Galaxy Two-point Correlation Function Research Articles

Towards a concordant model of halo occupation statistics

We use the conditional luminosity function (CLF) and data from the 2-degree Field Galaxy Redshift survey (2dFGRS) to constrain the average relation between light and mass in a Lambda cold dark matter (Lambda CDM) cosmology with Omega(m) = 0.23 and sigma(8) = 0.74 (hereafter WMAP3 cosmology). Reproducing the observed luminosity dependence of the galaxy two-point correlation function results in average mass-to-light ratios that are similar to 35 percent lower than those in a Lambda CDM cosmology with Omega(m), = 0.3 and sigma(8) = 0.9 (hereafter WMAP1 cosmology). This removes an important problem with previous halo occupation models which had a tendency to predict cluster mass-to-light ratios that were too high. For the WMAP3 cosmology, our model yields average mass-to-light ratios, central galaxy luminosities, halo occupation numbers, satellite fractions and luminosity-gap statistics, that are all in excellent agreement with those obtained from a 2dFGRS group catalogue and from other independent studies. We also use our CLF model to compute the probability distribution P(M vertical bar L-cen), that a central galaxy of luminosity L-cen resides in a halo of mass M. We find this distribution to be much broader than what is typically assumed in halo occupation distribution models, which has important implications for the interpretation of satellite kinematics and galaxy-galaxy lensing data. Finally, reproducing the luminosity dependence of the pairwise peculiar velocity dispersions in the 2dFGRS requires relatively low mass-to-light ratios for clusters and a satellite fraction that decreases strongly with increasing luminosity. This is only marginally consistent with the constraints obtained from the luminosity dependence of the galaxy two-point correlation function. We argue that a cosmology with parameters between those of the WMAP1 and WMAP3 cosmologies is likely to yield results with a higher level of consistency.

Modeling Luminosity‐dependent Galaxy Clustering through Cosmic Time

We employ high-resolution dissipationless simulations of the concordance LCDM cosmology to model the observed luminosity dependence and evolution of galaxy clustering through most of the age of the universe, from z~5 to z~0. We use a simple, non-parametric model which monotonically relates galaxy luminosities to the maximum circular velocity of dark matter halos (V_max) by preserving the observed galaxy luminosity function in order to match the halos in simulations with observed galaxies. The novel feature of the model is the use of the maximum circular velocity at the time of accretion, V_max,acc, for subhalos, the halos located within virial regions of larger halos. We argue that for subhalos in dissipationless simulations, V_max,acc reflects the luminosity and stellar mass of the associated galaxies better than the circular velocity at the epoch of observation, V_max,now. The simulations and our model L-V_max relation predict the shape, amplitude, and luminosity dependence of the two-point correlation function in excellent agreement with the observed galaxy clustering in the SDSS data at z~0 and in the DEEP2 samples at z~1 over the entire probed range of projected separations, 0.1<r_p/(Mpc/h)<10.0. In particular, the small-scale upturn of the correlation function from the power-law form in the SDSS and DEEP2 luminosity-selected samples is reproduced very well. At z~3-5, our predictions also match the observed shape and amplitude of the angular two-point correlation function of Lyman-break galaxies (LBGs) on both large and small scales, including the small-scale upturn.

The VIMOS-VLT Deep Survey

We investigate the dependence of galaxy clustering on the galaxy intrinsic luminosity at high redshift, using the data from the First Epoch VIMOS-VLT Deep Survey (VVDS). The size (6530 galaxies) and depth (I_{AB}<24) of the survey allows us to measure the projected two-point correlation function of galaxies, w_p(r_p) for a set of volume-limited samples up to an effective redshift =0.9 and median absolute magnitude -19.6< M_B < -21.3. Fitting w_p(r_p) with a single power-law model for the real-space correlation function xi(r)=(r/r_0)^{-gamma}, we measure the relationship of the correlation length r_0 and the slope gamma with the sample median luminosity for the first time at such high redshift. Values from our lower-redshift samples (0.1

Redshift-space distortions with the halo occupation distribution - II. Analytic model

We present an analytic model for the galaxy two-point correlation function in redshift space. The cosmological parameters of the model are the matter density Ω m , power spectrum normalization σ 8 , and velocity bias of galaxies α v , circumventing the linear theory distortion parameter β and eliminating nuisance parameters for non-linearities. The mode] is constructed within the framework of the halo occupation distribution (HOD), which quantifies galaxy bias on linear and non-linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain Ω m , σ 8 and α v in models that are constructed to have the same value of β at large scales as well as the same finger-of-god distortions at small scales.

