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Register a new userConstraints on the mass-richness relation from the abundance and weak lensing of SDSS clusters
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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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Constraining the relation between the richness $N$ and the halo mass $M$ over a wide redshift range for optically-selected clusters is a key ingredient for cluster-related science in optical surveys, including the Subaru Hyper Suprime-Cam (HSC) survey. We measure stacked weak lensing profiles around 1747 HSC CAMIRA clusters over a redshift range of $0.1leq z_{rm cl}leq 1.0$ with $Ngeq 15$ using the HSC first-year shear catalog covering $sim$$140$ ${rm deg^2}$. The exquisite depth and image quality of the HSC survey allow us to measure lensing signals around the high-redshift clusters at $0.7leq z_{rm cl}leq 1.0$ with a signal-to-noise ratio of 19 in the comoving radius range $0.5lesssim Rlesssim 15 h^{-1}{rm Mpc}$. We constrain richness-mass relations $P(ln N|M,z)$ of the HSC CAMIRA clusters assuming a log-normal distribution without informative priors on model parameters, by jointly fitting to the lensing profiles and abundance measurements under both Planck and WMAP cosmological models. We show that our model gives acceptable $p$-values when we add redshift dependent terms which are proportional to $ln (1+z)$ and $[ln (1+z)]^{2}$ into the mean and scatter relations of $P(ln N|M,z)$. Such terms presumably originate from the variation of photometric redshift errors as a function of the redshift. We show that the constraints on the mean relation $langle M|N rangle$ are consistent between the Planck and WMAP models, whereas the scatter values $sigma_{ln M|N}$ for the Planck model are systematically larger than those for the WMAP model. We also show that the scatter values for the Planck model increase toward lower richness values, whereas those for the WMAP model are consistent with constant values as a function of richness. This result highlights the importance of the scatter in the mass-richness relation for cluster cosmology.
The COnstrain Dark Energy with X-ray clusters (CODEX) sample contains the largest flux limited sample of X-ray clusters at $0.35 < z < 0.65$. It was selected from ROSAT data in the 10,000 square degrees of overlap with BOSS, mapping a total number of 2770 high-z galaxy clusters. We present here the full results of the CFHT CODEX program on cluster mass measurement, including a reanalysis of CFHTLS Wide data, with 25 individual lensing-constrained cluster masses. We employ $lensfit$ shape measurement and perform a conservative colour-space selection and weighting of background galaxies. Using the combination of shape noise and an analytic covariance for intrinsic variations of cluster profiles at fixed mass due to large scale structure, miscentring, and variations in concentration and ellipticity, we determine the likelihood of the observed shear signal as a function of true mass for each cluster. We combine 25 individual cluster mass likelihoods in a Bayesian hierarchical scheme with the inclusion of optical and X-ray selection functions to derive constraints on the slope $alpha$, normalization $beta$, and scatter $sigma_{ln lambda | mu}$ of our richness-mass scaling relation model in log-space: $left<ln lambda | mu right> = alpha mu + beta$, with $mu = ln (M_{200c}/M_{mathrm{piv}})$, and $M_{mathrm{piv}} = 10^{14.81} M_{odot}$. We find a slope $alpha = 0.49^{+0.20}_{-0.15}$, normalization $ exp(beta) = 84.0^{+9.2}_{-14.8}$ and $sigma_{ln lambda | mu} = 0.17^{+0.13}_{-0.09}$ using CFHT richness estimates. In comparison to other weak lensing richness-mass relations, we find the normalization of the richness statistically agreeing with the normalization of other scaling relations from a broad redshift range ($0.0<z<0.65$) and with different cluster selection (X-ray, Sunyaev-Zeldovich, and optical).
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 derive constraints on the matter density Om and the amplitude of matter clustering sig8 from measurements of large scale weak lensing (projected separation R=5-30hmpc) by clusters in the Sloan Digital Sky Survey MaxBCG catalog. The weak lensing signal is proportional to the product of Om and the cluster-mass correlation function xicm. With the relation between optical richness and cluster mass constrained by the observed cluster number counts, the predicted lensing signal increases with increasing Om or sig8, with mild additional dependence on the assumed scatter between richness and mass. The dependence of the signal on scale and richness partly breaks the degeneracies among these parameters. We incorporate external priors on the richness-mass scatter from comparisons to X-ray data and on the shape of the matter power spectrum from galaxy clustering, and we test our adopted model for xicm against N-body simulations. Using a Bayesian approach with minimal restrictive priors, we find sig8(Om/0.325)^{0.501}=0.828 +/- 0.049, with marginalized constraints of Om=0.325_{-0.067}^{+0.086} and sig8=0.828_{-0.097}^{+0.111}, consistent with constraints from other MaxBCG studies that use weak lensing measurements on small scales (R<=2hmpc). The (Om,sig8) constraint is consistent with and orthogonal to the one inferred from WMAP CMB data, reflecting agreement with the structure growth predicted by GR for an LCDM cosmological model. A joint constraint assuming LCDM yields Om=0.298 +/- 0.020 and sig8=0.831 +/- 0.020. Our cosmological parameter errors are dominated by the statistical uncertainties of the large scale weak lensing measurements, which should shrink sharply with current and future imaging surveys.
We present a statistical weak-lensing magnification analysis on an optically selected sample of 3029 texttt{CAMIRA} galaxy clusters with richness $N>15$ at redshift $0.2leq z <1.1$ in the Subaru Hyper Suprime-Cam (HSC) survey. We use two distinct populations of color-selected, flux-limited background galaxies, namely the low-$z$ and high-$z$ samples at mean redshifts of $approx1.1$ and $approx1.4$, respectively, from which to measure the weak-lensing magnification signal by accounting for cluster contamination as well as masking effects. Our magnification bias measurements are found to be uncontaminated according to validation tests against the null-test samples for which the net magnification bias is expected to vanish. The magnification bias for the full texttt{CAMIRA} sample is detected at a significance level of $9.51sigma$, which is dominated by the high-$z$ background. We forward-model the observed magnification data to constrain the normalization of the richness-to-mass ($N$--$M$) relation for the texttt{CAMIRA} sample with informative priors on other parameters. The resulting scaling relation is $Npropto {M_{500}}^{0.92pm0.13} (1 + z)^{-0.48pm0.69}$, with a characteristic richness of $N=left(17.72pm2.60right)$ and intrinsic log-normal scatter of $0.15pm0.07$ at $M_{500} = 10^{14}h^{-1}M_{odot}$. With the derived $N$--$M$ relation, we provide magnification-calibrated mass estimates of individual texttt{CAMIRA} clusters, with the typical uncertainty of $approx39%$ and $approx32%$ at richness$approx20$ and $approx40$, respectively. We further compare our magnification-inferred $N$--$M$ relation with those from the shear-based results in the literature, finding good agreement.
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