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Register a new userConstraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data
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We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find sigma_{ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between ln Lx and ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.
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Determining the scaling relations between galaxy cluster observables requires large samples of uniformly observed clusters. We measure the mean X-ray luminosity--optical richness (L_X--N_200) relation for an approximately volume-limited sample of more than 17,000 optically-selected clusters from the maxBCG catalog spanning the redshift range 0.1<z<0.3. By stacking the X-ray emission from many clusters using ROSAT All-Sky Survey data, we are able to measure mean X-ray luminosities to ~10% (including systematic errors) for clusters in nine independent optical richness bins. In addition, we are able to crudely measure individual X-ray emission from ~800 of the richest clusters. Assuming a log-normal form for the scatter in the L_X--N_200 relation, we measure sigma_ln{L}=0.86+/-0.03 at fixed N_200. This scatter is large enough to significantly bias the mean stacked relation. The corrected median relation can be parameterized by L_X = (e^alpha)(N_200/40)^beta 10^42 h^-2 ergs/s, where alpha = 3.57+/-0.08 and beta = 1.82+/-0.05. We find that X-ray selected clusters are significantly brighter than optically-selected clusters at a given optical richness. This selection bias explains the apparently X-ray underluminous nature of optically-selected cluster catalogs.
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.
The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202+/-10 km/s for small groups to more than 854+/-102 km/s for large clusters. We show the scatter to be at most 40.5+/-3.5%, declining to 14.9+/-9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within one-sigma of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass-observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.
Maximizing the utility of upcoming photometric cluster surveys requires a thorough understanding of the richness-mass relation of galaxy clusters. We use Monte Carlo simulations to study the impact of various sources of observational scatter on this relation. Cluster ellipticity, photometric errors, photometric redshift errors, and cluster-to-cluster variations in the properties of red-sequence galaxies contribute negligible noise. Miscentering, however, can be important, and likely contributes to the scatter in the richness-mass relation of galaxy maxBCG clusters at the low mass end, where centering is more difficult. We also investigate the impact of projection effects under several empirically motivated assumptions about cluster environments. Using SDSS data and the maxBCG cluster catalog, we demonstrate that variations in cluster environments can rarely (approx 1% - 5% of the time) result in significant richness boosts. Due to the steepness of the mass/richness function, the corresponding fraction of optically selected clusters that suffer from these projection effects is approx 5% - 15%. We expect these numbers to be generic in magnitude, but a precise determination requires detailed, survey-specific modeling.
We constrain the scaling relation between optical richness ($lambda$) and halo mass ($M$) for a sample of SDSS redMaPPer galaxy clusters within the context of the {it Planck} cosmological model. We use a forward modeling approach where we model the probability distribution of optical richness for a given mass, $P(ln lambda| M)$. To model the abundance and the stacked lensing profiles, we use an emulator specifically built to interpolate the halo mass function and the stacked lensing profile for an arbitrary set of halo mass and redshift, which is calibrated based on a suite of high-resolution $N$-body simulations. We apply our method to 8,312 SDSS redMaPPer clusters with $20le lambda le 100$ and $0.10le z_{lambda}le0.33$, and show that the log-normal distribution model for $P(lambda|M)$, with four free parameters, well reproduces the measured abundances and lensing profiles simultaneously. The constraints are characterized by the mean relation, $leftlangle ln{lambda}rightrangle(M)=A+Bln(M/M_{rm pivot})$, with $A=3.207^{+0.044}_{-0.046}$ and $B=0.993^{+0.041}_{-0.055}$ (68%~CL), where the pivot mass scale $M_{rm pivot}=3times 10^{14} h^{-1}M_odot$, and the scatter $sigma_{mathrm{lnlambda}|M}=sigma_0+qln(M/M_{rm pivot})$ with $sigma_0=0.456^{+0.047}_{-0.039}$ and $q=-0.169^{+0.035}_{-0.026}$. We find that a large scatter in halo masses is required at the lowest richness bins ($20le lambda lesssim 30$) in order to reproduce the measurements. Without such a large scatter, the model prediction for the lensing profiles tends to overestimate the measured amplitudes. This might imply a possible contamination of intrinsically low-richness clusters due to the projection effects. Such a low-mass halo contribution is significantly reduced when applying our method to the sample of $30le lambda le 100$.
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