The Feasibility of Constraining Dark Energy Using LAMOST Redshift Survey

We consider using future redshift surveys with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) to constrain the equation of state of dark energy ω. We analyze the Alcock & Paczynski (AP) effect imprinted on the two-point correlation function of galaxies in redshift space. The Fisher matrix analysis is applied to estimate the expected error bounds of ω0 and ωa from galaxy redshift surveys, ω0 and ωa being the two parameters in the equation of state parametrization ω(z) = ω0+ωaz/(1+z). Strong degeneracies between ω0 and ωa are found. The direction of the degeneracy in ω0−ωa plane, however, rotates counter-clockwise as the redshift increases. LAMOST can potentially contribute in the redshift range up to 0.5. In combination with other high redshift surveys, such as the proposed Kilo-Aperture Optical Spectrograph project (KAOS), the joint constraint derived from galaxy surveys at different redshift ranges is likely to efficiently break the degeneracy of ω0 and ωa. We do not anticipate that the nature of dark energy can be well constrained with LAMOST alone, but it may help to reduce the error bounds expected from other observations, such as the Supernova/Acceleration Probe (SNAP).

The Luminosity and Color Dependence of the Galaxy Correlation Function

We study the luminosity and color dependence of the galaxy two-point correlation function in the Sloan Digital Sky Survey, starting from a sample of ~200,000 galaxies over 2500 deg2. We concentrate our analysis on volume-limited subsamples of specified luminosity ranges, for which we measure the projected correlation function wp(rp), which is directly related to the real-space correlation function ξ(r). The amplitude of wp(rp) rises continuously with luminosity from Mr ≈ -17.5 to Mr ≈ -22.5, with the most rapid increase occurring above the characteristic luminosity L* (Mr ≈ -20.5). Over the scales 0.1 h-1 Mpc < rp < 10 h-1 Mpc, the measurements for samples with Mr > -22 can be approximated, imperfectly, by power-law three-dimensional correlation functions ξ(r) = (r/r0)-γ with γ ≈ 1.8 and r0(L*) ≈ 5.0 h-1 Mpc. The brightest subsample, -23 < Mr < -22, has a significantly steeper ξ(r). When we divide samples by color, redder galaxies exhibit a higher amplitude and steeper correlation function at all luminosities. The correlation amplitude of blue galaxies increases continuously with luminosity, but the luminosity dependence for red galaxies is less regular, with bright red galaxies exhibiting the strongest clustering at large scales and faint red galaxies exhibiting the strongest clustering at small scales. We interpret these results using halo occupation distribution (HOD) models assuming concordance cosmological parameters. For most samples, an HOD model with two adjustable parameters fits the wp(rp) data better than a power law, explaining inflections at rp ~ 1-3 h-1 Mpc as the transition between the one-halo and two-halo regimes of ξ(r). The implied minimum mass for a halo hosting a central galaxy more luminous than L grows steadily, with Mmin ∝ L at low luminosities and a steeper dependence above L*. The mass at which a halo has, on average, one satellite galaxy brighter than L is M1 ≈ 23Mmin(L), at all luminosities. These results imply a conditional luminosity function (at fixed halo mass) in which central galaxies lie far above a Schechter function extrapolation of the satellite population. The HOD model fits nicely explain the color dependence of wp(rp) and the cross correlation between red and blue galaxies. For galaxies with Mr < -21, halos slightly above Mmin have blue central galaxies, while more massive halos have red central galaxies and predominantly red satellite populations. The fraction of blue central galaxies increases steadily with decreasing luminosity and host halo mass. The strong clustering of faint red galaxies follows from the fact that nearly all of them are satellite systems in high-mass halos. The HOD fitting results are in good qualitative agreement with the predictions of numerical and semianalytic models of galaxy formation.

