Two-point Cross-correlation Function Research Articles

The LABOCA survey of the Extended Chandra Deep Field-South: clustering of submillimetre galaxies

We present a measurement of the spatial clustering of submillimetre galaxies (SMGs) at z = 1-3. Using data from the 870 micron LESS survey, we employ a novel technique to measure the cross-correlation between SMGs and galaxies, accounting for the full probability distributions for photometric redshifts of the galaxies. From the observed projected two-point cross-correlation function we derive the linear bias and characteristic dark matter (DM) halo masses for the SMGs. We detect clustering in the cross-correlation between SMGs and galaxies at the > 4 sigma level. For the SMG autocorrelation we obtain r_0 = 7.7 (+1.8,-2.3) h^-1 Mpc, and derive a corresponding DM halo mass of log(M_halo [h^-1 M_sun]) = 12.8 (+0.3,-0.5). Based on the evolution of DM haloes derived from simulations, we show that that the z = 0 descendants of SMGs are typically massive (~2-3 L*) elliptical galaxies residing in moderate- to high-mass groups (log(M_halo [h^-1 M_sun]) = 13.3 (+0.3,-0.5). From the observed clustering we estimate an SMG lifetime of ~100 Myr, consistent with lifetimes derived from gas consumption times and star-formation timescales, although with considerable uncertainties. The clustering of SMGs at z ~ 2 is consistent with measurements for optically-selected quasi-stellar objects (QSOs), supporting evolutionary scenarios linking starbursts and QSOs. Given that SMGs reside in haloes of characteristic mass ~ 6 x 10^12 h^-1 M_sun, we demonstrate that the redshift distribution of SMGs can be described remarkably well by the combination of two effects: the cosmological growth of structure and the evolution of the molecular gas fraction in galaxies. We conclude that the powerful starbursts in SMGs likely represent a short-lived but universal phase in massive galaxy evolution, associated with the transition between cold gas-rich, star-forming galaxies and passively evolving systems. [Abridged]

On the two-point cross-correlation function of anisotropic, spatially homogeneous ambient noise in the ocean and its relationship to the Green’s function

It is well established that the free-space Green's function can be recovered from the two-point cross-correlation function of a random noise field if the noise is white and isotropic. Ambient noise in the ocean rarely satisfies either of these conditions. However, a non-uniform spectrum could be pre-whitened by the application of a suitable filter but anisotropy cannot be so readily eliminated. To investigate the effects of vertical anisotropy, three azimuthally uniform, spatially homogeneous noise fields are analyzed, two of which are idealized, while the third is representative of ambient noise in the deep ocean. In each case, the coherence function, the cross-correlation function, and the derivative of the latter with respect to the correlation delay, are derived for vertical and horizontal alignments of the sensor pair. With vertical sensors, any step-function discontinuity in the directional density function is mapped into a delta function at an appropriate time delay in the derivative (with respect to time delay) of the cross-correlation function. No such mapping occurs with horizontal sensors. In this case, only horizontally traveling noise can generate delta functions in the derivative of the cross-correlation function, and these always appear at the retarded time on either side of the origin.

Alignments of galaxy group shapes with large-scale structure

In this paper we analyse the alignment of galaxy groups with the surrounding large scale structure traced by spectroscopic galaxies from the Sloan Digital Sky Survey Data Release 7. We characterise these alignments by means of an extension of the classical two-point cross-correlation function, developed by Paz et al. 2008 (arXiv:0804.4477, MNRAS 389 1127). We find a strong alignment signal between the projected major axis of group shapes and the surrounding galaxy distribution up to scales of 30 Mpc/h. This observed anisotropy signal becomes larger as the galaxy group mass increases, in excellent agreement with the corresponding predicted alignment obtained from mock catalogues and LCDM cosmological simulations. These measurements provide new direct evidence of the adequacy of the gravitational instability picture to describe the large-scale structure formation of our Universe.

