Power law correlations in galaxy distribution and finite volume effects from the Sloan Digital Sky Survey Data Release Four

We discuss the estimation of galaxy correlation properties in several volume limited samples, in different sky regions, obtained from the Fourth Data Release of the Sloan Digital Sky Survey. The small scale properties are characterized through the determination of the nearest neighbor probability distribution. By using a very conservative statistical analysis, in the range of scales [0.5,~30] Mpc/h we detect power-law correlations in the conditional density in redshift space, with an exponent \gamma=1.0 \pm 0.1. This behavior is stable in all different samples we considered thus it does not depend on galaxy luminosity. In the range of scales [~30,~100] Mpc/h we find evidences for systematic unaveraged fluctuations and we discuss in detail the problems induced by finite volume effects on the determination of the conditional density. We conclude that in such range of scales there is an evidence for a smaller power-law index of the conditional density. However we cannot distinguish between two possibilities: (i) that a crossover to homogeneity (corresponding to \gamma=0 in the conditional density) occurs before 100 Mpc/h, (ii) that correlations extend to scales of order 100 Mpc/h (with a smaller exponent 0 < \gamma <1). We emphasize that galaxy distributions in these samples present large fluctuations at the largest scales probed, corresponding to the presence of large scale structures extending up to the boundaries of the present survey. Finally we discuss several differences between the behavior of the conditional density in mock galaxy catalogs built from cosmological N-body simulations and real data. We discuss some theoretical implications of such a fact considering also the super-homogeneous features of primordial density fields.Comment: 13 pages, 19 figures, to be publsihed in Astronomy and Astrophysic

Halo Occupation Distribution Modeling of Clustering of Luminous Red Galaxies

We perform Halo Occupation Distribution (HOD) modeling to interpret small-scale and intermediate-scale clustering of 35,000 luminous early-type galaxies and their cross-correlation with a reference imaging sample of normal L* galaxies in the Sloan Digital Sky Survey. The modeling results show that most of these luminous red galaxies (LRGs) are central galaxies residing in massive halos of typical mass M ~ a few times 10^13 to 10^14 Msun/h, while a few percent of them have to be satellites within halos in order to produce the strong auto-correlations exhibited on smaller scales. The mean luminosity Lc of central LRGs increases with the host halo mass, with a rough scaling relation of Lc \propto M^0.5. The halo mass required to host on average one satellite LRG above a luminosity threshold is found to be about 10 times higher than that required to host a central LRG above the same threshold. We find that in massive halos the distribution of L* galaxies roughly follows that of the dark matter and their mean occupation number scales with halo mass as M^1.5. The HOD modeling results also allows for an intuitive understanding of the scale-dependent luminosity dependence of the cross-correlation between LRGs and L_* galaxies. Constraints on the LRG HOD provide tests to models of formation and evolution of massive galaxies, and they are also useful for cosmological parameter investigations. In one of the appendices, we provide LRG HOD parameters with dependence on cosmology inferred from modeling the two-point auto-correlation functions of LRGs.Comment: 21 pages, 10 figures, accepted for publication in Ap

Galaxy clustering and projected density profiles as traced by satellites in photometric surveys: Methodology and luminosity dependence

We develop a new method which measures the projected density distribution w_p(r_p)n of photometric galaxies surrounding a set of spectroscopically-identified galaxies, and simultaneously the projected correlation function w_p(r_p) between the two populations. In this method we are able to divide the photometric galaxies into subsamples in luminosity intervals when redshift information is unavailable, enabling us to measure w_p(r_p)n and w_p(r_p) as a function of not only the luminosity of the spectroscopic galaxy, but also that of the photometric galaxy. Extensive tests show that our method can measure w_p(r_p) in a statistically unbiased way. The accuracy of the measurement depends on the validity of the assumption in the method that the foreground/background galaxies are randomly distributed and thus uncorrelated with those galaxies of interest. Therefore, our method can be applied to the cases where foreground/background galaxies are distributed in large volumes, which is usually valid in real observations. We applied our method to data from SDSS including a sample of 10^5 LRGs at z~0.4 and a sample of about half a million galaxies at z~0.1, both of which are cross-correlated with a deep photometric sample drawn from the SDSS. On large scales, the relative bias factor of galaxies measured from w_p(r_p) at z~0.4 depends on luminosity in a manner similar to what is found at z~0.1, which are usually probed by autocorrelations of spectroscopic samples. On scales smaller than a few Mpc and at both z~0.4 and z~0.1, the photometric galaxies of different luminosities exhibit similar density profiles around spectroscopic galaxies at fixed luminosity and redshift. This provides clear support for the assumption commonly-adopted in HOD models that satellite galaxies of different luminosities are distributed in a similar way, following the dark matter distribution within their host halos.Comment: 38 pages, 12 figures, published in Ap

