Cross-correlation weak lensing of SDSS galaxy clusters. I. Measurements (original) (raw)
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Arxiv preprint arXiv: …, 2007
We interpret and model the statistical weak lensing measurements around 130,000 groups and clusters of galaxies in the Sloan Digital Sky Survey presented by . We present non-parametric inversions of the 2D shear profiles to the mean 3D cluster density and mass profiles in bins of both optical richness and cluster i-band luminosity. Since the mean cluster density profile is proportional to the cluster-mass correlation function, the mean profile is spherically symmetric by the assumptions of large-scale homogeneity and isotropy. We correct the inferred 3D profiles for systematic effects, including non-linear shear and the fact that cluster halos are not all precisely centered on their brightest galaxies. We also model the measured cluster shear profile as a sum of contributions from the brightest central galaxy, the cluster dark matter halo, and neighboring halos. We infer the relations between mean cluster virial mass and optical richness and luminosity over two orders of magnitude in cluster mass; the virial mass at fixed richness or luminosity is determined with a precision of ∼ 13% including both statistical and systematic errors. We also constrain the halo concentration parameter and halo bias as a function of cluster mass; both are in good agreement with predictions from N-body simulations of LCDM models. The methods employed here will be applicable to deeper, wide-area optical surveys that aim to constrain the nature of the dark energy, such as the Dark Energy Survey, the Large Synoptic Survey Telescope and space-based surveys.
Cross-correlation Weak Lensing of SDSS Galaxy Clusters. III. Mass-to-Light Ratios
Astrophysical Journal, 2009
We present measurements of the excess mass-to-light ratio measured around MaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with M 200 ∼ 5 × 10 12 h −1 M ⊙ to clusters with M 200 ∼ 10 15 h −1 M ⊙ . Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean ∆ρ(r) = ρ(r) −ρ for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density ∆ℓ(r) = ℓ(r) −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 25h −1 kpc to 22h −1 Mpc. 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 ρ(r) ≫ρ, the integrated mass-to-light profile (∆M/∆L)(r) 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 ρ(r) ∼ρ, 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 (∆M/∆L) 200 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 M/L = 362 ± 54h (statistical). There is additional uncertainty in the overall calibration at the ∼10% level. The parameter b 2 M/L 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 Ω m b −2 M/L = 0.20 ± 0.03, independent of the Hubble parameter.
The Galaxy-Mass Correlation Function Measured from Weak Lensing in the Sloan Digital Sky Survey
The Astronomical Journal, 2004
We present galaxy-galaxy lensing measurements over scales 0.025 to 10 h −1 Mpc in the Sloan Digital Sky Survey. Using a flux-limited sample of 127,001 lens galaxies with spectroscopic redshifts and mean luminosity L ∼ L * and 9,020,388 source galaxies with photometric redshifts, we invert the lensing signal to obtain the galaxy-mass correlation function ξ gm . We find ξ gm is consistent with a power-law, ξ gm = (r/r 0 ) −γ , with best-fit parameters γ = 1.79 ± 0.06 and r 0 = (5.4 ± 0.7)(0.27/Ω m ) 1/γ h −1 Mpc. At fixed separation, the ratio ξ gg /ξ gm = b/r where b is the bias and r is the correlation coefficient. Comparing to the galaxy auto-correlation function for a similarly selected sample of SDSS galaxies, we find that b/r is approximately scale independent over scales 0.2 − 6.7h −1 Mpc, with mean b/r = (1.3 ± 0.2)(Ω m /0.27). We also find no scale dependence in b/r for a volume limited sample of luminous galaxies (−23.0 < M r < −21.5). The mean b/r for this sample is b/r V lim = (2.0 ± 0.7)(Ω m /0.27). We split the lens galaxy sample into subsets based on luminosity, color, spectral type, and velocity dispersion, and see clear trends of the lensing signal with each of these parameters. The amplitude and logarithmic slope of ξ gm increases with galaxy luminosity. For high luminosities (L ∼ 5L * ), ξ gm deviates significantly from a power law. These trends with luminosity also appear in the subsample of red galaxies, which are more strongly clustered than blue galaxies. Subject headings: cosmology:observations -dark matter -gravitational lensing -large-scale structure of the universe
Weak-Lensing Measurements of 42 SDSS/RASS Galaxy Clusters
The Astrophysical Journal, 2001
We present a lensing study of 42 galaxy clusters imaged in Sloan Digital Sky Survey (SDSS) commissioning data. Cluster candidates are selected optically from SDSS imaging data and confirmed for this study by matching to X-ray sources found independently in the ROSAT all sky survey (RASS). Five color SDSS photometry is used to make accurate (∆z=0.018) photometric redshift estimates that are used to rescale and combine the lensing measurements. The mean shear from these clusters is detected to 2h −1 Mpc at the 7-σ level, corresponding to a mass within that radius of (4.2 ± 0.6)× 10 14 h −1 M ⊙ . The shear profile is well fit by a power law with index −0.9±0.3, consistent with that of an isothermal density profile. Clusters are divided by X-ray luminosity into two subsets, with mean L X of (0.14 ± 0.03) × 10 44 and (1.0 ± 0.09) × 10 44 h −2 ergs/s. The average lensing signal is converted to a projected mass density based on fits to isothermal density profiles. From this we calculate a mean r 500 (the radius at which the mean density falls to 500 times the critical density) and M(< r 500 ). The mass contained within r 500 differs substantially between the low-and high-L X bins, with (0.7 ± 0.2) × 10 14 and 2.7 +0.9 −1.1 × 10 14 h −1 M ⊙ respectively. This paper demonstrates our ability to measure ensemble cluster masses from SDSS imaging data. The full SDSS data set will include 1000 SDSS/RASS clusters. With this large data set we will measure the M-L X relation with high precision and put direct constraints on the mass density of the universe.
