flat Friedmann-Robertson-Walker universe is proposed. This scenario is based on the fact that in our model different parts of the Universe spend unequal periods of time in the matter-dominated era. The correction to the cold-dark-matter spatial two-point correlation function is derived. Specific cases are examined corresponding to observationally based distributions of the density. We show that this not only leads to no contradictions, but significantly improves the fit of theoretically predicted correlation functions to observations.

Stability of a chemically layered upper mantle

The possibility that the upper mantle at depths less than 670 km is chemically as well as mineralogically layered has been extensively discussed. One idea posits that sublithospheric upper mantle ( d < 400 km) is dominantly harzburgitic and of low intrinsic density compared with majoritic and clinopyroxene-rich piclogite which occupies the seismic transition region at depths between 400–670 km. The gravitational stability of the ‘harzburgite over piclogite’ arrangement (light above heavy) when heated from below is investigated here in order to better understand the dynamics of mixing. The calculations neglect the effects of plates, compressibility, viscous dissipation, phase change and radiogenic heating and focus on the role played by Δρ ρ 0 , the intrinsic density difference between the layers during mixing at fixed Rayleigh number. The dimensionless parameters of this problem include the thermal Rayleigh number based on the heat flux q 0 into the basal piclogitic layers ( Rq = α gq 0d 4 k κν ) , the ratio of chemical to thermal buoyancy Rρ = ( Δρ ρ 0 ) k αq 0d , and the thickness ratio of the two layers Δ. Here α, g, d, κ, k, ν, Δρ, ρ 0 represent the expansitivity, gravity, total depth, thermal diffusivity, thermal conductivity, kinematic viscosity, isothermal difference in density between the two layers (i.e. the intrinsic density difference) and density of the piclogitic bottom layer, respectively. A constant-viscosity Newtonian rheology is assumed for the sublithospheric upper mantle between 100–670 km. Three measures of the extent and thoroughness of mixing are used to quantify mixing; these include the variance of the compositional field, the two-point spatial correlation function for composition and the average composition within each layer. The spatial correlation enables one to define a dominant length scale characteristic of the size of the chemical anomalies (L ∗) . The adimensional variance, sometimes called the mixing intensity, may be used to define a mixing time. Simulations at fixed Rq but with Δρ ρ 0 = 0, 2, 4, 8% have been carried out for periods of time equivalent to the age of the Earth. The critical Rρ that separates well-mixed states from poorly mixed ones is Rρ ≈ 1 5 for Rq = 2 × 10 5. For nominal upper-mantle parameters this implies a critical intrinsic density difference Δρ ρ 0 ≈ 3% . The style of mixing is grossly different depending on whether Δρ ρ 0 is less than, or greater than, the critical value. Plume penetration with rapid changes in the average size of chemical heterogeneities is the dominant mechanism at low Δρ ρ 0 whereas for high Δρ ρ 0 viscous entrainment and the stretching of tendrils along the layer interface is the dominant mixing style. For density ratios near the critical value, the fraction of fertile (easily fused) peridotite within the dominantly harzburgitic upper mantle above the top of the transition region varies quasiperiodically with period ≈ 0.6 Ga, roughly equal to the supercontinent cycle time. Intermittent periods of increased lower-layer transport across the top of the transition zone may correlate with spikes in the volumetric rate of magma generation due to decompression melting of ascending fertile peridotite.

Exact solution of a deterministic sandpile model in one dimension.

We present an exact solution of a one-dimensional sandpile model for which sand is dropped along the wall and N=2 grains of sand fall over the neighboring downhill sites when the critical slope is exceeded. The slopes of N consecutive sites organize into a local state. The time evolution of the local states along the spatial direction shows a natural tree structure. As a result, various multifractals can be identified. The spatial two-point correlation function decreases exponentially with a correlation length of the order of the lattice spacing.

Constraints on large-scale clustering from the autocorrelation properties of the X-ray background

Expectations for the angular correlation function of intensity fluctuations of the extragalacitc 2-10 keV X-ray background are discussed in relation to the two-point spatial correlation functions, xi(r), of X-ray sources. A simple analytic formula for the amplitude of intensity correlations, Gamma(theta), holding in the low-redshift, small-separation approximation, is derived. The HEAO 1 A-2 upper limits on Gamma(theta) have been exploited to derive constraints on the local xi(r) functions of rich clusters of galaxies, of AGNs, and on the AGN-cluster cross-correlation, as well as on evolution of the correlation functions with cosmic time. X-ray data are found to be compatible with the Bahcall and Soneira estimates of xi(cluster-cluster) as well as with the results of recent studies of quasar clustering.

