The Linear Point: A cleaner cosmological standard ruler

We show how a characteristic length scale imprinted in the galaxy two-point correlation function, dubbed the "linear point", can serve as a comoving cosmological standard ruler. In contrast to the Baryon Acoustic Oscillation peak location, this scale is constant in redshift and is unaffected by non-linear effects to within $0.5$ percent precision. We measure the location of the linear point in the galaxy correlation function of the LOWZ and CMASS samples from the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) collaboration. We combine our linear-point measurement with cosmic-microwave-background constraints from the Planck satellite to estimate the isotropic-volume distance $D_{V}(z)$, without relying on a model-template or reconstruction method. We find $D_V(0.32)=1264\pm 28$ Mpc and $D_V(0.57)=2056\pm 22$ Mpc respectively, consistent with the quoted values from the BOSS collaboration. This remarkable result suggests that all the distance information contained in the baryon acoustic oscillations can be conveniently compressed into the single length associated with the linear point.Comment: The optimal two-point correlation function bin-size is employed. Results are updated and the distance constraints are improve

Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and PCA

We allow for nonlinear effects in the likelihood analysis of galaxy peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter Om and the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be a flat LCDM model (h=0.65, n=1, COBE) with only Om as a free parameter. Since the likelihood is driven by the nonlinear regime, we "break" the power spectrum at k_b=0.2 h/Mpc and fit a power law at k>k_b. This allows for independent matching of the nonlinear behavior and an unbiased fit in the linear regime. The analysis assumes Gaussian fluctuations and errors, and a linear relation between velocity and density. Tests using proper mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark3 and SFI data Om_m=0.32+-0.06 and 0.37+-0.09 respectively, with sigma_8*Om^0.6 = 0.49+-0.06 and 0.63+-0.08, in agreement with constraints from other data. The quoted 90% errors include cosmic variance. The improvement in likelihood due to the nonlinear correction is very significant for Mark3 and moderately so for SFI. When allowing deviations from LCDM, we find an indication for a wiggle in the power spectrum: an excess near k=0.05 and a deficiency at k=0.1 (cold flow). This may be related to the wiggle seen in the power spectrum from redshift surveys and the second peak in the CMB anisotropy. A chi^2 test applied to modes of a Principal Component Analysis (PCA) shows that the nonlinear procedure improves the goodness of fit and reduces a spatial gradient of concern in the linear analysis. The PCA allows addressing spatial features of the data and fine-tuning the theoretical and error models. It shows that the models used are appropriate for the cosmological parameter estimation performed. We address the potential for optimal data compression using PCA.Comment: 18 pages, LaTex, uses emulateapj.sty, ApJ in press (August 10, 2001), improvements to text and figures, updated reference

Autocorrelations of stellar light and mass in the low-redshift Universe

The final data release of the Sloan Digital Sky Survey (SDSS) provides reliable photometry and spectroscopy for about half a million galaxies with median redshift 0.09. Here we use these data to estimate projected autocorrelation functions w_p(r_p) for the light of galaxies in the five SDSS photometric bands. Comparison with the analogous stellar mass autocorrelation, estimated in a previous paper, shows that stellar luminosity is less strongly clustered than stellar mass in all bands and on all scales. Over the full nonlinear range 10 kpc/h < r_p < 10 Mpc/h our autocorrelation estimates are extremely well represented by power laws. The parameters of the corresponding spatial functions \xi(r) = (r/r_0)^\gamma vary systematically from r_0=4.5 Mpc/h and \gamma=-1.74 for the bluest band (the u band) to r_0=5.8 Mpc/h and \gamma=-1.83 for the reddest one (the z band). These may be compared with r_0=6.1 Mpc/h and \gamma=-1.84 for the stellar mass. Ratios of w_p(r_p) between two given wavebands are proportional to the mean colour of correlated stars at projected distance r_p from a randomly chosen star. The ratio of the stellar mass and luminosity autocorrelations measures an analogous mean stellar mass-to-light ratio (M*/L). All colours get redder and all mass-to-light ratios get larger with decreasing r_p, with the amplitude of the effects decreasing strongly to redder passbands. Even for the u-band the effects are quite modest, with maximum shifts of about 0.1 in u-g and about 25% in M*/L_u. These trends provide a precise characterisation of the well-known dependence of stellar populations on environment.Comment: 6 pages, 4 figures, accepted to MNRAS; three new paragraphs added: two at the end of Sec. 2 concerning cross-correlations between different bands and possible biases due to photometry errors, and one at the end of the paper discussing marked correlation function

