Acoustic Oscillations in the Early Universe and Today

During its first ~100,000 years, the universe was a fully ionized plasma with a tight coupling by Thompson scattering between the photons and matter. The trade--off between gravitational collapse and photon pressure causes acoustic oscillations in this primordial fluid. These oscillations will leave predictable imprints in the spectra of the cosmic microwave background and the present day matter-density distribution. Recently, the BOOMERANG and MAXIMA teams announced the detection of these acoustic oscillations in the cosmic microwave background (observed at redshift ~1000). Here, we compare these CMB detections with the corresponding acoustic oscillations in the matter-density power spectrum (observed at redshift ~0.1). These consistent results, from two different cosmological epochs, provide further support for our standard Hot Big Bang model of the universe.Comment: To appear in the journal Science. 6 pages, 1 color figur

The Interplay of Cluster and Galaxy Evolution

We review here the interplay of cluster and galaxy evolution. As a case study, we consider the Butcher-Oemler effect and propose that it is the result of the changing rate of cluster merger events in a hierarchical universe. This case study highlights the need for new catalogs of clusters and groups that possess quantified morphologies. We present such a sample here, namely the Sloan Digital Sky Survey (SDSS) C4 Catalog, which has been objectively-selected from the SDSS spectroscopic galaxy sample. We outline here the C4 algorithm and present first results based on the SDSS Early Data Release, including an X-ray luminosity-velocity dispersion (L_x-sigma) scaling relationship (as a function of cluster morphology), and the density-SFR relation of galaxies within C4 clusters (Gomez et al. 2003). We also discuss the merger of Coma and the NGC4839 group, and its effect on the galaxy populations in these systems. We finish with a brief discussion of a new sample of Hdelta-selected galaxies (i.e., k+a, post--starburst galaxies) obtained from the SDSS spectroscopic survey.Comment: Invited review at the JENAM 2002 Workshop on "Galaxy Evolution in Groups and Clusters", Porto, Sep 5-7 2002, eds. Lobo, Serote-Roos and Biviano, Kluwer in pres

Detecting the Baryons in Matter Power Spectra

We examine power spectra from the Abell/ACO rich cluster survey and the 2dF Galaxy Redshift Survey (2dfGRS) for observational evidence of features produced by the baryons. A non-negligible baryon fraction produces relatively sharp oscillatory features at specific wavenumbers in the matter power spectrum. However, the mere existence of baryons will also produce a global suppression of the power spectrum. We look for both of these features using the false discovery rate (FDR) statistic. We show that the window effects on the Abell/ACO power spectrum are minimal, which has allowed for the discovery of discrete oscillatory features in the power spectrum. On the other hand, there are no statistically significant oscillatory features in the 2dFGRS power spectrum, which is expected from the survey's broad window function. After accounting for window effects, we apply a scale-independent bias to the 2dFGRS power spectrum, P_{Abell}(k) = b^2P_{2dF}(k) and b = 3.2. We find that the overall shapes of the Abell/ACO and the biased 2dFGRS power spectra are entirely consistent over the range 0.02 <= k <= 0.15hMpc^-1. We examine the range of Omega_{matter} and baryon fraction for which these surveys could detect significant suppression in power. The reported baryon fractions for both the Abell/ACO and 2dFGRS surveys are high enough to cause a detectable suppression in power (after accounting for errors, windows and k-space sampling). Using the same technique, we also examine, given the best fit baryon density obtained from BBN, whether it is possible to detect additional suppression due to dark matter-baryon interaction. We find that the limit on dark matter cross section/mass derived from these surveys are the same as those ruled out in a recent study by Chen, Hannestad and Scherrer.Comment: 11 pages of text, 6 figures. Submitted to Ap

Construction and evaluation of classifiers for forensic document analysis

In this study we illustrate a statistical approach to questioned document examination. Specifically, we consider the construction of three classifiers that predict the writer of a sample document based on categorical data. To evaluate these classifiers, we use a data set with a large number of writers and a small number of writing samples per writer. Since the resulting classifiers were found to have near perfect accuracy using leave-one-out cross-validation, we propose a novel Bayesian-based cross-validation method for evaluating the classifiers.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS379 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Possible Detection of Baryonic Fluctuations in the Large-Scale Structure Power Spectrum

