Biasing and High‐Order Statistics from the Southern‐Sky Redshift Survey (original) (raw)
Related papers
Biasing and high-order statistics from the SSRS2
arXiv (Cornell University), 1998
We analyze different volume-limited samples extracted from the Southern Sky Redshift Survey (SSRS2), using counts-in-cells to compute the Count Probability Distribution Function (CPDF).From the CPDF we derive volumeaveraged correlation functions to fourth order and the normalized skewness and kurtosis S 3 =ξ 3 /ξ 2 2 and S 4 =ξ 4 /ξ 2 3. We find that the data satisfies the hierarchical relations in the range 0.3 < ∼ξ 2 < ∼ 10. In this range, we find S 3 to be scale-independent with a value of ∼ 1.8, in good agreement with the values measured from other optical redshift surveys probing different volumes, but significantly smaller than that inferred from the APM angular catalog. In addition, the measured values of S 3 do not show a significant dependence on the luminosity of the galaxies considered. This result is supported by several tests of systematic errors that could affect our measures and estimates of the cosmic variance determined from mock catalogs extracted from N-body simulations. This result is in marked contrast to what would be expected from the strong dependence of the two-point correlation function on luminosity in the framework of a linear biasing model. We discuss the implications of our results and compare them to some recent models of the galaxy distribution which address the problem of bias.
Monthly Notices of the Royal Astronomical Society, 2005
We present an analysis of the relative bias between early-and late-type galaxies in the Two-degree Field Galaxy Redshift Survey (2dFGRS) -as defined by the η parameter of , which quantifies the spectral type of galaxies in the survey. Our analysis examines the joint counts in cells between early-and late-type galaxies, using approximately cubical cells with sides ranging from 7h −1 Mpc to 42h −1 Mpc. We measure the variance of the counts in cells using the method of Efstathiou et al. (1990), which we find requires a correction for a finite volume effect equivalent to the integral constraint bias of the autocorrelation function. Using a maximum likelihood technique we fit lognormal models to the one-point density distribution, and develop methods of dealing with biases in the recovered variances resulting from this technique. We use a modified χ 2 technique to determine to what extent the relative bias is consistent with a simple linear bias relation; this analysis results in a significant detection of nonlinearity/stochasticity even on large scales. We directly fit deterministic models for the joint density distribution function, f (δ E , δ L ), to the joint counts in cells using a maximum likelihood technique. Our results are consistent with a scale invariant relative bias factor on all scales studied. Linear bias is ruled out on scales less than ℓ = 28h −1 Mpc. A power-law bias model is a significantly better fit to the data on all but the largest scales studied; the relative goodness of fit of this model as compared to that of the linear bias model suggests that any nonlinearity is negligible for ℓ 40h −1 Mpc, consistent with the expectation from theory that the bias should become linear on large scales.
Monthly Notices of the Royal Astronomical Society, 2005
We present new results for the 3-point correlation function, ζ, measured as a function of scale, luminosity and colour from the final version of the two-degree field galaxy redshift survey (2dFGRS). The reduced three point correlation function, Q 3 ∼ ζ/ξ 2 , is estimated for different triangle shapes and sizes, employing a full covariance analysis. The form of Q 3 is consistent with the expectations for the Λ-cold dark matter model, confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on Gaussian primordial fluctuations. However, we find a clear offset in amplitude between Q 3 for galaxies and the predictions for the dark matter. We are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9-σ level. On weakly non-linear scales, we can interpret our results in terms of galaxy bias parameters. We find a linear bias term that is consistent with unity, b 1 = 0.93 +0.10 −0.08 and a quadratic bias c 2 = b 2 /b 1 = −0.34 +0.11 −0.08 . This is the first significant detection of a non-zero quadratic bias, indicating a small but important non-gravitational contribution to the three point function. Our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations, so we can combine this with the measurement of the power spectrum of 2dFGRS galaxies to constrain the amplitude of matter fluctuations. We find that the rms linear theory variance in spheres of radius 8h −1 Mpc is σ 8 = 0.88 +0.12 −0.10 , providing an independent confirmation of values derived from other techniques. On non-linear scales, where ξ > 1, we find that Q 3 has a strong dependence on scale, colour and luminosity.