The Astrophysical Journal, 2012
The shapes of distant galaxies are sheared by intervening galaxy clusters. We examine this effect in Stripe 82, a 275 square degree region observed multiple times in the Sloan Digital Sky Survey and coadded to achieve greater depth. We obtain a mass-richness calibration that is similar to other SDSS analyses, demonstrating that the coaddition 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 marginalizing 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.
The Astronomical …, 2000
We present measurements of galaxy-galaxy weak lensing from 225 deg2 of early commissioning imaging data from the Sloan Digital Sky Survey (SDSS). We measure a mean tangential shear around a stacked sample of foreground galaxies in three bandpasses (g@, r@, and i@) out to angular radii of 600@@, detecting the shear signal at very high statistical signiÐcance. The shear proÐle is well described by a power law with best-Ðt slope of g \ 0.7È1.1 (95% conÐdence). In the range h \ 10@@È600@@, c T \ c T0 (1@/h)g, the mean tangential shear is approximately 6^1 ] 10~4 in all three bands. A variety of rigorous tests demonstrate the reality of the gravitational lensing signal and conÐrm the uncertainty estimates. In particular, we obtain shear measurements consistent with zero when we rotate the background galaxies by 45¡, replace foreground galaxies with random points, or replace foreground galaxies with bright stars. We interpret our results by assuming that all matter correlated with galaxies belongs to the galaxies. We model the mass distributions of the foreground galaxies, which have a mean luminosity SL (h \ 5@@)T \ 8.7^0.7 ] 109 h~2 1.4^0.12 ] 1010 h~2 1.8^0.14 ] 1010 h~2 as L g{_ , L r{_ , L i{_ , approximately isothermal spheres characterized by a velocity dispersion and a truncation radius s. p v The velocity dispersion is constrained to be km s~1 at 95% conÐdence (145È195 km s~1 p v \ 150È190 including systematic uncertainties), consistent with previous determinations but with smaller error bars. Our detection of shear at large angular radii sets a 95% conÐdence lower limit s [ 140@@, corresponding to a physical radius of 260 h~1 kpc, implying that the dark halos of typical luminous galaxies extend to very large radii. However, it is likely that this is being systematically biased to large value by di †use matter in the halos of groups and clusters of galaxies. We also present a preliminary determination of the galaxy-mass correlation function, Ðnding a correlation length similar to the galaxy autocorrelation function and consistency with a low matter density universe with modest bias.
Astronomical Journal, 2000
We present measurements of galaxy-galaxy weak lensing from 225 deg2 of early commissioning imaging data from the Sloan Digital Sky Survey (SDSS). We measure a mean tangential shear around a stacked sample of foreground galaxies in three bandpasses (g@, r@, and i@) out to angular radii of 600@@, detecting the shear signal at very high statistical signiÐcance. The shear proÐle is well described by a power law with best-Ðt slope of g \ 0.7È1.1 (95% conÐdence). In the range h \ 10@@È600@@, c T \ c T0 (1@/h)g, the mean tangential shear is approximately 6^1 ] 10~4 in all three bands. A variety of rigorous tests demonstrate the reality of the gravitational lensing signal and conÐrm the uncertainty estimates. In particular, we obtain shear measurements consistent with zero when we rotate the background galaxies by 45¡, replace foreground galaxies with random points, or replace foreground galaxies with bright stars. We interpret our results by assuming that all matter correlated with galaxies belongs to the galaxies. We model the mass distributions of the foreground galaxies, which have a mean luminosity SL (h \ 5@@)T \ 8.7^0.7 ] 109 h~2 1.4^0.12 ] 1010 h~2 1.8^0.14 ] 1010 h~2 as L g{_ , L r{_ , L i{_ , approximately isothermal spheres characterized by a velocity dispersion and a truncation radius s. p v The velocity dispersion is constrained to be km s~1 at 95% conÐdence (145È195 km s~1 p v \ 150È190 including systematic uncertainties), consistent with previous determinations but with smaller error bars. Our detection of shear at large angular radii sets a 95% conÐdence lower limit s [ 140@@, corresponding to a physical radius of 260 h~1 kpc, implying that the dark halos of typical luminous galaxies extend to very large radii. However, it is likely that this is being systematically biased to large value by di †use matter in the halos of groups and clusters of galaxies. We also present a preliminary determination of the galaxy-mass correlation function, Ðnding a correlation length similar to the galaxy autocorrelation function and consistency with a low matter density universe with modest bias.