Cross-correlation function of acoustic fields generated by random high-frequency sourcesa)

Long-range correlations of noise fields in arbitrary inhomogeneous, moving or motionless fluids are studied in the ray approximation. Using the stationary phase method, two-point cross-correlation function of noise is shown to approximate the sum of the deterministic Green's functions describing sound propagation in opposite directions between the two points. Explicit relations between amplitudes of respective ray arrivals in the noise cross-correlation function and the Green's functions are obtained and verified against specific problems allowing an exact solution. Earlier results are extended by simultaneously accounting for sound absorption, arbitrary distribution of noise sources in a volume and on surfaces, and fluid inhomogeneity and motion. The information content of the noise cross-correlation function is discussed from the viewpoint of passive acoustic characterization of inhomogeneous flows.

Jet Noise: Acoustic Analogy informed by Large Eddy Simulation

A novel approach to the development of a hybrid prediction methodology for jet noise is described. Modeling details and numerical techniques are optimized for each of the three components of the model. Far-field propagation is modeled by solution of a system of adjoint linear Euler equations, capturing convective and refraction effects using a spatially developing jet mean flow provided by a Reynolds-averaged Navier―Stokes computational fluid dynamics solution. Sound generation is modeled following Goldstein's acoustic analogy, including a Gaussian function model for the two-point cross correlation of the fourth-order velocity fluctuations in the acoustic source. Parameters in this model describing turbulent length and time scales are assumed to be proportional to turbulence information also taken from the Reynolds-averaged Navier―Stokes computational fluid dynamics prediction. The constants of proportionality are, however, not determined empirically, but extracted by comparison with turbulence length and time scales obtained from a large eddy simulation prediction. The large eddy simulation results are shown to be in good agreement with experimental data for the fourth-order two-point cross-correlation functions. The large eddy simulation solution is then used to determine the amplitude parameter and also to examine which components of the cross correlation are largest, enabling inclusion of all identified dominant terms in the Gaussian source model. The acoustic source description in the present approach is therefore determined with no direct input from experimental data. This model is applied to the prediction of sound to the experimental configuration of the European Union JEAN project, and gives encouraging agreement with experimental data across a wide spectral range and for both sideline and peak noise angles. This paper also examines the accuracy of various commonly made simplifications, for example: a locally parallel mean flow approximation rather than consideration of the spatially evolving mean jet flow and scattering from the nozzle; the assumption of small radial variation in Green function over the turbulence correlation length; the application of the far-field approximation in the Green function; and the impact of isotropic assumptions made in previous acoustic source models.

Not enough evidence to support the correlation between gamma-ray bursts and foreground galaxy clusters in the Swift Era

The correlation between distant Gamma-Ray Bursts (GRBs) and foreground galaxy clusters is re-examined by using the well localized (with an accuracy down to a few arcsec) Swift/XRT GRBs. The galaxy clusters are compiled from both the X-ray selected ROSAT brightest cluster sample (BCS) and the BCS extension by requiring δ ≥ 0° and b ≥ 20°. The Swift/XRT GRBs fulfilling the above selection criteria are cross-correlated with the clusters. Both Nearest–Neighbor analysis and the angular two-point cross-correlation function show that there is not enough evidence supporting the correlation between the GRBs and foreground clusters. We suggest that the non-correlation is probably related to the GRB number-flux relation slope.

