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We perform a measurement of the mass-richness relation of the redMaPPer galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky Survey (SDSS). We have carefully characterized a broad range of systematic uncertainties, including shear calibration errors, photo-z biases, dilution by member galaxies, source obscuration, magnification bias, incorrect assumptions about cluster mass profiles, cluster centring, halo triaxiality and projection effects. We also compare measurements of the lensing signal from two independently produced shear and photometric redshift catalogues to characterize systematic errors in the lensing signal itself. Using a sample of 5570 clusters from 0.1 ≤ z ≤ 0.33, the normalization of our power-law mass versus λ relation is log10[M200m/h-1☉] = 14.344 ± 0.021 (statistical) ±0.023 (systematic) at a richness λ=40, a 7 per cent calibration uncertainty, with a power-law index of 1.33+0.09 -0.10 (1σ). The detailed systematics characterization in this work renders it the definitive weak lensing mass calibration for SDSS redMaPPer clusters at this time. [ABSTRACT FROM AUTHOR]

The shapes of distant galaxies are sheared by intervening galaxy clusters. We examine this effect in Stripe 82, a 275 deg² region observed multiple times in the Sloan Digital Sky Survey (SDSS) and co-added to achieve greater depth. We obtain a mass-richness calibration that is similar to other SDSS analyses, demonstrating that the co-addition process did not adversely affect the lensing signal. We also propose a new parameterization of the effect of tomography on the cluster lensing signal which does not require binning in redshift, and we show that using this parameterization we can detect tomography for stacked clusters at varying redshifts. Finally, due to the sensitivity of the tomographic detection to accurately marginalize over the effect of the cluster mass, we show that tomography at low redshift (where dependence on exact cosmological models is weak) can be used to constrain mass profiles in clusters. [ABSTRACT FROM AUTHOR]

We present details of the construction and characterization of the coaddition of the Sloan Digital Sky Survey (SDSS) Stripe 82 ugriz imaging data. This survey consists of 275 deg2 of repeated scanning by the SDSS camera over –50° ⩽ α ⩽ 60° and –1.°25 ⩽ δ ⩽ +1.°25 centered on the Celestial Equator. Each piece of sky has ∼20 runs contributing and thus reaches ∼2 mag fainter than the SDSS single pass data, i.e., to r ∼ 23.5 for galaxies. We discuss the image processing of the coaddition, the modeling of the point-spread function (PSF), the calibration, and the production of standard SDSS catalogs. The data have an r-band median seeing of 1.″1 and are calibrated to ⩽1%. Star color-color, number counts, and PSF size versus modeled size plots show that the modeling of the PSF is good enough for precision five-band photometry. Structure in the PSF model versus magnitude plot indicates minor PSF modeling errors, leading to misclassification of stars as galaxies, as verified using VVDS spectroscopy. There are a variety of uses for this wide-angle deep imaging data, including galactic structure, photometric redshift computation, cluster finding and cross wavelength measurements, weak lensing cluster mass calibrations, and cosmic shear measurements. [ABSTRACT FROM AUTHOR]

Stripe 82 in the Sloan Digital Sky Survey was observed multiple times, allowing deeper images to be constructed by co-adding the data. Here, we analyze the ellipticities of background galaxies in this 275 deg2 region, searching for evidence of distortions due to cosmic shear. We do so using measurements of both the shear-shear correlation function and power spectrum, with the latter determined using both “quadratic” and “pseudo” estimation techniques. We show how we verified these methods using mock catalogs. We also describe our methods for modeling and correcting for the effects of the point-spread function (PSF) in our shape measurements, and we also describe our prescription for estimating photometric redshifts (photo-z's) for our galaxy sample. In particular, we assess the impact of potential systematic effects due to the PSF and to photo-z's, and show that these are under control in our analysis. We find consistent correlation function and power spectrum results, where the E-mode cosmic shear signal is detected in both real and Fourier space with >5σ significance on degree scales, while the B-mode is consistent with zero as expected. The amplitude of the signal constrains the combination of the matter density Ωm and fluctuation amplitude σ8 to be Ω0.7mσ8 = 0.252+0.032– 0.052. [ABSTRACT FROM AUTHOR]