Cross-correlation Weak Lensing of SDSS galaxy Clusters II: Cluster Density Profiles and the Mass--Richness Relation

We interpret and model the statistical weak lensing measurements around 130,000 groups and clusters of galaxies in the Sloan Digital Sky Survey presented by Sheldon et al. 2007 (Paper I). We present non-parametric inversions of the 2D shear profiles to the mean 3D cluster density and mass profiles in bins of both optical richness and cluster i-band luminosity. We correct the inferred 3D profiles for systematic effects, including non-linear shear and the fact that cluster halos are not all precisely centered on their brightest galaxies. We also model the measured cluster shear profile as a sum of contributions from the brightest central galaxy, the cluster dark matter halo, and neighboring halos. We infer the relations between mean cluster virial mass and optical richness and luminosity over two orders of magnitude in cluster mass; the virial mass at fixed richness or luminosity is determined with a precision of 13% including both statistical and systematic errors. We also constrain the halo concentration parameter and halo bias as a function of cluster mass; both are in good agreement with predictions of LCDM models. The methods employed here will be applicable to deeper, wide-area optical surveys that aim to constrain the nature of the dark energy, such as the Dark Energy Survey, the Large Synoptic Survey Telescope and space-based surveys

Statistics for citizen science: extracting signals of change from noisy ecological data

1. Policy-makers increasingly demand robust measures of biodiversity change over short time periods. Long-term monitoring schemes provide high-quality data, often on an annual basis, but are taxonomically and geographically restricted. By contrast, opportunistic biological records are relatively unstructured but vast in quantity. Recently, these data have been applied to increasingly elaborate science and policy questions, using a range of methods. At present we lack a firm understanding of which methods, if any, are capable of delivering unbiased trend estimates on policy-relevant timescales. 2. We identified a set of candidate methods that employ data filtering criteria and/or correction factors to deal with variation in recorder activity. We designed a computer simulation to compare the statistical properties of these methods under a suite of realistic data collection scenarios. We measured the Type I error rates of each method-scenario combination, as well as the power to detect genuine trends. 3. We found that simple methods produce biased trend estimates, and/or had low power. Most methods are robust to variation in sampling effort, but biases in spatial coverage, sampling effort per visit, and detectability, as well as turnover in community composition all induced some methods to fail. No method was wholly unaffected by all forms of variation in recorder activity, although some performed well enough to be useful. 4. We warn against the use of simple methods. Sophisticated methods that model the data collection process offer the greatest potential to estimate timely trends, notably Frescalo and Occupancy-Detection models. 5. The potential of these methods and the value of opportunistic data would be further enhanced by assessing the validity of model assumptions and by capturing small amounts of information about sampling intensity at the point of data collection

Autosomal Resequence Data Reveal Late Stone Age Signals of Population Expansion in Sub-Saharan African Foraging and Farming Populations

BACKGROUND:A major unanswered question in the evolution of Homo sapiens is when anatomically modern human populations began to expand: was demographic growth associated with the invention of particular technologies or behavioral innovations by hunter-gatherers in the Late Pleistocene, or with the acquisition of farming in the Neolithic? METHODOLOGY/PRINCIPAL FINDINGS:We investigate the timing of human population expansion by performing a multilocus analysis of > or = 20 unlinked autosomal noncoding regions, each consisting of approximately 6 kilobases, resequenced in approximately 184 individuals from 7 human populations. We test the hypothesis that the autosomal polymorphism data fit a simple two-phase growth model, and when the hypothesis is not rejected, we fit parameters of this model to our data using approximate Bayesian computation. CONCLUSIONS/SIGNIFICANCE:The data from the three surveyed non-African populations (French Basque, Chinese Han, and Melanesians) are inconsistent with the simple growth model, presumably because they reflect more complex demographic histories. In contrast, data from all four sub-Saharan African populations fit the two-phase growth model, and a range of onset times and growth rates is inferred for each population. Interestingly, both hunter-gatherers (San and Biaka) and food-producers (Mandenka and Yorubans) best fit models with population growth beginning in the Late Pleistocene. Moreover, our hunter-gatherer populations show a tendency towards slightly older and stronger growth (approximately 41 thousand years ago, approximately 13-fold) than our food-producing populations (approximately 31 thousand years ago, approximately 7-fold). These dates are concurrent with the appearance of the Late Stone Age in Africa, supporting the hypothesis that population growth played a significant role in the evolution of Late Pleistocene human cultures

MaxBCG: A Red Sequence Galaxy Cluster Finder

Measurements of galaxy cluster abundances, clustering properties, and mass to- light ratios in current and future surveys can provide important cosmological constraints. Digital wide-field imaging surveys, the recently-demonstrated fidelity of red-sequence cluster detection techniques, and a new generation of realistic mock galaxy surveys provide the means for construction of large, cosmologicallyinteresting cluster samples, whose selection and properties can be understood in unprecedented depth. We present the details of the "maxBCG" algorithm, a cluster-detection technique tailored to multi-band CCD-imaging data. MaxBCG primarily relies on an observational cornerstone of massive galaxy clusters: they are marked by an overdensity of bright, uniformly red galaxies. This detection scheme also exploits classical brightest cluster galaxies (BCGs), which are often found at the center of these same massive clusters. (ABRIDGED)Comment: 39 pages, 16 figures, 1 table. Accepted to Ap