Modelling non-linear effects in the redshift space two-point correlation function and its implications for the pairwise velocity dispersion

The anisotropies in the galaxy two-point correlation function measured from redshift survey exhibits deviations from the predictions of the linear theory of redshift space distortion on scales as large as 20 h -1 Mpc where we expect linear theory to hold in real space. Any attempt at analysing the anisotropies in the redshift correlation function and determining the linear distortion parameter β requires these deviations to be correctly modelled and taken into account. These deviations are usually attributed to galaxy random motions and these are incorporated in the analysis through a phenomenological model in which the linear redshift correlation is convolved with the random pairwise velocity distribution function along the line of sight. We show that a substantial fraction of the deviations arise from non-linear effects in the mapping from real to redshift space caused by the coherent flows. Models that incorporate this effect provide as good a fit to N-body results as the phenomenological model which only includes the effect of random motions. We find that the pairwise velocity dispersions predicted by all of the models that we have considered are in excess of the values determined directly from the N-body simulations. This indicates a shortcoming in our understanding of the statistical properties of peculiar velocities and their relation to redshift distortion.

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.

Large-scale magnetic fields: galaxy two-point correlation function

We study the effect of large scale tangled magnetic fields on the galaxy two-point correlation function in the redshift space. We show that (a) the magnetic field effects can be comparable the gravity-induced clustering for present magnetic field strength $B_0 \simeq 5 \times 10^{-8}$ G, (b) the absence of this signal from the present data gives an upper bound $B_0 \la 3 \times 10^{-8}$ G, (c) the future data can probe the magnetic fields of $\simeq 10^{-8}$ G. A comparison with other constraints on the present magnetic field shows that they are marginally compatible.However if the magenetic fields corresponding to $B_0 \simeq 10^{-8}$ G existed at the last scattering surface they will cause unacceptably large CMBR anisotropies.

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.

The 2dF Galaxy Redshift Survey: luminosity dependence of galaxy clustering

We investigate the dependence of the strength of galaxy clustering on intrinsic luminosity using the Anglo-Australian two degree field galaxy redshift survey (2dFGRS). The 2dFGRS is over an order of magnitude larger than previous redshift surveys used to address this issue. We measure the projected two-point correlation function of galaxies in a series of volume-limited samples. The projected correlation function is free from any distortion of the clustering pattern induced by peculiar motions and is well described by a power-law in pair separation over the range 0.1 < r /h Mpc < 10. The clustering of L* galaxies in real space is well fit by a correlation length r0 = 4.9 +/- 0.3 /h Mpc and power-law slope gamma = 1.71 +/- 0.06. The clustering amplitude increases slowly with absolute magnitude for galaxies fainter than M*, but rises more strongly at higher luminosities. At low luminosities, our results agree with measurements from the SSRS2 by Benoist et al. However, we find a weaker dependence of clustering strength on luminosity at the highest luminosities. The correlation function amplitude increases by a factor of 4.0 between $M_{b_{J}} -5\log_{10}h = -18$ and -22.5, and the most luminous galaxies are 3.0 times more strongly clustered than L* galaxies. The power-law slope of the correlation function shows remarkably little variation for samples spanning a factor of 20 in luminosity. Our measurements are in very good agreement with the predictions of the hierarchical galaxy formation models of Benson et al.