Monthly Notices of the Royal Astronomical Society, 2014
This is the first in a series of papers in which we measure accurate weak-lensing masses for 51 of the most X-ray luminous galaxy clusters known at redshifts 0.15 z Cl 0.7, in order to calibrate X-ray and other mass proxies for cosmological cluster experiments. The primary aim is to improve the absolute mass calibration of cluster observables, currently the dominant systematic uncertainty for cluster count experiments. Key elements of this work are the rigorous quantification of systematic uncertainties, high quality data reduction and photometric calibration, and the "blind" nature of the analysis to avoid confirmation bias. Our target clusters are drawn from X-ray catalogs based on the ROSAT All-Sky Survey, and provide a versatile calibration sample for many aspects of cluster cosmology. We have acquired widefield, high-quality imaging using the Subaru and CFHT telescopes for all 51 clusters, in at least three bands per cluster. For a subset of 27 clusters, we have data in at least five bands, allowing accurate photometric redshift estimates of lensed galaxies. In this paper, we describe the cluster sample and observations, and detail the processing of the SuprimeCam data to yield high-quality images suitable for robust weak-lensing shape measurements and precision photometry. For each cluster, we present wide-field three-color optical images and maps of the weak-lensing mass distribution, the optical light distribution, and the X-ray emission. These provide insights into the large-scale structure in which the clusters are embedded. We measure the offsets between X-ray flux centroids and the Brightest Cluster Galaxies in the clusters, finding these to be small in general, with a median of 20 kpc. For offsets 100 kpc, weak-lensing mass measurements centered on the Brightest Cluster Galaxies agree well with values determined relative to the X-ray centroids; miscentering is therefore not a significant source of systematic uncertainty for our weak-lensing mass measurements. In accompanying papers we discuss the key aspects of our photometric calibration and photometric redshift measurements (Kelly et al.), and measure cluster masses using two methods, including a novel Bayesian weak-lensing approach that makes full use of the photometric redshift probability distributions for individual background galaxies (Applegate et al.). In subsequent papers, we will incorporate these weak-lensing mass measurements into a self-consistent framework to simultaneously determine cluster scaling relations and cosmological parameters.
Combined strong and weak lensing analysis of 28 clusters from the Sloan Giant Arcs Survey★
Monthly Notices of the Royal Astronomical Society, 2012
We study the mass distribution of a sample of 28 galaxy clusters using strong and weak lensing observations. The clusters are selected via their strong lensing properties as part of the Sloan Giant Arcs Survey (SGAS) from the Sloan Digital Sky Survey (SDSS). Mass modelling of the strong lensing information from the giant arcs is combined with weak lensing measurements from deep Subaru/Suprime-cam images to primarily obtain robust constraints on the concentration parameter and the shape of the mass distribution. We find that the concentration c vir is a steep function of the mass, c vir ∝ M −0.59±0.12 vir , with the value roughly consistent with the lensing-bias-corrected theoretical expectation for high-mass (∼10 15 h −1 M) clusters. However, the observationally inferred concentration parameters appear to be much higher at lower masses (∼10 14 h −1 M), possibly a consequence of the modification to the inner density profiles provided by baryon cooling. The steep mass-concentration relation is also supported from direct stacking analysis of the tangential shear profiles. In addition, we explore the 2D shape of the projected mass distribution by stacking weak lensing shear maps of individual clusters with prior information on the position angle from strong lens modelling, and find significant evidence for a large mean ellipticity with the best-fitting value of e = 0.47 ± 0.06 for the mass distribution of the stacked sample. We find that the luminous cluster member galaxy distribution traces the overall mass distribution very well, although the distribution of fainter cluster galaxies appears to be more extended than the total mass.
Galaxy cluster strong lensing cosmography
Astronomy & Astrophysics, 2022
Cluster strong lensing cosmography is a promising probe of the background geometry of the Universe and several studies have emerged thanks to the increased quality of observations using space- and ground-based telescopes. For the first time, we used a sample of five cluster strong lenses to measure the values of cosmological parameters and combine them with those from classical probes. In order to assess the degeneracies and the effectiveness of strong-lensing cosmography in constraining the background geometry of the Universe, we adopted four cosmological scenarios. We found good constraining power on the total matter density of the Universe (Ωm) and the equation of state of the dark energy parameter w. For a flat wCDM cosmology, we found Ωm = 0.30−0.11+0.09 and w = −1.12−0.32+0.17 from strong lensing only. Interestingly, we show that the constraints from the cosmic microwave background (CMB) are improved by factors of 2.5 and 4.0 on Ωm and w, respectively, when combined with our p...