The scale of homogeneity of the galaxy distribution in SDSS DR6
The assumption that the Universe, on sufficiently large scales, is homogeneous and isotropic is crucial to our current understanding of cosmology. In this Letter, we test if the observed galaxy distribution is actually homogeneous on large scales. We have carried out a multifractal analysis of the galaxy distribution in a volume-limited subsample from the Sloan Digital Sky Survey (SDSS) Data Release 6. This considers the scaling properties of different moments of galaxy number counts in spheres of varying radius, r, centred on galaxies. This analysis gives the spectrum of generalized dimension Dq(r), where q > 0 quantifies the scaling properties in overdense regions and q < 0 in underdense regions. We expect Dq(r) = 3 for a homogeneous, random point distribution. In our analysis, we have determined Dq(r) in the range -4 <= q <= 4 and 7 <= r <= 98h-1 Mpc. In addition to the SDSS data, we have analysed several random samples which are homogeneous by construction. Sim...
New Statistical Methods for Analysis of Large Surveys: Distributions and Correlations
International Astronomical Union Colloquium, 2002
The aim of this paper is to describe new statistical methods for determination of the correlations among and distributions of physical parameters from a multivariate data with general and arbitrary truncations and selection biases. These methods, developed in collaboration with B. Efron of Department of Statistics at Stanford, can be used for analysis of combined data from many surveys with different and varied observational selection criteria. For clarity I will use the luminosity function of AGNs and its evolution to demonstrate the methods. I will first describe the general features of data truncation and present a brief review of past methods of analysis. Then I will describe the new methods and results from simulations testing their accuracy. Finally I will present the results from application of the methods to a sample of quasars.
The 2dF Galaxy Redshift Survey: stochastic relative biasing between galaxy populations
Monthly Notices of The Royal Astronomical Society, 2004
It is well known that the clustering of galaxies depends on galaxy type.Such relative bias complicates the inference of cosmological parameters from galaxy redshift surveys, and is a challenge to theories of galaxy formation and evolution. In this paper we perform a joint counts-in-cells analysis on galaxies in the 2dF Galaxy Redshift Survey, classified by both colour and spectral type, eta, as early or late type galaxies. We fit three different models of relative bias to the joint probability distribution of the cell counts, assuming Poisson sampling of the galaxy density field. We investigate the nonlinearity and stochasticity of the relative bias, with cubical cells of side 10Mpc \leq L \leq 45Mpc (h=0.7). Exact linear bias is ruled out with high significance on all scales. Power law bias gives a better fit, but likelihood ratios prefer a bivariate lognormal distribution, with a non-zero `stochasticity' - i.e. scatter that may result from physical effects on galaxy formation other than those from the local density field. Using this model, we measure a correlation coefficient in log-density space (r_LN) of 0.958 for cells of length L=10Mpc, increasing to 0.970 by L=45Mpc. This corresponds to a stochasticity sigma_b/bhat of 0.44\pm0.02 and 0.27\pm0.05 respectively. For smaller cells, the Poisson sampled lognormal distribution presents an increasingly poor fit to the data, especially with regard to the fraction of completely empty cells. We compare these trends with the predictions of semianalytic galaxy formation models: these match the data well in terms of overall level of stochasticity, variation with scale, and fraction of empty cells.
Modern Statistical Methods for Astronomy.pdf
Modern astronomical research is beset with a vast range of statistical challenges, ranging from reducing data from megadatasets to characterizing an amazing variety of variable celestial objects or testing astrophysical theory. Linking astronomy to the world of modern statistics, this volume is a unique resource, introducing astronomers to advanced statistics through ready-to-use code in the public-domain R statistical software environment.
The Astrophysical Journal, 2011
The three-point correlation function (3PCF) provides an important view into the clustering of galaxies that is not available to its lower order cousin, the two-point correlation function (2PCF). Higher order statistics, such as the 3PCF, are necessary to probe the non-Gaussian structure and shape information expected in these distributions. We measure the clustering of spectroscopic galaxies in the Main Galaxy Sample of the Sloan Digital Sky Survey, focusing on the shape or configuration dependence of the reduced 3PCF in both redshift and projected space. This work constitutes the largest number of galaxies ever used to investigate the reduced 3PCF, using over 220,000 galaxies in three volume-limited samples. We find significant configuration dependence of the reduced 3PCF at 3-27 h -1 Mpc, in agreement with ΛCDM predictions and in disagreement with the hierarchical ansatz. Below 6 h -1 Mpc, the redshift space reduced 3PCF shows a smaller amplitude and weak configuration dependence in comparison with projected measurements suggesting that redshift distortions, and not galaxy bias, can make the reduced 3PCF appear consistent with the hierarchical ansatz. The reduced 3PCF shows a weaker dependence on luminosity than the 2PCF, with no significant dependence on scales above 9 h -1 Mpc. On scales less than 9 h -1 Mpc, the reduced 3PCF appears more affected by galaxy color than luminosity. We demonstrate the extreme sensitivity of the 3PCF to systematic effects such as sky completeness and binning scheme, along with the difficulty of resolving the errors. Some comparable analyses make assumptions that do not consistently account for these effects.