Galaxy Clustering Evolution in the CNOC2 High‐Luminosity Sample

The redshift evolution of the galaxy two-point correlation function is a fundamental cosmological statistic. To identify similar galaxy populations at different redshifts, we select a strict volume-limited sample culled from the 6100 cataloged Canadian Network for Observational Cosmology field galaxy redshift survey (CNOC2) galaxies. Our high-luminosity subsample selects galaxies having k-corrected and evolution-compensated R luminosities, M, above -20 mag (H0 = 100 km s-1 Mpc-1 ), where M(R) -20.3 mag. This subsample contains about 2300 galaxies distributed between redshifts 0.1 and 0.65 spread over a total of 1.55 deg2 of sky. A similarly defined low-redshift sample is drawn from the Las Campanas Redshift Survey. We find that the comoving two-point correlation function can be described as ξ(r|z) = (r00/r)γ(1 + z)-(3+-γ), with r00 = 5.03 ± 0.08 h-1 Mpc, = -0.17 ± 0.18, and γ = 1.87 ± 0.07 over the z = 0.03-0.65 redshift range, for ΩM = 0.2 and Λ = 0. The measured clustering amplitude and its evolution are dependent on the adopted cosmology. The measured evolution rates for ΩM = 1 and flat ΩM = 0.2 background cosmologies are = 0.80 ± 0.22 and = -0.81 ± 0.19, respectively, with r00 = 5.30 ± 0.1 and 4.85 ± 0.1 h-1 Mpc, respectively. The sensitivity of the derived correlations to the evolution corrections and details of the measurements is presented. The analytic prediction of biased clustering evolution for only the low-density, ΛCDM cosmology is readily consistent with the observations, with biased clustering in an open cosmology somewhat marginally excluded and a biased ΩM = 1 model predicting clustering evolution that is more than 6 standard deviations from the measured value.

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:

A Database ofCOBE‐normalized Cold Dark Matter Simulations

We have simulated the formation and evolution of large-scale structure in the universe, for 68 different COBE-normalized cosmological models. For each cosmological model, we have performed between one and three simulations, for a total of 160 simulations. This constitutes the largest database of cosmological simulations ever assembled, and the largest cosmological parameter space ever covered by such simulations. We are making this database available to the astronomical community. We provide instructions for accessing the database and for converting the data from computational units to physical units. The database includes tilted cold dark matter (TCDM) models, tilted open cold dark matter (TOCDM) models, and tilted Λ cold dark matter (TΛCDM) models. (For several simulations, the primordial exponent n of the power spectrum is near unity, hence these simulations can be considered as untilted.) The simulations cover a four-dimensional cosmological parameter phase space, the parameters being the present density parameter Ω0, cosmological constant λ0, and Hubble constant H0, and the rms density fluctuation σ8 at scale 8 h-1 Mpc. All simulations were performed using a P3M algorithm with 643 particles on a 1283 mesh, in a cubic volume of comoving size 128 Mpc. Each simulation starts at a redshift of 24 and is carried up to the present. More simulations will be added to the database in the future. We have performed a limited amount of data reduction and analysis of the final states of the simulations. We computed the rms density fluctuation, the two-point correlation function, the velocity moments, and the properties of clusters. Our results are the following: 1. The numerical value σ of the rms density fluctuation differs from the value σ obtained by integrating the power spectrum at early times and extrapolating linearly up the present. This results from the combined effects of discreteness in the numerical representation of the power spectrum, the presence of a Gaussian factor in the initial conditions, and late-time nonlinear evolution. The first of these three effects is negligible. The second and third are comparable, and can both modify the value of σ8 by up to 10%. Nonlinear effects, however, are important only for models with σ8 > 0.6, and can result in either an increase or a decrease in σ8. 2. The observed galaxy two-point correlation function is well reproduced (assuming an unbiased relation between galaxies and mass) by models with σ8 ~ 0.8, nearly independently of the values of the other parameters, Ω0, λ0, and H0. For models with σ8 > 0.8, the correlation function is too large and its slope is too steep. For models with σ8 0.9, it has a U shape, which is probably a numerical artifact caused by the finite number of particles used in the simulations. For all models, clusters have densities in the range 100-1000 times the mean background density, the spin parameters λ are in the range 0.008-0.2, with the median near 0.05, and about of the clusters are prolate. Rotationally supported disks do not form in these simulations.

