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Register a new userThe Cluster Mass Function from Early SDSS Data: Cosmological Implications
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Neta A. Bahcall
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The mass function of clusters of galaxies is determined from 400 deg^2 of early commissioning imaging data of the Sloan Digital Sky Survey; ~300 clusters in the redshift range z = 0.1 - 0.2 are used. Clusters are selected using two independent selection methods: a Matched Filter and a red-sequence color magnitude technique. The two methods yield consistent results. The cluster mass function is compared with large-scale cosmological simulations. We find a best-fit cluster normalization relation of sigma_8*omega_m^0.6 = 0.33 +- 0.03 (for 0.1 ~< omega_m ~< 0.4), or equivalently sigma_8 = (0.16/omega_m)^0.6. The amplitude of this relation is significantly lower than the previous canonical value, implying that either omega_m is lower than previously expected (omega_m = 0.16 if sigma_8 = 1) or sigma_8 is lower than expected (sigma_8 = 0.7 if omega_m = 0.3). The best-fit mass function parameters are omega_m = 0.19 (+0.08,-0.07) and sigma_8 = 0.9 (+0.3,-0.2). High values of omega_m (>= 0.4) and low sigma_8 (=< 0.6) are excluded at >~ 2 sigma.
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The cluster correlation function and its richness dependence are determined from 1108 clusters of galaxies -- the largest sample of clusters studied so far -- found in 379 deg^2 of Sloan Digital Sky Survey early data. The results are compared with previous samples of optically and X-ray selected clusters. The richness-dependent correlation function increases monotonically from an average correlation scale of ~ 12 h^{-1} Mpc for poor clusters to ~ 25 h^{-1} Mpc for the richer, more massive clusters with a mean separation of ~ 90 h^{-1} Mpc. X-ray selected clusters suggest slightly stronger correlations than optically selected clusters (~ 2-sigma). The results are compared with large-scale cosmological simulations. The observed richness-dependent cluster correlation function is well represented by the standard flat LCDM model (Omega_m ~= 0.3, h ~= 0.7), and is inconsistent with the considerably weaker correlations predicted by Omega_m = 1 models. An analytic relation for the correlation scale versus cluster mean separation, r_0 - d, that best describes the observations and the LCDM prediction is r_0 ~= 2.6 sqrt{d} (for d ~= 20 - 90 h^{-1} Mpc). Data from the complete Sloan Digital Sky Survey, when available, will greatly enhance the accuracy of the results and allow a more precise determination of cosmological parameters.
The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local Universe. In this Letter we present some of the initial results on the angular 2-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18<r*<22, is shown to be consistent with results from existing wide-field, photographic-based surveys and narrower CCD galaxy surveys. On scales between 1 arcminute and 1 degree the correlation function is well described by a power-law with an exponent of ~ -0.7. The amplitude of the correlation function, within this angular interval, decreases with fainter magnitudes in good agreement with analyses from existing galaxy surveys. There is a characteristic break in the correlation function on scales of approximately 1-2 degrees. On small scales, < 1, the SDSS correlation function does not appear to be consistent with the power-law form fitted to the 1< theta <0.5 deg data. With a data set that is less than 2% of the full SDSS survey area, we have obtained high precision measurements of the power-law angular correlation function on angular scales 1 < theta < 1 deg, which are robust to systematic uncertainties. Because of the limited area and the highly correlated nature of the error covariance matrix, these initial results do not yet provide a definitive characterization of departures from the power-law form at smaller and larger angles. In the near future, however, the area of the SDSS imaging survey will be sufficient to allow detailed analysis of the small and large scale regimes, measurements of higher-order correlations, and studies of angular clustering as a function of redshift and galaxy type.
We present the cosmological parameters constraints obtained from the combination of galaxy cluster mass function measurements (Vikhlinin et al., 2009a,b) with new cosmological data obtained during last three years: updated measurements of cosmic microwave background anisotropy with Wilkinson Microwave Anisotropy Probe (WMAP) observatory, and at smaller angular scales with South Pole Telescope (SPT), new Hubble constant measurements, baryon acoustic oscillations and supernovae Type Ia observations. New constraints on total neutrino mass and effective number of neutrino species are obtained. In models with free number of massive neutrinos the constraints on these parameters are notably less strong, and all considered cosmological data are consistent with non-zero total neutrino mass Sigma m_ u approx 0.4 eV and larger than standard effective number of neutrino species, N_eff approx 4. These constraints are compared to the results of neutrino oscillations searches at short baselines. The updated dark energy equation of state parameters constraints are presented. We show that taking in account systematic uncertainties, current cluster mass function data provide similarly powerful constraints on dark energy equation of state, as compared to the constraints from supernovae Type Ia observations.
A sample of white dwarfs is selected from SDSS DR3 imaging data using their reduced proper motions, based on improved proper motions from SDSS plus USNO-B combined data. Numerous SDSS and followup spectra (Kilic et al. 2005) are used to quantify completeness and contamination of the sample; kinematic models are used to understand and correct for velocity-dependent selection biases. A luminosity function is constructed covering the range 7 < M_bol < 16, and its sensitivity to various assumptions and selection limits is discussed. The white dwarf luminosity function based on 6000 stars is remarkably smooth, and rises nearly monotonically to M_bol = 15.3. It then drops abruptly, although the small number of low-luminosity stars in the sample and their unknown atmospheric composition prevent quantitative conclusions about this decline. Stars are identified that may have high tangential velocities, and a preliminary luminosity function is constructed for them.
We compute the angular power spectrum C_l from 1.5 million galaxies in early SDSS data on large angular scales, l<600. The data set covers about 160 square degrees, with a characteristic depth of order 1 Gpc/h in the faintest (21<r<22) of our four magnitude bins. Cosmological interpretations of these results are presented in a companion paper by Dodelson et al (2001). The data in all four magnitude bins are consistent with a simple flat ``concordance model with nonlinear evolution and linear bias factors of order unity. Nonlinear evolution is particularly evident for the brightest galaxies. A series of tests suggest that systematic errors related to seeing, reddening, etc., are negligible, which bodes well for the sixtyfold larger sample that the SDSS is currently collecting. Uncorrelated error bars and well-behaved window functions make our measurements a convenient starting point for cosmological model fitting.
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