QSO-LRG two-point cross-correlation function and redshift-space distortions

We have measured the bias of QSOs as a function of QSO luminosity at xed redshift (z < 1) by cross-correlating them with luminous red galaxies (LRGs) in the same spatial volume, hence breaking the degeneracy between QSO luminosity and redshift. We use three QSO samples from 2SLAQ, 2QZ and Sloan Digital Sky Survey (SDSS) covering a QSO absolute magnitude range, -24.5 <M < -21.5, and cross-correlate them with 2SLAQ (z ≈ 0.5) and AAOmega (z ≈ 0.7) photometric and spectroscopic LRGs in the same redshift ranges. The spectroscopic QSO samples, in the spectroscopic LRG areas, contain up to 700 QSOs and in photometric LRG areas up to 7000 QSOs. The 2D and 3D cross-clustering measurements are generally in good agreement. Our (2SLAQ) QSO-LRG clustering amplitude (r = 6.98 ± 0.6 h Mpc) as measured from the semiprojected cross-correlation function appears similar to the (2SLAQ) LRG-LRG autocorrelation amplitude (r = 7.45 ± 0.35 h Mpc) and both are higher than the (2QZ + 2SLAQ) QSO-QSO amplitude (r ≈ 5.0 h Mpc). Our measurements show remarkably little QSO-LRG cross-clustering dependence on QSO luminosity. This result is unexpected on the basis of simple high-peak biasing models, where more luminous QSOs are assumed to occupy rarer and so more clustered high-mass peaks. Assuming a standard ΛCDM model and values for b measured from LRG autocorrelation analyses, from the spectroscopic samples at z ≈ 0.55 we nd b = 2.3 ± 0.5 at M ≈-24 and b = 1.6 ± 0.3 at M ≈-22. Averaging over all the spectroscopic and photometric samples, we nd an average value of b = 1.8 ± 0.1 at z ≈ 0.6 and M ≈-23. The implied dark matter halo mass inhabited by QSOs is ≈ 10 h M, again approximately independent of QSO luminosity. We have also made a z-space distortion analysis of the QSO-LRG cross-clustering at z ≈ 0.55. The velocity dispersion tted to QSO-LRG cross-correlation, ξ (σ, π), at ±600 km s is close to that expected given the larger QSO redshift errors. The dynamical infall result for the combined 2SLAQ, 2QZ and SDSS QSO sample gives β = 0.23 ± 0.15 which implies b = 3.2 ± 2.1, assuming the standard cosmological model. Although noisier, this latter value is consistent with the value of b = 1.9 ± 0.2 obtained from the amplitude of the cross-correlation function in the same redshift range. © 2009 The Authors. Journal compilation

The clustering of radio galaxies atz≃ 0.55 from the 2SLAQ LRG survey

We examine the clustering properties of low-power radio galaxies at redshift 0.4 < z < 0.8, using data from the 2SLAQ Luminous Red Galaxy (LRG) survey, and find that radio-detected LRGs (with typical optical luminosities of 3–5L* and 1.4 GHz radio powers in the range 1024–1026W Hz−1) are significantly more clustered than a matched population of radio-quiet (≲1024W Hz−1) LRGs with the same distribution in optical luminosity and colour. The measured scalelength of the two-point cross-correlation function between the full LRG sample and the radio-detected LRGs is 9.57 ± 0.50 h−1Mpc, compared to 8.47 ± 0.27 h−1Mpc for the matched sample of radio-quiet LRGs; while the implied scalelength of the auto-correlation function, r0, is 12.3 ± 1.2 h−1Mpc and 9.02 ± 0.52 h−1Mpc for the radio-detected and radio-quiet samples, respectively. We further interpret our clustering measurements in the halo model framework and demonstrate that the radio-detected LRGs have typical halo masses of 10.1 ± 1.4 × 1013h−1M⊙ and bias of 2.96 ± 0.17, compared to 6.44 ± 0.32 × 1013h−1M⊙ and 2.49 ± 0.02 for the radio-quiet sample. A model in which the radio-detected LRGs are almost all central galaxies within haloes provides the best fit to the measured clustering, and we estimate that at least 30 per cent of all 2SLAQ LRGs with the same clustering amplitude as the radio-detected LRGs are currently radio loud. Our results imply that radio-detected galaxies in the 2SLAQ LRG sample typically occupy more massive haloes than other LRGS of the same optical luminosity, so the probability of finding a radio-loud active galactic nucleus (AGN) in a massive galaxy at z∼ 0.55 is influenced by the halo mass and/or cluster environment in addition to the well-known dependence on optical luminosity. If we model the radio-detected fraction of LRGs, Frad, as a function of halo mass M, then the data are well-fitted by a power law of the form Frad∝M0.65±0.23. The observed relationship between radio emission and clustering strength could plausibly arise either through a higher fuelling rate of gas on to the central black holes of galaxies in the most massive haloes (producing more powerful radio jets) or through the presence of a denser IGM (which would provide a more efficient working surface for the jets, thus boosting their observed radio luminosity). Further work is needed to determine which of these effects is dominant.

