On vote-taking and complete decoding of certain error-correcting codes

It is shown how complete decoding of maximum distance separable codes can be accomplished by a vote-taking algorithm or an equivalent distance correlation method. It is also indicated where this method of decoding might find application

Seeing in the dark – II. Cosmic shear in the Sloan Digital Sky Survey

Statistical weak lensing by large-scale structure – cosmic shear – is a promising cosmological tool, which has motivated the design of several large upcoming surveys. Here, we present a measurement of cosmic shear using co-added Sloan Digital Sky Survey (SDSS) imaging in 168 square degrees of the equatorial region, with r < 23.5 and i < 22.5, a source number density of 2.2 per arcmin^2 and mean redshift of z_(med) = 0.52. These co-adds were generated using a new method described in the companion Paper I that was intended to minimize systematic errors in the lensing measurement due to coherent point spread function anisotropies that are otherwise prevalent in the SDSS imaging data. We present measurements of cosmic shear out to angular separations of 2°, along with systematics tests that (combined with those from Paper I on the catalogue generation) demonstrate that our results are dominated by statistical rather than systematic errors. Assuming a cosmological model corresponding to Wilkinson Microwave Anisotropy Probe 7(WMAP7) and allowing only the amplitude of matter fluctuations σ_8 to vary, we find a best-fitting value of σ_8=0.636^(+0.109)_(−0.154) (1σ); without systematic errors this would be σ_8=0.636^(+0.099)_(−0.137) (1σ). Assuming a flat Λ cold dark matter model, the combined constraints with WMAP7 are σ_8=0.784^(+0.028)_(−0.026)(1σ)^(+0.055)_(−0.054)(2σ) and Ω_mh^2=0.1303^(+0.0047)_(−0.0048)(1σ)^(+0.009)_(−0.009)(2σ); the 2σ error ranges are, respectively, 14 and 17 per cent smaller than WMAP7 alone

Seeing in the dark – I. Multi-epoch alchemy

Weak lensing by large-scale structure is an invaluable cosmological tool given that most of the energy density of the concordance cosmology is invisible. Several large ground-based imaging surveys will attempt to measure this effect over the coming decade, but reliable control of the spurious lensing signal introduced by atmospheric turbulence and telescope optics remains a challenging problem. We address this challenge with a demonstration that point spread function (PSF) effects on measured galaxy shapes in the Sloan Digital Sky Survey (SDSS) can be corrected with existing analysis techniques. In this work, we co-add existing SDSS imaging on the equatorial stripe in order to build a data set with the statistical power to measure cosmic shear, while using a rounding kernel method to null out the effects of the anisotropic PSF. We build a galaxy catalogue from the combined imaging, characterize its photometric properties and show that the spurious shear remaining in this catalogue after the PSF correction is negligible compared to the expected cosmic shear signal. We identify a new source of systematic error in the shear–shear autocorrelations arising from selection biases related to masking. Finally, we discuss the circumstances in which this method is expected to be useful for upcoming ground-based surveys that have lensing as one of the science goals, and identify the systematic errors that can reduce its efficacy

Measuring dark matter ellipticity of Abell 901/902 using Particle Based Lensing

We present a non-parametric measure of the ellipticity and the alignment of the dark matter halos in Abell 901/902 supercluster. This super-cluster is a system of four separate peaks in a $0.5^{\circ}\times0.5^{\circ}$ field of view. We map the mass distribution of each individual peak using an improved version of Particle Based Lensing (PBL) and measure the ellipticity of the dark matter halos associated with two of the peaks directly from the mass map and by fitting them to a singular isothermal ellipse. The parametric and non-parametric measurements are consistent for A901b while the position angle for the Southwest Group is different for the two techniques. We account for this discrepancy to substructure present in the Southwest Peak. We estimate an axis ratio of $0.37\pm 0.1$ for A901b and $0.54^{+0.08}_{-0.09}$ for the Southwest Group.Comment: submitted to APJ, 25 pages, 13 figure

Intrinsic galaxy alignments from the 2SLAQ and SDSS surveys: luminosity and redshift scalings and implications for weak lensing surveys

Correlations between intrinsic shear and the density field on large scales, a potentially important contaminant for cosmic shear surveys, have been robustly detected at low redshifts with bright galaxies in Sloan Digital Sky Survey (SDSS) data. Here we present a more detailed characterization of this effect, which can cause anticorrelations between gravitational lensing shear and intrinsic ellipticity (GI correlations). This measurement uses 36 278 luminous red galaxies (LRGs) from the SDSS spectroscopic sample with 0.15 3σ detections of the effect on large scales (up to 60 h−1 Mpc) for all galaxy subsamples within the SDSS LRG sample; for the 2SLAQ sample, we find a 2σ detection for a bright subsample, and no detection for a fainter subsample. Fitting formulae are provided for the scaling of the GI correlations with luminosity, transverse separation and redshift (for which the 2SLAQ sample, while small, provides crucial constraints due to its longer baseline in redshift). We estimate contamination in the measurement of σ8 for future cosmic shear surveys on the basis of the fitted dependence of GI correlations on galaxy properties. We find contamination to the power spectrum ranging from −1.5 per cent (optimistic) to −33 per cent (pessimistic) for a toy cosmic shear survey using all galaxies to a depth of R= 24 using scales l≈ 500, though the central value of predicted contamination is −6.5 per cent. This corresponds to a bias in σ8 of Δσ8=−0.004 (optimistic), −0.02 (central) or −0.10 (pessimistic). We provide a prescription for inclusion of this error in cosmological parameter estimation codes. The principal uncertainty is in the treatment of the L≤L★ blue galaxies, for which we have no detection of the GI signal, but which could dominate the GI contamination if their GI amplitude is near our upper limits. Characterization of the tidal alignments of these galaxies, especially at redshifts relevant for cosmic shear, should be a high priority for the cosmic shear communit