Correlation properties of loose groups

view Abstract Citations (12) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Correlation Properties of Loose Groups Maia, M. A. G. ; da Costa, L. Nicolaci Abstract The two-point spatial correlation function for loose groups of galaxies is computed, using the recently compiled catalog of groups in the southern hemisphere. We find that the correlation function for groups has a similar slope to that of galaxies but with a smaller amplitude, confirming an earlier result obtained from a similar analysis of the CfA group catalog. This implies that groups of galaxies are more randomly distriubuted than galaxies, which may be consistent with the predictions of Kashlinsky for a gravitational clustering scenario for the formation of large-scale structures. Publication: The Astrophysical Journal Pub Date: February 1990 DOI: 10.1086/168332 Bibcode: 1990ApJ...349..477M Keywords: Angular Correlation; Galactic Clusters; Galactic Structure; Astronomical Catalogs; Data Correlation; Spatial Distribution; Astrophysics; GALAXIES: CLUSTERING full text sources ADS |

Arguments in favour of physical reality of the peculiar (200÷300) Mpc scale in the distribution of the rich clusters of galaxies

It is necessary to examine the significance of the recently discovered peak of spatial two-point correlation function determined for the rich Abel clusters. We discuss the different possibilities to do it and propose the programme of further observations.

Frequency shifts of spectral lines produced by scattering from spatially random media

Scattering of polychromatic light by a medium whose dielectric susceptibility is a random function of position is considered within the accuracy of the first Born approximation. It is shown, in particular, that if the two-point spatial correlation function of the dielectric susceptibility has Gaussian form and the spectrum of the incident light has a Gaussian profile, the spectrum of the scattered light may be shifted toward the shorter or the longer wavelengths, depending on the angle of scattering. The results are analogous to those derived recently in connection with radiation from partially coherent sources [ Nature (London)326, 363 ( 1987)].

The spatial correlation function of cD Abell clusters

We calculated the spatial two-point correlation function of cD clusters in Abell's statistical sample using estimated redshifts and found that positive correlation exists on all scales except around 70 Mpc and 170 Mpc (H 0 = 100 km s −1 Mpc −1). In particular, positive correlation persists on the super large scale around 300 Mpc. This is particularly interesting in view of the known relationships among cD clusters, radio sources and superclusters.

The mean density and two-point correlation function for the CfA redshift survey slices

The effect of large-scale inhomogeneities on the determination of the mean number density and the two-point spatial correlation function were investigated for two complete slices of the extension of the Center for Astrophysics (CfA) redshift survey (de Lapparent et al., 1986). It was found that the mean galaxy number density for the two strips is uncertain by 25 percent, more so than previously estimated. The large uncertainty in the mean density introduces substantial uncertainty in the determination of the two-point correlation function, particularly at large scale; thus, for the 12-deg slice of the CfA redshift survey, the amplitude of the correlation function at intermediate scales is uncertain by a factor of 2. The large uncertainties in the correlation functions might reflect the lack of a fair sample.

The Center for Astrophysics Redshift Survey: Luminosity Function and Two-Point Correlation Function

We compare the luminosity function and the two-point spatial correlation function for the two slices of the CfA redshift survey extension to mB(0) ≤ 15.5 [8h ≤ RA. ≤ 17h and 26.5° ≤ DEC. ≤ 38.5°], with those for the early survey limited to mB(0) ≤ 14.5 [bII ≥ 40°, and DEC. ≥ 0°]. The derived properties of the two samples agree within the errors. The parameters of the luminosity function are M* = −19.1±0.1 and α = −1.2±0.1 for the 15.5 sample, and M* = −19.3±0.1 and α = −1.1 ± 0.1 for the 14.5 sample. We use an inhomogeneity-independent method to calculate the luminosity function. The slopes of the correlation functions for the two samples are −1.5 ± 0.35, shallower than the canonical slope of −1.8. The correlation lengths are 7.5 ± 5h−1 Mpc, larger than the correlation length of 5h−1 Mpc matched to the theoretical models. Because of the 25% uncertainty in the mean density of the 15.5 sample, the correlation function is indeterminate on scales larger than ∼ 20h−1 Mpc.

Relationship between specific surface area and spatial correlation functions for anisotropic porous media

A result of Debye, Anderson, and Brumberger [P. Debye, H. R. Anderson, Jr., and H. Brumberger, J. Appl. Phys. 28, 679 (1957)] for isotropic porous media states that the derivative of the two-point spatial correlation at the origin is equal to minus one-quarter of the specific surface area. This result is generalized for nonisotropic media by noting that the angular average of the anisotropic two-point spatial correlation function has the same relationship to the specific surface area.

Use of digital image analysis to estimate fluid permeability of porous materials: Application of two-point correlation functions

Scanning electron microscope images of cross sections of several porous specimens have been digitized and analyzed using image processing techniques. The porosity and specific surface area may be estimated directly from measured two-point spatial correlation functions. The measured values of porosity and image specific surface were combined with known values of electrical formation factors to estimate fluid permeability using one version of the Kozeny-Carman empirical relation. For glass bead samples with measured permeability values in the range of a few darcies, our estimates agree well (±10–20%) with the measurements. For samples of Ironton-Galesville sandstone with a permeability in the range of hundreds of millidarcies, our best results agree with the laboratory measurements again within about 20%. For Berea sandstone with still lower permeability (tens of millidarcies), our predictions from the images agree within 10–30%. Best results for the sandstones were obtained by using the porosities obtained at magnifications of about 100× (since less resolution and better statistics are required) and the image specific surface obtained at magnifications of about 500× (since greater resolution is required).