Environmental Effects on Real‐Space and Redshift‐Space Galaxy Clustering

Galaxy formation inside dark matter halos, as well as the formation of the halo itself, can be affected by the large-scale environment. Evaluating the imprint of environmental effects on galaxy clustering is crucial for construing precise cosmological constraints from galaxy redshift survey data. We investigate the environmental impact on both real-space and redshift-space galaxy clustering statistics using a semianalytic model (SAM) derived from the Millenium Simulation. We compare clustering statistics from original SAM galaxy samples to shuffled samples with the environmental influences on galaxy properties eliminated. Among the luminosity-threshold samples examined, the one with the lowest threshold luminosity (~0.2 -->L*) is the most affected by environmental effects, having a ~10% decrease in the real-space two-point correlation function (2PCF) after shuffling. By decomposing the 2PCF into five different components based on the source of pairs, we show that the change in the 2PCF can be explained by the age and richness (galaxy occupation number) dependence of halo clustering. The 2PCFs in redshift space are found to change in a similar manner after shuffling. If the environmental effects are neglected, halo occupation distribution modeling of the real-space and redshift-space clustering may have a less than 6.5% systematic uncertainty in constraining -->σ8Ωm0.6 from the most affected SAM sample, and substantially smaller uncertainties for the other, more luminous samples. We argue that the effect could be even smaller in reality. In the Appendix, we present a method to decompose the 2PCF, which can be applied to measure the two-point autocorrelation functions of galaxy subsamples in a volume-limited galaxy sample and their two-point cross-correlation functions in a single run using only one random catalog.

The optimal phase of the generalised Poincaré dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps

Several studies have proposed that the shape of the Universe may be a Poincare dodecahedral space (PDS) rather than an infinite, simply connected, flat space. Both models assume a close to flat FLRW metric of about 30% matter density. We study two predictions of the PDS model. (i) For the correct model, the spatial two-point cross-correlation function, $\ximc$, of temperature fluctuations in the covering space, where the two points in any pair are on different copies of the surface of last scattering (SLS), should be of a similar order of magnitude to the auto-correlation function, $\xisc$, on a single copy of the SLS. (ii) The optimal orientation and identified circle radius for a generalised PDS model of arbitrary twist $\phi$, found by maximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield $\phi \in \{\pm 36°\}$. We optimise the cross-correlation at scales < 4.0 h^-1 Gpc using a Markov chain Monte Carlo (MCMC) method over orientation, circle size and $\phi$. Both predictions were satisfied: (i) an optimal generalised PDS solution was found, with a strong cross-correlation between points which would be distant and only weakly correlated according to the simply connected hypothesis, for two different foreground-reduced versions of the WMAP 3-year all-sky map, both with and without the kp2 Galaxy mask: the face centres are $(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d, -4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has twist \phi= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of this occurring in the simply connected model, assuming a uniform distribution $\phi \in [0,2\pi]$, is about 6-9%.

Spatial clustering in the ESO-Sculptor survey: two-point correlation functions by galaxy type at redshifts 0.1–0.5

Context: Galaxy clustering shows segregation effects with galaxy type, color and luminosity, which bring clues on the relationship with the underlying density field. Aims: We explore these effects among the populations of giant and dwarf galaxies detected in the ESO-Sculptor survey. Methods: We calculate the spatial two-point auto and cross-correlation functions for the 765 galaxies with R_c≤ 21.5 and 0.1 ≤ z ≤ 0.51 and for subsets by spectral type and luminosity. Results: At separation of 0.3 h-1 Mpc, pairs of early-type galaxies dominate the clustering over all the other types of pairs. At intermediate scales, 0.3-5 h-1 Mpc, mixed pairs of dwarf and giant galaxies contribute equally as pairs of giant galaxies, whereas the latter dominate at ≃10 h-1 Mpc. Moreover, the correlation functions per galaxy type display the expected transition between the 1-halo and 2-halo regimes in the scenario of hierarchical merging of dark matter halos. The 1-halo component of the early-type galaxies largely outdoes that for the late spiral galaxies, and that for the dwarf galaxies is intermediate between both. In contrast, the 2-halo component of the early-type galaxies and late spiral galaxies are comparable, whereas that for the dwarf galaxies is consistent with null clustering. Conclusions: We link the clustering segregation of the early-type and late spiral galaxies to their spatial distribution within the underlying dark matter halos. The early-type galaxies are preferentially located near the centers of the most massive halos, whereas late spiral galaxies tend to occupy their outskirts or the centers of less massive halos. This appears to be independent of luminosity for the early-type galaxies, whereas faint late spiral galaxies might reside in less dense regions than their bright analogs. The present analysis also unveils unprecedented results on the contribution from dwarf galaxies: at the scale at which they significantly cluster inside the halos (≤0.3 h-1 Mpc), they are poorly mixed with the late spiral galaxies, and appear preferentially as satellites of early-type galaxies. Based on observations collected at the European Southern Observatory (ESO), La Silla, Chile. All appendices are only available in electronic form at http://www.aanda.org