The Third Gravitational Lensing Accuracy Testing (GREAT3) Challenge Handbook

The GRavitational lEnsing Accuracy Testing 3 (GREAT3) challenge is the third in a series of image analysis challenges, with a goal of testing and facilitating the development of methods for analyzing astronomical images that will be used to measure weak gravitational lensing. This measurement requires extremely precise estimation of very small galaxy shape distortions, in the presence of far larger intrinsic galaxy shapes and distortions due to the blurring kernel caused by the atmosphere, telescope optics, and instrumental effects. The GREAT3 challenge is posed to the astronomy, machine learning, and statistics communities, and includes tests of three specific effects that are of immediate relevance to upcoming weak lensing surveys, two of which have never been tested in a community challenge before. These effects include realistically complex galaxy models based on high-resolution imaging from space; spatially varying, physically-motivated blurring kernel; and combination of multiple different exposures. To facilitate entry by people new to the field, and for use as a diagnostic tool, the simulation software for the challenge is publicly available, though the exact parameters used for the challenge are blinded. Sample scripts to analyze the challenge data using existing methods will also be provided. See http://great3challenge.info and http://great3.projects.phys.ucl.ac.uk/leaderboard/ for more information.Comment: 30 pages, 13 figures, submitted for publication, with minor edits (v2) to address comments from the anonymous referee. Simulated data are available for download and participants can find more information at http://great3.projects.phys.ucl.ac.uk/leaderboard

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

New Constraints on the Complex Mass Substructure in Abell 1689 from Gravitational Flexion

In a recent publication, the flexion aperture mass statistic was found to provide a robust and effective method by which substructure in galaxy clusters might be mapped. Moreover, we suggested that the masses and mass profile of structures might be constrained using this method. In this paper, we apply the flexion aperture mass technique to HST ACS images of Abell 1689. We demonstrate that the flexion aperture mass statistic is sensitive to small-scale structures in the central region of the cluster. While the central potential is not constrained by our method, due largely to missing data in the central 0.5$^\prime$ of the cluster, we are able to place constraints on the masses and mass profiles of prominent substructures. We identify 4 separate mass peaks, and use the peak aperture mass signal and zero signal radius in each case to constrain the masses and mass profiles of these substructures. The three most massive peaks exhibit complex small-scale structure, and the masses indicated by the flexion aperture mass statistic suggest that these three peaks represent the dominant substructure component of the cluster ($\sim 7\times 10^{14}h^{-1}M_\odot$). Their complex structure indicates that the cluster -- far from being relaxed -- may have recently undergone a merger. The smaller, subsidiary peak is located coincident with a group of galaxies within the cluster, with mass $\sim 1\times10^{14}h^{-1}M_\odot$. These results are in excellent agreement with previous substructure studies of this cluster.Comment: 18 pages, 10 figures, MNRAS accepted (7 Dec 2010

ALFALFA HI Data Stacking I. Does the Bulge Quench Ongoing Star Formation in Early-Type Galaxies?

We have carried out an HI stacking analysis of a volume-limited sample of ~5000 galaxies with imaging and spectroscopic data from GALEX and the Sloan Digital Sky Survey, which lie within the current footprint of the Arecibo Legacy Fast ALFA (ALFALFA) Survey. Our galaxies are selected to have stellar masses greater than 10^10 Msun and redshifts in the range 0.025<z<0.05. We extract a sub-sample of 1833 "early-type" galaxies with inclinations less than 70deg, with concentration indices C>2.6 and with light profiles that are well fit by a De Vaucouleurs model. We then stack HI line spectra extracted from the ALFALFA data cubes at the 3-D positions of the galaxies from these two samples in bins of stellar mass, stellar mass surface density, central velocity dispersion, and NUV-r colour. We use the stacked spectra to estimate the average HI gas fractions M_HI/M_* of the galaxies in each bin. Our main result is that the HI content of a galaxy is not influenced by its bulge. The average HI gas fractions of galaxies in both our samples correlate most strongly with NUV-r colour and with stellar surface density. The relation between average HI fraction and these two parameters is independent of concentration index C. We have tested whether the average HI gas content of bulge-dominated galaxies on the red sequence, differs from that of late-type galaxies on the red sequence. We find no evidence that galaxies with a significant bulge component are less efficient at turning their available gas reservoirs into stars. This result is in contradiction with the "morphological quenching" scenario proposed by Martig et al. (2009).Comment: 21 pages, 15 figures. Accepted for publication in MNRAS. Version with high resolution figures available at http://www.mpa-garching.mpg.de/GASS/pubs.ph