Statistical Study of the Galaxy Distribution
Large-scale structures in the Universe provide crucial information about formation of structures and can be used to test cosmological models. The good agreement between large-scale observations and the now-standard Lambda-Cold Dark Matter (ΛCDM) model gives hope for this model to be a lasting foundation. Going a step further, these observations have been used for precision cosmology to constrain cosmological parameters inside the model. Large-scale structures are mainly studied through galaxy surveys, while on the other hand, cosmological models give predictions in terms of the global matter density field. Thus we need to understand the relationship between the matter density field and galaxy field, which is still a subject of research. Yet galaxy surveys have the advantage to map very large volumes. Recent galaxy surveys such as the Sloan Digital Sky Survey (SDSS, York et al. (2000)) and the 2 degree Field (2dF, Colless et al. (2001)) map unprecedented 3D volumes in the Universe. They have notably confirmed the view of large-scale structures as a collection of giant bubble-like voids separated by sheets and filaments of galaxies. This pattern has become known as the "Cosmic Web" (Bond et al. (1996), Springel et al. (2005)). The SDSS survey also enabled the first convincing detection of Baryon Acoustic Oscillations (BAOs) in large-scale structures (Eisenstein et al. (2005)), which opened a new field in precision cosmology. Future galaxy surveys will map always bigger volumes, with more galaxies and continue to improve our knowledge of large-scale structures and cosmological models. Though data sets are of crucial importance, statistical methods extracting the information also have an important role. They should be optimized in order to exploit the full potential of these surveys. The purpose of this chapter is to review the different methods that can be used. A first class of methods that we present is based on Fourier analysis, using the correlation function and the power spectrum. It originates from the simplicity of the Gaussian field, fully described by its second order moments. The Gaussian model gives a simple approximation of the matter density field, that works well on large scales. Another reason for the study of correlation function and power spectrum is that they are well understood and can be predicted in ΛCDM models. Recently, Fourier analysis has been used to study BAOs. These structures are remnants of acoustic waves, traveling in the hot plasma before recombination, and that have stayed frozen in large-scale structures. The detection of BAOs in the SDSS has been a strong support for the ΛCDM model. Besides, they provide a statistical standard ruler since their absolute 8 www.intechopen.com 2 Will-beset by IN -TECH size is known with small uncertainty. Thus their measurement in galaxy catalogues gives information on distances, and enables to constrain cosmological parameters. A second class of methods use geometrical and topological tools to describe large-scale-structures. Among this class of methods, we present the Minkowski functionals and the genus statistic, providing a rigorous mathematical framework for the analysis. Among other advantages, Minkowski functionals are known analytically for gaussian random fields. Historically, the main application of those statistics was to determine the scale at which the distribution is gaussian, i.e. approximately the scale of linear evolution. Among other applications, we show how they can be used for model discrimination, or to provide a standard ruler in galaxy catalogues. Finally we present the approach based on fractal analysis to characterize the galaxy distribution. It is motivated by the well-established scale-invariance of the galaxy clustering at small scales (r < 10h −1 Mpc). Yet fractality on all scales would put into question current cosmological models, which assume large-scale homogeneity. It would also call into question the correlation function analysis, which assumes a well-defined mean density of the field. We discuss the question of the large-scale homogeneity. We show how the extension to multifractal analysis can represent more general distributions, in particular the distribution of galaxies, and enable to study the scale of homogeneity.
Empirical Validation of the Ising Galaxy Bias Model
2019
Repp and Szapudi (2019) present a physically-motivated galaxy bias model which remains physical in low-density regions and which also provides a better fit to simulation data than do typical survey-analysis bias models. Given plausible simplifying assumptions, the physics of this model (surprisingly) proves to be analogous to the Ising model of statistical mechanics. In the present work we present a method of testing this Ising bias model against empirical galaxy survey data. Using this method, we compare our model (as well as three reference models -- linear, quadratic, and logarithmic) to SDSS, 6dFGS, and COSMOS2015 results, finding that for spectroscopic redshift surveys, the Ising bias model provides a superior fit compared to the reference models. Photometric redshifts, on the other hand, introduce enough error into the radial coordinate that none of the models yields a good fit. A physically meaningful galaxy bias model is necessary for optimal extraction of cosmological infor...