Characterization of avalanche-like events in a confined plasma

One mechanism for transport of energy and particles in a plasma is by discrete, intermittent, uncorrelated events, often called avalanches. This paper reports observations and quantitative characterization of avalanche events in a magnetically confined plasma. The observations are primarily of electron temperature fluctuations. Avalanches are identified by their large spatial scale, up to the system size, by self-similar behavior in the frequency spectrum and the autocorrelation function and by propagation. The two-point cross-correlation function allows determination of a characteristic velocity, which typically varies from several hundred meters per second in the outer part of the plasma to zero or even inward near the axis. This can be interpreted as resulting from the prevalence of negative avalanches (i.e., holes) near the axis. The presence of a long-tailed probability distribution is indicated by a Hurst parameter (H) in the range 0.80 to 0.95, which becomes smaller in the outer quarter of the plasma radius. Density fluctuation spectra from the plasma core also show self-similar behavior. Power transport estimates show that about half of the heat flux is carried by the avalanche events under conditions with no magnetohydrodynamic activity. These observations are qualitatively similar to results of modeling calculations based on drift wave turbulence. It is reasonable to infer that avalanches are the macroscopic manifestation of turbulence which inherently has a small spatial scale and, thus, allow a local, gyro-Bohm scaling process to show global Bohm-type behavior.

PROPER ORTHOGONAL DECOMPOSITION OF TURBULENT FLOWS FOR AEROACOUSTIC AND HYDROACOUSTIC APPLICATIONS

This paper describes the use of proper orthogonal decomposition (POD) for problems in which sound radiation is caused by turbulent flow interacting with rigid surfaces. For a complete solution the statistics of the turbulent velocity fluctuations must be defined, and it is customary to base these on spectral analysis. This paper will describe how proper orthogonal modes provide a better approach than spectral analysis for inhomogeneous turbulent flows. One of the additional advantages of POD is that sound radiation problems may be analyzed in the time domain and this may prove useful in rotor noise applications where time-domain calculations are frequently used. For flows that are stationary in time or homogeneous in at least one direction, it will be shown that there are advantages in using a combination of POD and a linear stochastic estimator to describe the flow. This provides a decomposition of the two-point cross-correlation function of the turbulence that requires fewer modes than POD.

A comparison of the PSCz and Stromlo -- APM redshift surveys

We present a direct comparison of the clustering properties of two redshift surveys covering a common volume of space: the recently completed IRAS Point Source Catalogue redshift survey (PSCz) containing 14500 galaxies with a limiting flux of 0.6 Jy at 60 � m, and the optical Stromlo-APM survey containing 1787 galaxies in a region of 4300 deg 2 in the south Galactic cap. We use three methods to compare the clustering properties: the counts-in-cells comparison of Efstathiou (1995, hereafter E95), the two-point cross correlation function, and the Tegmark (1998) ‘null-buster’ test. We find that the Stromlo variances are systematically higher than those of PSCz, as expected due to the deficit of early-type galaxies in IRAS samples. However we find that the differences between the cell counts are consistent with a linear bias between the two surveys, with a relative bias parameter brel ≡ bStromlo/bPSCz ≈ 1.3 which appears approximately scale-independent. The correlation coefficientR between optical and IRAS densities on scales ∼ 20 h −1 Mpc is R ≥ 0.72 at 95% c.l., placing limits on types of ‘stochastic bias’ which affect optical and IRAS galaxies differently.