A Coarse-Grained Field Theory for Density Fluctuations and Correlation Functions of Galactic Objects

We present a coarse-grained field theory of density fluctuations for a Newtonian self-gravitating many-body system and apply it to a homogeneous Universe with small density fluctuations. The theory treats the clustering of galaxies and clusters in terms of the field of density fluctuations. The Jeans length $\lambda_0$, a unique physical scale for a gravitating system, appears naturally as the characteristic scale underlying the large scale structure. Under Gaussian approximation the analytic expressions of $\xi(r)$ and $P(k)$ are obtained. The correlation amplitude is proportional to the galactic mass, and is oscillating over large scales $\sim 100$ $h^{-1}$ Mpc and damped to zero. The spectrum amplitude is inversely proportional to the galactic number density.The preliminary results qualitatively explain some pronounced features of large scale structures.Comment: 7 pages, 4 figures. to appear in A&

Systematic Effects on Determination of the Growth Factor from Redshift-space Distortions

The linear growth factor of density perturbations is believed to be a powerful observable of future redshift surveys to probe physical properties of dark energy and to distinguish among gravity theories. We investigate systematic effects on determination of the growth factor f from a measurement of redshift-space distortions. Using N-body simulations we identify dark matter halos over a broad mass range. We compute the power spectra and correlation functions for the halos and then examine how well the redshift distortion parameter beta=f/b can be reconstructed as a function of halo mass. We find that beta measured for a fixed halo mass is generally a function of scale even on large scales, in contrast with the common expectation that beta approaches a constant described by Kaiser's formula on such scales. The scale dependence depends on the halo mass, being stronger for smaller halos. It also cannot be easily explained with the well-known distribution function of the halo peculiar velocities. We demonstrate that the biasing for smaller halos has larger nonlinearity and stochasticity, thus the linear bias assumption becomes worse for smaller halos. Only for massive halos with b>1.5, beta approaches the linear theory prediction on scales of r or pi/k>30Mpc/h. Luminous red galaxies (LRG), targeted by the SDSS-III's BOSS survey, tend to reside in very massive halos. Our results indicate that if the LRG is used for the measurement of redshift distortions, f can be measured unbiasedly. On the other hand, if one considers to use emission line galaxies, which are targeted by the BigBOSS survey and inhabited in halos of a broad mass range, the scale dependence of beta must be taken into account carefully; otherwise one might give incorrect constraints on dark energy or modified gravity theories. We also find that beta reconstructed in Fourier space behaves better than that in configuration space.Comment: 12 pages, 9 figures, submitted to ApJ, revised according to referee repor

Determine the galaxy bias factors on large scales using bispectrum method

We study whether the bias factors of galaxies can be unbiasedly recovered from their power spectra and bispectra. We use a set of numerical N-body simulations and construct large mock galaxy catalogs based upon the semi-analytical model of Croton et al. (2006). We measure the reduced bispectra for galaxies of different luminosity, and determine the linear and first nonlinear bias factors from their bispectra. We find that on large scales down to that of the wavenumber k=0.1h/Mpc, the bias factors b1 and b2 are nearly constant, and b1 obtained with the bispectrum method agrees very well with the expected value. The nonlinear bias factor b2 is negative, except for the most luminous galaxies with M<-23 which have a positive b2. The behavior of b2 of galaxies is consistent with the b2 mass dependence of their host halos. We show that it is essential to have an accurate estimation of the dark matter bispectrum in order to have an unbiased measurement of b1 and b2. We also test the analytical approach of incorporating halo occupation distribution to model the galaxy power spectrum and bispectrum. The halo model predictions do not fit the simulation results well on the precision requirement of current cosmological studies.Comment: 9 pages, 8 figures, accepted for publication in Ap