A Simulation of Galaxy Formation and Clustering

We discuss early results from the first N-body/hydrodynamical simulation to resolve the formation of galaxies in a volume large enough for their clustering properties to be reliably determined. The simulation follows the formation of galaxies by gas cooling within dark halos of mass a few times 1011 M☉ and above, in a flat cold dark matter universe with a positive cosmological constant. Over 2200 galaxies form in our simulated volume of (100 Mpc)3. Assigning luminosities to the model galaxies using a spectral population synthesis model results in a K-band luminosity function in excellent agreement with observations. The two-point correlation function of galaxies in the simulation evolves very little since z = 3, and it has a shape close to a power law over 4 orders of magnitude in amplitude. At the present day, the galaxy correlation function in the simulation is antibiased relative to the mass on small scales and unbiased on large scales. It provides a reasonable match to observations.

Cosmological Redshift Distortion: Deceleration, Bias, and Density Parameters from Future Redshift Surveys of Galaxies

The observed two-point correlation functions of galaxies in redshift space become anisotropic because of the geometry of the universe, as well as because of the presence of the peculiar velocity field. On the basis of linear perturbation theory, we expand the induced anisotropies of the correlation functions with respect to the redshift z and obtain analytic formulae to infer the deceleration parameter q0, the density parameter Ω0, and the derivative of the bias parameter d ln b/dz at z = 0 in terms of the observable statistical quantities. The present method does not require any assumption of the shape and amplitude of the underlying fluctuation spectrum and thus can be applied to future redshift surveys of galaxies, including the Sloan Digital Sky Survey. We also evaluate quantitatively the systematic error in estimating the value of β0 ≡ Ω00.6/b from a galaxy redshift survey on the basis of a conventional estimator for β0, which neglects both the geometrical distortion effect and the time evolution of the parameter β(z). If the magnitude limit of the survey is as faint as 18.5 (in B band) as in the case of the Sloan Digital Sky Survey, the systematic error ranges between -20% and 10% depending on the cosmological parameters. Although such systematic errors are smaller than the statistical errors in the current surveys, they will definitely dominate the expected statistical error for future surveys.

Spatial Correlation Function and Pairwise Velocity Dispersion of Galaxies: Cold Dark Matter Models versus the Las Campanas Survey

We show, with the help of large N-body simulations, that both the real-space two-point correlation function and pairwise velocity dispersion of galaxies can be measured reliably from the Las Campanas Redshift Survey. The real-space correlation function is well fitted by the power law ξ(r) = (r0/r)γ with r0 = (5.06 ± 0.12) h-1 Mpc and γ = 1.862 ± 0.034, and the pairwise velocity dispersion at 1 h-1 Mpc is 570 ± 80 km s-1. A detailed comparison between these observational results and the predictions of current cold dark matter (CDM) cosmogonies is carried out. We construct 60 mock samples for each theoretical model from a large set of high-resolution N-body simulations, which allows us to include various observational selection effects in the analyses and to use exactly the same methods for both real and theoretical samples. We demonstrate that such a procedure is essential in the comparison between models and observations. The observed two-point correlation function is significantly flatter than the mass correlation function in current CDM models on scales 1 h-1 Mpc. The observed pairwise velocity dispersion is also lower than that of dark matter particles in these models. We propose a simple antibias model to explain these discrepancies. This model assumes that the number of galaxies per unit dark matter mass, N/M, decreases with the mass of dark haloes. The predictions of CDM models with σ8 Ω0.60~0.4-0.5 and Γ ~ 0.2 are in agreement with the observational results, if the trend of N/M with M is at the level already observed for rich clusters of galaxies. Thus CDM models with Γ ~ 0.2 and with cluster-abundance normalization are consistent with the observed correlation function and pairwise velocity dispersion of galaxies. A high level of velocity bias is not required in these models.

