Biasing and High‐Order Statistics from the Southern‐Sky Redshift Survey (original) (raw)
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...
Arxiv preprint astro-ph/9805126, 1998
Abstract: In a recent analysis of number counts in the ESP survey Scaramella et al.(1998) claim to find evidence for a cross-over to homogeneity at large scales, and against a fractal behaviour with dimension $ D\ approx 2$. In this comment we note firstly that, if such a cross-over exists as described by the authors, the scale characterizing it is~ 100-300 Mpc/h. This invalidates the``standard''analysis of the same catalogue given elsewhere by the authors which results in a``correlation length''of only r_0= 4 Mpc/h. Furthermore we show that the ...
Maximum Likelihood Comparisons of Tully-Fisher and Redshift Data: Constraints on Ω and Biasing
We compare Tully-Fisher (TF) data for 838 galaxies within cz = 3000 km s −1 from the Mark III catalog to the peculiar velocity and density fields predicted from the 1.2 Jy IRAS redshift survey. Our goal is to test the relation between the galaxy density and velocity fields predicted by gravitational instability theory and linear biasing, and thereby to estimate β I ≡ Ω 0.6 /b I , where b I is the linear bias parameter for IRAS galaxies on a 300 km s −1 scale. Adopting the IRAS velocity and density fields as a prior model, we maximize the likelihood of the raw TF observables, taking into account the full range of selection effects and properly treating triple-valued zones in the redshiftdistance relation. Extensive tests with realistic simulated galaxy catalogs demonstrate that the method produces unbiased estimates of β I and its error. When we apply the method to the real data, we model the presence of a small but significant velocity quadrupole residual (∼ 3.3% of Hubble flow), which we argue is due to density fluctuations incompletely sampled by IRAS. The method then yields a maximum likelihood estimate β I = 0.49 ± 0.07 (1 σ error). We discuss the constraints on Ω and biasing that follow from this estimate of β I if we assume a COBE-normalized CDM power spectrum. Our model also yields the one dimensional noise in the velocity field, including IRAS prediction errors, which we find to be 125 ± 20 km s −1 .
Testing homogeneity on large scales in the Sloan Digital Sky Survey Data Release One
Monthly Notices of the Royal Astronomical Society, 2005
The assumption that the universe is homogeneous and isotropic on large scales is one of the fundamental postulates of cosmology. We have tested the large scale homogeneity of the galaxy distribution in the Sloan Digital Sky Survey Data Release One (SDSS-DR1) using volume limited subsamples extracted from the two equatorial strips which are nearly two dimensional (2D). The galaxy distribution was projected on the equatorial plane and we carried out a 2D multi-fractal analysis by counting the number of galaxies inside circles of different radii r in the range 5 h −1 Mpc to 150 h −1 Mpc centred on galaxies. Different moments of the count-in-cells were analysed to identify a range of length-scales (60 − 70 h −1 Mpc to 150h −1 Mpc) where the moments show a power law scaling behaviour and to determine the scaling exponent which gives the spectrum of generalised dimension D q. If the galaxy distribution is homogeneous, D q does not vary with q and is equal to the Euclidean dimension which in our case is 2. We find that D q varies in the range 1.7 to 2.2. We also constructed mock data from random, homogeneous point distributions and from ΛCDM N-body simulations with bias b = 1, 1.6 and 2, and analysed these in exactly the same way. The values of D q in the random distribution and the unbiased simulations show much smaller variations and these are not consistent with the actual data. The biased simulations, however, show larger variations in D q and these are consistent with both the random and the actual data. Interpreting the actual data as a realisation of a biased ΛCDM universe, we conclude that the galaxy distribution is homogeneous on scales larger than 60 − 70 h −1 Mpc.
Monthly Notices of the Royal Astronomical Society, 2005
We present a power-spectrum analysis of the final 2dF Galaxy Redshift Survey (2dFGRS), employing a direct Fourier method. The sample used comprises 221 414 galaxies with measured redshifts. We investigate in detail the modelling of the sample selection, improving on previous treatments in a number of respects. A new angular mask is derived, based on revisions to the photometric calibration. The redshift selection function is determined by dividing the survey according to rest-frame colour, and deducing a self-consistent treatment of k-corrections and evolution for each population. The covariance matrix for the power-spectrum estimates is determined using two different approaches to the construction of mock surveys, which are used to demonstrate that the input cosmological model can be correctly recovered. We discuss in detail the possible differences between the galaxy and mass power spectra, and treat these using simulations, analytic models and a hybrid empirical approach. Based on these investigations, we are confident that the 2dFGRS power spectrum can be used to infer the matter content of the universe. On large scales, our estimated power spectrum shows evidence for the 'baryon oscillations' that are predicted in cold dark matter (CDM) models. Fitting to a CDM model, assuming a primordial n s = 1 spectrum, h = 0.72 and negligible neutrino mass, the preferred parameters are m h = 0.168 ± 0.016 and a baryon fraction b / m = 0.185 ± 0.046 (1σ errors). The value of m h is 1σ lower than the 0.20 ± 0.03 in our 2001 analysis of the partially