Understanding the PSCz Galaxy Power Spectrum with N-body Simulations

By comparing the PSCz galaxy power spectrum with the results of nested pure dark matter N-body simulations, we try to understand how infrared-selected galaxies populate dark-matter haloes, paying special attention to the method of halo identification in the simulations. We thus test the hypothesis that baryonic physics negligibly affects the distribution of galaxies down to the smallest scales yet observed. We are successful in reproducing the PSCz power spectrum on scales < ~40 h/Mpc, near our resolution limit, by imposing a central density cut-off on simulated haloes, which gives a rough minimum mass and circular velocity of haloes in which PSCz galaxies formed.Comment: 12 pages, 16 figures (one added), conforms to version in MNRA

Absence of anti-correlations and of baryon acoustic oscillations in the galaxy correlation function from the Sloan Digital Sky Survey DR7

One of the most striking features predicted by standard models of galaxy formation is the presence of anti-correlations in the matter distribution at large enough scales (r>r_c). Simple arguments show that the location of the length-scale r_c, marking the transition from positive to negative correlations, is the same for any class of objects as for the full matter distribution, i.e. it is invariant under biasing. This scale is predicted by models to be at about the same distance of the scale signaling the baryonic acoustic oscillation scale r_{bao}. We test these predictions in the newest SDSS galaxy samples.We find that, in several MG samples, the correlation function remains positive at scales >250 Mpc/h, while in the concordance LCDM it should be negative beyond r_c\approx 120 Mpc/h. In other samples the correlation function becomes negative at scales <50 Mpc/h. To investigate the origin of these differences we consider in detail the propagation of errors on the sample density into the estimation of the correlation function. We conclude that these are important at large enough separations, and that they are responsible for the observed differences between different estimators and for the measured sample to sample variations of the correlation function. We conclude that, in the newest SDSS samples, the large scale behavior of the galaxy correlation function is affected by intrinsic errors andv olume-dependent systematic effects which make the detection of correlations to be only an estimate of a lower limit of their amplitude, spatial extension and statistical errors. We point out that these results represent an important challenge to LCDM models as they largely differ from its predictions.(Abridged version).Comment: Version accepted for publication in Astronomy and Astrophysics; 10 pages, 13 .eps figures. Substantial changes with respect to version v1, more detailed explanations of the methods and results. Main results are unchanged. Version v3 with few typos correcte

Scale Dependence of Dark Energy Antigravity

We investigate the effects of negative pressure induced by dark energy (cosmological constant or quintessence) on the dynamics at various astrophysical scales. Negative pressure induces a repulsive term (antigravity) in Newton's law which dominates on large scales. Assuming a value of the cosmological constant consistent with the recent SnIa data we determine the critical scale $r_c$ beyond which antigravity dominates the dynamics ($r_c \sim 1Mpc$) and discuss some of the dynamical effects implied. We show that dynamically induced mass estimates on the scale of the Local Group and beyond are significantly modified due to negative pressure. We also briefly discuss possible dynamical tests (eg effects on local Hubble flow) that can be applied on relatively small scales (a few $Mpc$) to determine the density and equation of state of dark energy.Comment: Contributed talk at the 2nd Hellenic Cosmology Workshop at NOA (Athens) Jan. 2001.To appear in the proceedings. Based on work done in collaboration with M. Axenides and E. Florato

A galaxy-halo model of large-scale structure

We present a new, galaxy-halo model of large-scale structure, in which the galaxies entering a given sample are the fundamental objects. Haloes attach to galaxies, in contrast to the standard halo model, in which galaxies attach to haloes. The galaxy-halo model pertains mainly to the relationships between the power spectra of galaxies and mass, and their cross-power spectrum. With surprisingly little input, an intuition-aiding approximation to the galaxy-matter cross-correlation coefficient R(k) emerges, in terms of the halo mass dispersion. This approximation seems valid to mildly non-linear scales (k < ~3 h/Mpc), allowing measurement of the bias and the matter power spectrum from measurements of the galaxy and galaxy-matter power spectra (or correlation functions). This is especially relevant given the recent advances in precision in measurements of the galaxy-matter correlation function from weak gravitational lensing. The galaxy-halo model also addresses the issue of interpreting the galaxy-matter correlation function as an average halo density profile, and provides a simple description of galaxy bias as a function of scale.Comment: 13 pages, 9 figures, submitted to MNRAS. Minor changes, suggested by refere