Cosmological Constraints from SDSS maxBCG Cluster Abundances

We perform a maximum likelihood analysis of the cluster abundance measured in the SDSS using the maxBCG cluster finding algorithm. Our analysis is aimed at constraining the power spectrum normalization $\sigma_8$, and assumes flat cosmologies with a scale invariant spectrum, massless neutrinos, and CMB and supernova priors Omega_m*h^2=0.128+/-0.01 and h=0.72+/-0.05 respectively. Following the method described in the companion paper Rozo et al. 2007, we derive \sigma_8=0.92+/-0.10$ (1-sigma) after marginalizing over all major systematic uncertainties. We place strong lower limits on the normalization, sigma_8>0.76 (95% CL) (>0.68 at 99% CL). We also find that our analysis favors relatively low values for the slope of the Halo Occupation Distribution (HOD), alpha=0.83+/-0.06. The uncertainties of these determinations will substantially improve upon completion of an ongoing campaign to estimate dynamical, weak lensing, and X-ray cluster masses in the SDSS maxBCG cluster sample.Comment: 10 pages, 6 figures, ApJ Submitte

Cosmological Constraints from the SDSS maxBCG Cluster Catalog

We use the abundance and weak lensing mass measurements of the SDSS maxBCG cluster catalog to simultaneously constrain cosmology and the richness--mass relation of the clusters. Assuming a flat \LambdaCDM cosmology, we find \sigma_8(\Omega_m/0.25)^{0.41} = 0.832\pm 0.033 after marginalization over all systematics. In common with previous studies, our error budget is dominated by systematic uncertainties, the primary two being the absolute mass scale of the weak lensing masses of the maxBCG clusters, and uncertainty in the scatter of the richness--mass relation. Our constraints are fully consistent with the WMAP five-year data, and in a joint analysis we find \sigma_8=0.807\pm 0.020 and \Omega_m=0.265\pm 0.016, an improvement of nearly a factor of two relative to WMAP5 alone. Our results are also in excellent agreement with and comparable in precision to the latest cosmological constraints from X-ray cluster abundances. The remarkable consistency among these results demonstrates that cluster abundance constraints are not only tight but also robust, and highlight the power of optically-selected cluster samples to produce precision constraints on cosmological parameters.Comment: comments welcom

Precision Measurements of the Cluster Red Sequence using an Error Corrected Gaussian Mixture Model

The red sequence is an important feature of galaxy clusters and plays a crucial role in optical cluster detection. Measurement of the slope and scatter of the red sequence are affected both by selection of red sequence galaxies and measurement errors. In this paper, we describe a new error corrected Gaussian Mixture Model for red sequence galaxy identification. Using this technique, we can remove the effects of measurement error and extract unbiased information about the intrinsic properties of the red sequence. We use this method to select red sequence galaxies in each of the 13,823 clusters in the maxBCG catalog, and measure the red sequence ridgeline location and scatter of each. These measurements provide precise constraints on the variation of the average red galaxy populations in the observed frame with redshift. We find that the scatter of the red sequence ridgeline increases mildly with redshift, and that the slope decreases with redshift. We also observe that the slope does not strongly depend on cluster richness. Using similar methods, we show that this behavior is mirrored in a spectroscopic sample of field galaxies, further emphasizing that ridgeline properties are independent of environment.Comment: 33 pages, 14 Figures; A typo in Eq.A11 is fixed. The C++/Python codes for ECGMM can be downloaded from: https://sites.google.com/site/jiangangecgmm

Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data

We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find \sigma_{\ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between \ln Lx and \ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.Comment: 14 pages, 6 figures, submitted to Ap

Why are the K dwarfs in the Pleiades so Blue?

The K dwarfs in the Pleiades fall nearly one half magnitude below a main sequence isochrone when plotted in a color-magnitude diagram utilizing V magnitude as the luminosity index and B-V as the color index. This peculiarity has been known for forty years but has gone unexplained and mostly ignored. When compared to Praesepe members, the Pleiades K dwarfs again are subluminous (or blue) in a color-magnitude diagram using B-V as the color index. However, using V-I as the color index, stars in the two clusters are coincident to M_V ~ 10; using V-K as the color index, Pleiades late K and M stars fall above the main sequence locus defined by Praesepe members. We believe that the anomalous spectral energy distributions for the Pleiades K dwarfs, as compared to older clusters, are a consequence of rapid stellar rotation and may be primarily due to spottedness. If so, the required areal filling factor for the cool component has to be very large (=> 50%). Weak-lined T Tauri stars have similar color anomalies, and we suspect this is a common feature of all very young K dwarfs (sp. type > K3). The peculiar spectral energy distribution needs to be considered in deriving accurate pre-main sequence isochrone-fitting ages for clusters like the Pleiades since the age derived will depend on the temperature index used.Comment: 41 pages, 15 figures, AASTeX5.0. Accepted 05 May 2003; Scheduled for publication in the Astronomical Journal (August 2003