The magnification effect of gravitational lensing is a powerful probe of the distribution of matter in the universe, yet it is frequently overlooked due to the fact that its signal to noise is smaller than that of lensing shear. Because its systematic errors are quite different from those of shear, magnification is nevertheless an important approach with which to study the distribution of large scale structure. We present lensing mass profiles of spectroscopic luminous red galaxies (LRGs) and galaxy clusters determined through measurements of the weak lensing magnification of photometric LRGs in their background. We measure the change in detected galaxy counts as well as the increased average galaxy flux behind the lenses. In addition, we examine the average change in source color due to extinction by dust in the lenses. By simultaneously fitting these three probes we constrain the mass profiles and dust-to-mass ratios of the lenses in six bins of lens richness. For each richness bin we fit an NFW halo mass, brightest cluster galaxy (BCG) mass, second halo term, and dust-to-mass ratio. The resulting mass-richness relation is consistent with previous analyses of the catalogs, and limits on the dust-to-mass ratio in the lenses are in agreement with expectations. We explore the effects of including the (low signal-to-noise) flux magnification and reddening measurements in the analysis compared to using only the counts magnification data; the additional probes significantly improve the agreement between our measured mass-richness relation and previous results.
Accurate measurement of galaxy cluster masses is an essential component not only in studies of cluster physics, but also for probes of cosmology. However, different mass measurement techniques frequently yield discrepant results. The SDSS MaxBCG catalogs mass-richness relation has previously been constrained using weak lensing shear, Sunyaev-Zeldovich (SZ), and X-ray measurements. The mass normalization of the clusters as measured by weak lensing shear is >~25% higher than that measured using SZ and X-ray methods, a difference much larger than the stated measurement errors in the analyses. We constrain the mass-richness relation of the MaxBCG galaxy cluster catalog by measuring the gravitational lensing magnification of type I quasars in the background of the clusters. The magnification is determined using the quasars variability and the correlation between quasars variability amplitude and intrinsic luminosity. The mass-richness relation determined through magnification is in agreement with that measured using shear, confirming that the lensing strength of the clusters implies a high mass normalization, and that the discrepancy with other methods is not due to a shear-related systematic measurement error. We study the dependence of the measured mass normalization on the cluster halo orientation. As expected, line-of-sight clusters yield a higher normalization; however, this minority of haloes does not significantly bias the average mass-richness relation of the catalog.
We introduce a technique to measure gravitational lensing magnification using the variability of type I quasars. Quasars variability amplitudes and luminosities are tightly correlated, on average. Magnification due to gravitational lensing increases the quasars apparent luminosity, while leaving the variability amplitude unchanged. Therefore, the mean magnification of an ensemble of quasars can be measured through the mean shift in the variability-luminosity relation. As a proof of principle, we use this technique to measure the magnification of quasars spectroscopically identified in the Sloan Digital Sky Survey, due to gravitational lensing by galaxy clusters in the SDSS MaxBCG catalog. The Palomar-QUEST Variability Survey, reduced using the DeepSky pipeline, provides variability data for the sources. We measure the average quasar magnification as a function of scaled distance (r/R200) from the nearest cluster; our measurements are consistent with expectations assuming NFW cluster profiles, particularly after accounting for the known uncertainty in the clusters centers. Variability-based lensing measurements are a valuable complement to shape-based techniques because their systematic errors are very different, and also because the variability measurements are amenable to photometric errors of a few percent and to depths seen in current wide-field surveys. Given the data volume expected from current and upcoming surveys, this new technique has the potential to be competitive with weak lensing shear measurements of large scale structure.