Large Scale Power Spectrum from Peculiar Velocities Via Likelihood Analysis

The power spectrum (PS) of mass density fluctuations, independent of `biasing', is estimated from the Mark III catalog of peculiar velocities using Bayesian statistics. A parametric model is assumed for the PS, and the free parameters are determined by maximizing the probability of the model given the data. The method has been tested using detailed mock catalogs. It has been applied to generalized CDM models with and without COBE normalization. The robust result for all the models is a relatively high PS, with $P(k) \Omega^{1.2} = (4.8 \pm 1.5) \times 10^3 (Mpc/h)^3$ at $k=0.1 h/Mpc$. An extrapolation to smaller scales using the different CDM models yields $\sigma_8 \Omega^{0.6} = 0.88 \pm 0.15$. The peak is weakly constrained to the range $0.02 \leq k \leq 0.06 h/Mpc$. These results are consistent with a direct computation of the PS (Kolatt & Dekel 1996). When compared to galaxy-density surveys, the implied values for $\beta$ ($\equiv \Omega^{0.6}/b$) are of order unity to within 25%. The parameters of the COBE-normalized, flat CDM model are confined by a 90% likelihood contour of the sort $\Omega h_{50}^\mu n^\nu = 0.8 \pm 0.2$, where $\mu = 1.3$ and $\nu = 3.4, 2.0$ for models with and without tensor fluctuations respectively. For open CDM the powers are $\mu = 0.95$ and $\nu = 1.4$ (no tensor fluctuations). A $\Gamma$-shape model free of COBE normalization yields only a weak constraint: $\Gamma = 0.4 \pm 0.2$.Comment: 19 pages, 8 figures, 2 tables. Accepted for publication in The Astrophysical Journa

A New Statistic for Analyzing Baryon Acoustic Oscillations

We introduce a new statistic omega_l for measuring and analyzing large-scale structure and particularly the baryon acoustic oscillations. omega_l is a band-filtered, configuration space statistic that is easily implemented and has advantages over the traditional power spectrum and correlation function estimators. Unlike these estimators, omega_l can localize most of the acoustic information into a single dip at the acoustic scale while also avoiding sensitivity to the poorly constrained large scale power (i.e., the integral constraint) through the use of a localized and compensated filter. It is also sensitive to anisotropic clustering through pair counting and does not require any binning. We measure the shift in the acoustic peak due to nonlinear effects using the monopole omega_0 derived from subsampled dark matter catalogues as well as from mock galaxy catalogues created via halo occupation distribution (HOD) modeling. All of these are drawn from 44 realizations of 1024^3 particle dark matter simulations in a 1h^{-1}Gpc box at z=1. We compare these shifts with those obtained from the power spectrum and conclude that the results agree. This indicates that any distance measurements obtained from omega_0 and P(k) will be consistent with each other. We also show that it is possible to extract the same amount of acoustic information using either omega_0 or P(k) from equal volume surveys.Comment: 12 pages, 7 figures. ApJ accepted. Edit: Now updated with final accepted versio

Measuring galaxy segregation using the mark connection function

(abridged) The clustering properties of galaxies belonging to different luminosity ranges or having different morphological types are different. These characteristics or `marks' permit to understand the galaxy catalogs that carry all this information as realizations of marked point processes. Many attempts have been presented to quantify the dependence of the clustering of galaxies on their inner properties. The present paper summarizes methods on spatial marked statistics used in cosmology to disentangle luminosity, colour or morphological segregation and introduces a new one in this context, the mark connection function. The methods used here are the partial correlation functions, including the cross-correlation function, the normalised mark correlation function, the mark variogram and the mark connection function. All these methods are applied to a volume-limited sample drawn from the 2dFGRS, using the spectral type as the mark. We show the virtues of each method to provide information about the clustering properties of each population, the dependence of the clustering on the marks, the similarity of the marks as a function of the pair distances, and the way to characterise the spatial correlation between the marks. We demonstrate by means of these statistics that passive galaxies exhibit stronger spatial correlation than active galaxies at small scales (r <20 Mpc/h). The mark connection function, introduced here, is particularly useful for understanding the spatial correlation between the marks.Comment: 6 pages, 5 figures, accepted for publication in Astronomy and Astrophysic

Gravitational Collapse of Dust with a Cosmological Constant

The recent analysis of Markovic and Shapiro on the effect of a cosmological constant on the evolution of a spherically symmetric homogeneous dust ball is extended to include the inhomogeneous and degenerate cases. The histories are shown by way of effective potential and Penrose-Carter diagrams.Comment: 2 pages, 2 figures (png), revtex. To appear in Phys. Rev.