Reobservation of Close QSO Groups: The Size Evolution and Shape of Lyα Forest Absorbers

In order to study the size and shape of the absorbers that lie in front of the QSOs, in particular the Ly? forest, we present an analysis of 785 absorption lines in the spectra of five QSOs in close groupings: a pair (LB 9605: 1517+2357 at z = 1.834 and LB 9612: 1517+2356 at z = 1.903, with a separation of 102'' between them) and a triplet (KP 76: 1623+2651A at z = 2.467, KP 77: 1623+2653 at z = 2.526, and KP 78: 1623+2651B at z = 2.605, with separations of 127'', 147'', and 177'' between pairs 76:78, 76:77, and 77:78, respectively). Both of these QSO groups have been observed before, but these data represent a drastic increase in signal-to-noise ratio and/or wavelength coverage over earlier data and provide a qualitatively different view of the nature of the absorbers. The pair samples a scale critical in determining the size upper bound of Ly? absorbers, with significant leverage in redshift compared to previous studies. In the case of the triplet, this represents the spatially densest sample of Ly? forest absorbers ever studied and an almost ideally suited probe of the shape of absorbers. We observe a significant number of Ly? lines in common between the triplet sight lines, for lines stronger than rest equivalent width W0 > 0.4 ? (and no detected metal lines) and velocity differences up to 200 km s-1, corresponding to a two-point correlation function ?=1.88 -->+ 0.78?0.50 on scales of 0.5-0.8 h-1 Mpc with z = 2.14 and inconsistent at the 99.999% level with the absence of any clustering. These data also show that a significant fraction of the W0 > 0.4 ? Ly? forest absorbers spans all three sight lines to the KP triplet, indicating that the strong-lined absorbers are consistent with nearly round shapes, chosen from a range of possible cylinders of different elongations. This may be inconsistent with results from hydrodynamic/gravitational simulations of H I in the early Universe, indicating that the theoretical counterparts of Ly? forest clouds are long and filamentary. Furthermore, there is a probable correlation of W0 with ?v suggestive of the clouds being flattened and expanding with the Hubble flow in their long dimension, as would be indicative of sheets or filaments. This is supported by the uniformity of line strengths between the three sight lines for W0 > 0.4 ?. We conclude, tentatively, that the W0 > 0.4 ? Ly? forest objects are sheetlike. In contrast, the weaker lines, 0.2 ? > W0 > 0.4 ?, show no evidence of spanning the sight lines of these groups but have sizes significantly larger than the luminous portions of galaxies and C IV absorbers as revealed by closer separation QSO pairs. When the LB sight-line pair is included with other pairs at different redshifts and sight-line separations, one finds no strong evidence for evolution of Ly? absorber size with redshift. We also show that there is no evidence of large-scale structure in the Ly? forest consistent with ionization of H II by foreground QSOs as seen in the spectrum of background QSOs (the foreground proximity effect). Finally, we see a marginal detection of the sight-line two-point cross-correlation function for C IV lines ?=2.05 -->+ 1.82?1.21 over scales of 0.5-1 h-1 Mpc. This is significantly weaker than ? measured by autocorrelation along single sight lines for 200 km s-1 < ?v < 600 km s-1, suggesting that most of the latter signal may be due to the internal motions within absorbers that are smaller than 0.5 h-1 Mpc.

Fluctuation Properties of Precipitation. Part II: Reconsideration of the Meaning and Measurement of Raindrop Size Distributions

Abstract For M drop size categories, rain is frequently viewed simply as the superposition of M, statistically independent Poisson-distributed drop fluxes each described by its own mean concentration. Implicit in such a Poissonian model is the assumption of uncorrelated counts among the drops. However, it is well known that drop size distributions are the result of the processes of collision, coalescence, and breakup, which should lead to correlations. This inconsistency is resolved in this work. Using 1-min disdrometer measurements, two-point cross-correlation functions are used to show that drop counts at different sizes are correlated rather than independent. Moreover, it is argued that it is more appropriate to characterize rain statistically as a doubly stochastic Poisson process (Poisson mixture) among a collection of M correlated random variables (fluxes) each having its own probability distribution of unpredictable (random) mean values and its own coherence time, τM. It is also shown that a drop s...