The Ω0Dependence of the Evolution of ξ(r)

The evolution of the two-point correlation function, ξ(r, z), and the pairwise velocity dispersion, σ(r, z), for both the matter, ξρρ, and halo population, ξhh, in three different cosmological models, (Ω0, λ0) = (1, 0), (0.2, 0), and (0.2, 0.8), are described. If the evolution of ξ is parameterized by ξ(r, z) = (1 + z)-(3+)ξ(r, 0), where ξ(r, 0) = (r/r0)-γ, then ρρ ranges from 1.04 ± 0.09 for (1, 0) and 0.18 ± 0.12 for (0.2, 0), as measured by the evolution of ξρρ at 1 Mpc (from z ~ 5 to the present epoch). For halos, depends indeed on their mean overdensity. Halos with a mean overdensity of ~2000 were used to compute the halo two-point correlation function, ξhh, tested with two different group-finding algorithms: the friends of friends algorithm and the spherical overdensity algorithm. It is certainly believed that the rate of growth of this ξhh will give a good estimate of the evolution of the galaxy two-point correlation function, at least from z ~ 1 to the present epoch. The values we get for hh range from 1.54 for (1, 0) to -0.36 for (0.2, 0), as measured by the evolution of ξhh from z ~ 1.0 to the present epoch. These values could be used to constrain the cosmological scenario.

Light Propagation in Inhomogeneous Universes. I. Methodology and Preliminary Results

We describe a numerical algorithm that simulates the propagation of light in inhomogeneous universes. This algorithm computes the trajectories of light rays between the observer, located at redshift z = 0, and distant sources located at high redshift using the multiple lens plane method. The deformation and deflection of light beams as they interact with each lens plane are computed using the filled-beam approximation. We use a particle-particle/particle-mesh (P3M) N-body numerical code to simulate the formation of large-scale structure in the universe. We extend the length resolution of the simulations to submegaparsec scales by using a Monte Carlo method for locating galaxies inside the computational volume according to the underlying distribution of background matter. The observed galaxy two-point correlation function is reproduced. This algorithm constitutes a major improvement over previous methods, which either neglected the presence of large-scale structure, neglected the presence of galaxies, neglected the contribution of distant matter (matter located far from the beam), or used the Zeldovich approximation for simulating the formation of large-scale structure. In addition, we take into account the observed morphology-density relation when assigning morphological types to galaxies, something that was ignored in all previous studies. To test this algorithm, we perform 1981 simulations for three different cosmological models: an Einstein-de Sitter model with density parameter Ω0 = 1, an open model with Ω0 = 0.2, and a flat, low-density model with Ω0 = 0.2 and a cosmological constant of λ0 = 0.8. In all models, the initial density fluctuations correspond to a cold dark matter power spectrum normalized to COBE. In each simulation, we compute the shear and magnification resulting from the presence of inhomogeneities. Our results are the following: (1) The magnification is totally dominated by the convergence, with the shear contributing less than one part in 104. (2) Most of the cumulative shear and magnification is contributed by matter located at intermediate redshifts, z = 1-2. (3) The actual value of the redshift at which the largest contribution to shear and magnification occurs depends on the cosmological model. In particular, the lens planes contributing the most are located at larger redshift for models with smaller Ω0. (4) The number of galaxies directly hit by the beam increases with redshift, while the contribution of lens planes to the shear and magnification decrease with increasing lens plane redshift for z > 2, which indicates that the bulk of the shear and magnification does not originate from direct hits, but rather from the tidal influence of nearby and more distant galaxies and background matter. (5) The average contributions of background matter and nearby galaxies to the shear is comparable for models with small Ω0. For the Einstein-de Sitter model, the contribution of the background matter exceeds the contribution of nearby galaxies by nearly 1 order of magnitude.

Galaxy counts and the galaxy two-point angular correlation function to I=23

We present new results on the two-point angular correlation function of galaxies. The results have been determined from two large-format CCD surveys, covering 13 deg2 in total. At all magnitudes the two-point correlation function is well described by a power law with an index, J, equal to - 0.8. The amplitude of the correlation function decreases with increasing magnitude; however, the precise behaviour is not reproduced in models that include reasonable amounts of clustering evolution. We also present new data on the I-band galaxy number counts. A model that fits the count data well is a model that has a cosmological constant and a local galaxy number density equal to 1.76 x 1O-2(Ho/100)3 Mpc-3 •