The distribution of stellar mass in the low-redshift Universe

We use a complete and uniform sample of almost half a million galaxies from the Sloan Digital Sky Survey to characterise the distribution of stellar mass in the low-redshift Universe. Galaxy abundances are well determined over almost four orders of magnitude in stellar mass, and are reasonably but not perfectly fit by a Schechter function with characteristic stellar mass m* = 6.7 x 10^10 M_sun and with faint-end slope \alpha = -1.155. For a standard cosmology and a standard stellar Initial Mass Function, only 3.5% of the baryons in the low-redshift Universe are locked up in stars. The projected autocorrelation function of stellar mass is robustly and precisely determined for r_p < 30 Mpc/h. Over the range 10 kpc/kpc < r_p < 10 Mpc/h it is extremely well represented by a power law. The corresponding three-dimensional autocorrelation function is \xi*(r) = (r/6.1 Mpc/h)^{-1.84}. Relative to the dark matter, the bias of the stellar mass distribution is approximately constant on large scales, but varies by a factor of five for r_p < 1 Mpc/h. This behaviour is approximately but not perfectly reproduced by current models for galaxy formation in the concordance LCDM cosmology. Detailed comparison suggests that a fluctuation amplitude \sigma_8 ~ 0.8 is preferred to the somewhat larger value adopted in the Millennium Simulation models with which we compare our data. This comparison also suggests that observations of stellar mass autocorrelations as a function of redshift might provide a powerful test for the nature of Dark Energy.Comment: 12 pages, 11 figures, accepted for publication in Monthly Notices, two appendices added to explore possible systematic biases due to the stellar mass definition and surface density limit

A multiscale approach to environment and its influence on the colour distribution of galaxies

We present a multiscale approach to measurements of galaxy density, applied to a volume-limited sample constructed from SDSS DR5. We populate a rich parameter space by obtaining independent measurements of density on different scales for each galaxy, avoiding the implicit assumptions involved, e.g., in the construction of group catalogues. As the first application of this method, we study how the bimodality in galaxy colour distribution (u-r) depends on multiscale density. The u-r galaxy colour distribution is described as the sum of two gaussians (red and blue) with five parameters: the fraction of red galaxies (f_r) and the position and width of the red and blue peaks (mu_r, mu_b, sigma_r and sigma_b). Galaxies mostly react to their smallest scale (< 0.5 Mpc) environments: in denser environments red galaxies are more common (larger f_r), redder (larger mu_r) and with a narrower distribution (smaller sigma_r), while blue galaxies are redder (larger mu_b) but with a broader distribution (larger sigma_b). There are residual correlations of f_r and mu_b with 0.5 - 1 Mpc scale density, which imply that total or partial truncation of star formation can relate to a galaxy's environment on these scales. Beyond 1 Mpc (0.5 Mpc for mu_r) there are no positive correlations with density. However f_r (mu_r) anti-correlates with density on >2 (1) Mpc scales at fixed density on smaller scales. We examine these trends qualitatively in the context of the halo model, utilizing the properties of haloes within which the galaxies are embedded, derived by Yang et al, 2007 and applied to a group catalogue. This yields an excellent description of the trends with multiscale density, including the anti-correlations on large scales, which map the region of accretion onto massive haloes. Thus we conclude that galaxies become red only once they have been accreted onto haloes of a certain mass.Comment: 22 pages, 14 figures. Accepted for publication in MNRAS

The complex universe: recent observations and theoretical challenges

The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical characterization of these structures shows that galaxy distribution is inhomogeneous in these samples, being characterized by large-amplitude fluctuations of large spatial extension. Over a large range of scales, both the average conditional density and its variance show a nontrivial scaling behavior: at small scales, r<20 Mpc/h, the average (conditional) density scales as 1/r. At larger scales, the density depends only weakly (logarithmically) on the system size and density fluctuations follow the Gumbel distribution of extreme value statistics. These complex behaviors are different from what is expected in a homogeneous distribution with Gaussian fluctuations. The observed density inhomogeneities pose a fundamental challenge to the standard picture of cosmology but it also represent an important opportunity which points to new directions with respect to many cosmological puzzles. Indeed, the fact that matter distribution is not uniform, in the limited range of scales sampled by observations, rises the question of understanding how inhomogeneities affect the large-scale dynamics of the universe. We discuss several attempts which try to model inhomogeneities in cosmology, considering their effects with respect to the role and abundance of dark energy and dark matter.Comment: 30 pages, 10 figure