The Dependence of Galaxy Clustering on Luminosity

We present statistical results of a two-point galaxy-galaxy cross-correlation function analysis. These studies use appropriate cuts in redshift and limiting apparent magnitude in the two catalogs explored and provide useful information about the dependence of galaxy luminosity on local density. We estimate projected two-point cross-correlation functions w(rp) for samples of center galaxies taken from the Las Campanas Redshift Survey with different mean luminosities against Edinburgh/Durham Southern Catalogue L L* galaxies. Power-law best fits for w(rp) with center galaxies L > L* and L < L* give spatial cross-correlation functions with parameters r0 5.5 ± 0.2 h-1 Mpc, γ 1.8 ± 0.2 and r0 3.5 ± 0.6 h-1 Mpc, γ 2.2 ± 0.2, respectively. Possible differences among results of studies of clustering dependence on luminosity reported in previous works might be dominated by systematics because of sample selection effects. Our analyses indicate that the statistical properties of the large-scale distribution of galaxies depend on intrinsic luminosity, arguing against a universal value of the correlation length. Our results suggest a continuous clustering dependence on absolute magnitude, giving support to previous indications that a smaller biasing factor corresponds to low-luminosity galaxies.

Detailed Analysis of the Cross‐Correlation Function between the X‐Ray Background and Foreground Galaxies

Recent ROSAT surveys suggest that galaxies constitute the new class of X-ray sources required to explain the full phenomenology of the cosmic X-Ray Background (XRB). To test this hypothesis, we compute the two-point cross-correlation function Wxg(theta) between 62 Einstein-IPC fields (.81-3.5 keV) and the APM Northern galaxy catalog (13.5<E<19.0). At zero-lag (theta=0), we detect a 3.5sigma correlation signal with an amplitude of Wxg(0)=.045+/-.013. At non-zero lag (theta>0), the angular dependence of Wxg has two main features: the main signal for theta<4', and an almost flat plateau with an amplitude of Wxg(theta>4')=.015, likely to result from the diffuse X-ray emission by clusters of galaxies. Taking the point-spread function of the X-ray instrument into account, we find that the mean X-ray flux of galaxies with <E>=17.5+/-.3 is (8.1+/-4.7) 10^(-16) ergs/cm^2/s. This agrees with the X-ray flux expected from earlier direct studies of brighter galaxies, which were shown to result in a total galaxy contribution to the XRB of about 13%. We discuss how this powerful cross-correlation method can be used to measure the flux of X-ray sources well below the detection limit of X-ray instruments, and, perhaps, to probe otherwise undetectable faint diffuse X-ray emission.

Stokes Parameters in Cosmic Microwave Background Measurements

We compute numerically the scalar- and tensor-mode induced Stokes parameters of the cosmic microwave background, by taking into account the basis rotation effects. It is found that the tensor contribution to the polarization power spectrum get enhanced and dominates over the scalar contribution for low multipoles in a universe with or without recombination. Furthermore, we show that all full-sky averaged two-point cross-correlation functions of the Stokes parameters vanish. We thus comment on the cross-correlation between the anisotropy and polarization of the CMB, and calculate the expected signal to noise ratio for the polarization experiment underway.

Statistical analysis of correlation between the positions of quasars and the uppsala galaxies

The question of the association of quasars with galaxies is re-examined using 785 quasars at | b| ⩾ 30, δ ⩾ − 02°30′ in the new Hewitt and Burbidge Catalog (1980) and all galaxies in the “Uppsala General Catalogue of Galaxies” (Nilson, 1973). The results of the two-point cross-correlation function are presented and they show that there are on the average 0.153 ± 0.011 more galaxies within 10'.0 of a QSO than would be expected if the QSOs were distributed randomly. We find the marginal significance of the tendency for correlation between QSOs and galaxies to increase with increasing redshifts z or apparent magnitudes V. The nearest neighbor test has also been taken to analyse the same data as well as get further evidence for the apparent association between QSOs and galaxies.