We present a joint analysis of the power spectra of density fluctuations from three independent cosmological redshift surveys; the PSCz galaxy catalog, the APM galaxy cluster catalog and the Abell/ACO cluster catalog. Over the range 0.03 <= k <= 0.15 h/Mpc,the amplitudes of these three power spectra are related through a simple linear biasing model with b = 1.5 and b = 3.6 for Abell/ACO versus APM and Abell/ACO versus the PSCz respectively. Furthermore, the shape of these power spectra are remarkably similar despite the fact that they are comprised of significantly different objects (individual galaxies through to rich clusters). Individually, each of these surveys show visible evidence for ``valleys'' in their power spectra. We use a newly developed statistical technique called the False Discovery Rate, to show that these ``valleys'' are statistically significant. One favored cosmological explanation for such features in the power spectrum is the presence of a non-negligible baryon fraction (Omega_b/Omega_m) in the Universe which causes acoustic oscillations in the transfer function of adiabatic inflationary models. We have performed a maximum-likelihood marginalization over four important cosmological parameters of this model (Omega_m, Omega_b, n_s, H_o). We use a prior on H_0 = 69(+/-15), and find Omega_mh^2 = 0.12(+0.03/-0.02), Omega_bh^2 =0.029(+0.011/-0.015), n_s = 1.08^(+0.17/-0.20) (2 sigma confidence limits) which are fully consistent with the favored values of these cosmological parameters from the recent Cosmic Microwave Background (CMB) experiments. This agreement strongly suggests that we have detected baryonic oscillations in the power spectrum of matter at a level expected from a Cold Dark Matter model normalized to fit these CMB measurements.Comment: 13 pages, 4 figures, ApJ in press. Typos fixed. Replaced Figure 4 with improved versio

Controlling the False Discovery Rate in Astrophysical Data Analysis

The False Discovery Rate (FDR) is a new statistical procedure to control the number of mistakes made when performing multiple hypothesis tests, i.e. when comparing many data against a given model hypothesis. The key advantage of FDR is that it allows one to a priori control the average fraction of false rejections made (when comparing to the null hypothesis) over the total number of rejections performed. We compare FDR to the standard procedure of rejecting all tests that do not match the null hypothesis above some arbitrarily chosen confidence limit, e.g. 2 sigma, or at the 95% confidence level. When using FDR, we find a similar rate of correct detections, but with significantly fewer false detections. Moreover, the FDR procedure is quick and easy to compute and can be trivially adapted to work with correlated data. The purpose of this paper is to introduce the FDR procedure to the astrophysics community. We illustrate the power of FDR through several astronomical examples, including the detection of features against a smooth one-dimensional function, e.g. seeing the ``baryon wiggles'' in a power spectrum of matter fluctuations, and source pixel detection in imaging data. In this era of large datasets and high precision measurements, FDR provides the means to adaptively control a scientifically meaningful quantity -- the number of false discoveries made when conducting multiple hypothesis tests.Comment: 15 pages, 9 figures. Submitted to A

Environmental Dependence of the Fundamental Plane of Galaxy Clusters

Galaxy clusters approximate a planar (FP) distribution in a three-dimensional parameter space which can be characterized by optical luminosity, half-light radius, and X-ray luminosity. Using a high-quality catalog of cluster redshifts, we find the nearest neighbor cluster for those common to an FP study and the cluster catalog. Examining scatter about the FP, we find 99.2% confidence that it is dependent on nearest neighbor distance. Our study of X-Ray clusters finds that those with high central gas densities are systematically closer to neighbor clusters. If we combine results here with those of Fritsch and Buchert, we find an explanation for some of our previous conclusions: Clusters in close proximity to other clusters are more likely to have massive cooling flows because they are more relaxed and have higher central gas densities.Comment: Accepted for publication in Astrophysical Journal Letters. Moderate revisions, including more statistical analysis and discussion. Latex, 7 page

Nonparametric Inference for the Cosmic Microwave Background

The Cosmic Microwave Background (CMB), which permeates the entire Universe, is the radiation left over from just 380,000 years after the Big Bang. On very large scales, the CMB radiation field is smooth and isotropic, but the existence of structure in the Universe - stars, galaxies, clusters of galaxies - suggests that the field should fluctuate on smaller scales. Recent observations, from the Cosmic Microwave Background Explorer to the Wilkinson Microwave Anisotropy Project, have strikingly confirmed this prediction. CMB fluctuations provide clues to the Universe's structure and composition shortly after the Big Bang that are critical for testing cosmological models. For example, CMB data can be used to determine what portion of the Universe is composed of ordinary matter versus the mysterious dark matter and dark energy. To this end, cosmologists usually summarize the fluctuations by the power spectrum, which gives the variance as a function of angular frequency. The spectrum's shape, and in particular the location and height of its peaks, relates directly to the parameters in the cosmological models. Thus, a critical statistical question is how accurately can these peaks be estimated. We use recently developed techniques to construct a nonparametric confidence set for the unknown CMB spectrum. Our estimated spectrum, based on minimal assumptions, closely matches the model-based estimates used by cosmologists, but we can make a wide range of additional inferences. We apply these techniques to test various models and to extract confidence intervals on cosmological parameters of interest. Our analysis shows that, even without parametric assumptions, the first peak is resolved accurately with current data but that the second and third peaks are not.Comment: Invited review for "Statistical Science". Accepted for publication in Feburary 2004 journa