The Bayesian gravitational shear estimation algorithm developed by Bernstein and Armstrong (2014) can potentially be used to overcome multiplicative noise bias and recover shear using very low signal-to-noise ratio (S/N) galaxy images. In that work t
he authors confirmed the method is nearly unbiased in a simplified demonstration, but no test was performed on images with realistic pixel noise. Here I present a full implementation for fitting models to galaxy images, including the effects of a point spread function (PSF) and pixelization. I tested the implementation using simulated galaxy images modeled as Sersic profiles with n=1 (exponential) and n=4 (De Vaucouleurs), convolved with a PSF and a flat pixel response function. I used a round Gaussian model for the PSF to avoid potential PSF-fitting errors. I simulated galaxies with mean observed, post-PSF full-width at half maximum equal to approximately 1.2 times that of the PSF, with log-normal scatter. I also drew fluxes from a log-normal distribution. I produced independent simulations, each with pixel noise tuned to produce different mean S/N ranging from 10-1000. I applied a constant shear to all images. I fit the simulated images to a model with the true Sersic index to avoid modeling biases. I recovered the input shear with fractional error less than 2 x 10^{-3} in all cases. In these controlled conditions, and in the absence of other multiplicative errors, this implementation is sufficiently unbiased for current surveys and approaches the requirements for planned surveys.
We present redshift probability distributions for galaxies in the SDSS DR8 imaging data. We used the nearest-neighbor weighting algorithm presented in Lima et al. 2008 and Cunha et al. 2009 to derive the ensemble redshift distribution N(z), and indiv
idual redshift probability distributions P(z) for galaxies with r < 21.8. As part of this technique, we calculated weights for a set of training galaxies with known redshifts such that their density distribution in five dimensional color-magnitude space was proportional to that of the photometry-only sample, producing a nearly fair sample in that space. We then estimated the ensemble N(z) of the photometric sample by constructing a weighted histogram of the training set redshifts. We derived P(z) s for individual objects using the same technique, but limiting to training set objects from the local color-magnitude space around each photometric object. Using the P(z) for each galaxy, rather than an ensemble N(z), can reduce the statistical error in measurements that depend on the redshifts of individual galaxies. The spectroscopic training sample is substantially larger than that used for the DR7 release, and the newly added PRIMUS catalog is now the most important training set used in this analysis by a wide margin. We expect the primary source of error in the N(z) reconstruction is sample variance: the training sets are drawn from relatively small volumes of space. Using simulations we estimated the uncertainty in N(z) at a given redshift is 10-15%. The uncertainty on calculations incorporating N(z) or P(z) depends on how they are used; we discuss the case of weak lensing measurements. The P(z) catalog is publicly available from the SDSS website.
We present measurements of the excess mass-to-light ratio measured aroundMaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with masses ranging from ~5x10^{12} to ~10^{15} M_{sun}/h. Using
cross-correlation weak lensing, we measure the excess mass density profile above the universal mean Delta rho(r) = rho(r) - bar{rho} for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density Delta l(r) = l(r) - bar{l} measured in the z=0.25 i-band. For both mass and light, we de-project the profiles to produce 3D mass and light profiles over scales from 25 kpc/ to 22 Mpc/h. From these profiles we calculate the cumulative excess mass M(r) and excess light L(r) as a function of separation from the BCG. On small scales, where rho(r) >> bar{rho}, the integrated mass-to-light profile may be interpreted as the cluster mass-to-light ratio. We find the M/L_{200}, the mass-to-light ratio within r_{200}, scales with cluster mass as a power law with index 0.33+/-0.02. On large scales, where rho(r) ~ bar{rho}, the M/L approaches an asymptotic value independent of cluster richness. For small groups, the mean M/L_{200} is much smaller than the asymptotic value, while for large clusters it is consistent with the asymptotic value. This asymptotic value should be proportional to the mean mass-to-light ratio of the universe <M/L>. We find <M/L>/b^2_{ml} = 362+/-54 h (statistical). There is additional uncertainty in the overall calibration at the ~10% level. The parameter b_{ml} is primarily a function of the bias of the L <~ L_* galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find Omega_m/b^2_{ml} = 0.02+/-0.03, independent of the Hubble parameter.
This is the first in a series of papers on the weak lensing effect caused by clusters of galaxies in Sloan Digital Sky Survey. The photometrically selected cluster sample, known as MaxBCG, includes ~130,000 objects between redshift 0.1 and 0.3, rangi
ng in size from small groups to massive clusters. We split the clusters into bins of richness and luminosity and stack the surface density contrast to produce mean radial profiles. The mean profiles are detected over a range of scales, from the inner halo (25 kpc/h) well into the surrounding large scale structure (30 Mpc/h), with a significance of 15 to 20 in each bin. The signal over this large range of scales is best interpreted in terms of the cluster-mass cross-correlation function. We pay careful attention to sources of systematic error, correcting for them where possible. The resulting signals are calibrated to the ~10% level, with the dominant remaining uncertainty being the redshift distribution of the background sources. We find that the profiles scale strongly with richness and luminosity. We find the signal within a given richness bin depends upon luminosity, suggesting that luminosity is more closely correlated with mass than galaxy counts. We split the samples by redshift but detect no significant evolution. The profiles are not well described by power laws. In a subsequent series of papers we invert the profiles to three-dimensional mass profiles, show that they are well fit by a halo model description, measure mass-to-light ratios and provide a cosmological interpretation.
