In order to study the galaxy population of galaxy clusters with photometric data one must be able to accurately discriminate between cluster members and non-members. The redMaPPer cluster finding algorithm treats this problem probabilistically. Here,
we utilize SDSS and GAMA spectroscopic membership rates to validate the redMaPPer membership probability estimates for clusters with $zin[0.1,0.3]$. We find small - but correctable - biases, sourced by three different systematics. The first two were expected a priori, namely blue cluster galaxies and correlated structure along the line of sight. The third systematic is new: the redMaPPer template fitting exhibits a non-trivial dependence on photometric noise, which biases the original redMaPPer probabilities when utilizing noisy data. After correcting for these effects, we find exquisite agreement ($approx 1%$) between the photometric probability estimates and the spectroscopic membership rates, demonstrating that we can robustly recover cluster membership estimates from photometric data alone. As a byproduct of our analysis we find that on average unavoidable projection effects from correlated structure contribute $approx 6%$ of the richness of a redMaPPer galaxy cluster. This work also marks the second public release of the SDSS redMaPPer cluster 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 si
gnal 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.
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.
The precision of cosmological parameters derived from galaxy cluster surveys is limited by uncertainty in relating observable signals to cluster mass. We demonstrate that a small mass-calibration follow-up program can significantly reduce this uncert
ainty and improve parameter constraints, particularly when the follow-up targets are judiciously chosen. To this end, we apply a simulated annealing algorithm to maximize the dark energy information at fixed observational cost, and find that optimal follow-up strategies can reduce the observational cost required to achieve a specified precision by up to an order of magnitude. Considering clusters selected from optical imaging in the Dark Energy Survey, we find that approximately 200 low-redshift X-ray clusters or massive Sunyaev-Zeldovich clusters can improve the dark energy figure of merit by 50%, provided that the follow-up mass measurements involve no systematic error. In practice, the actual improvement depends on (1) the uncertainty in the systematic error in follow-up mass measurements, which needs to be controlled at the 5% level to avoid severe degradation of the results; and (2) the scatter in the optical richness-mass distribution, which needs to be made as tight as possible to improve the efficacy of follow-up observations.
Self-calibration techniques for analyzing galaxy cluster counts utilize the abundance and the clustering amplitude of dark matter halos. These properties simultaneously constrain cosmological parameters and the cluster observable-mass relation. It wa
s recently discovered that the clustering amplitude of halos depends not only on the halo mass, but also on various secondary variables, such as the halo formation time and the concentration; these dependences are collectively termed assembly bias. Applying modified Fisher matrix formalism, we explore whether these secondary variables have a significant impact on the study of dark energy properties using the self-calibration technique in current (SDSS) and the near future (DES, SPT, and LSST) cluster surveys. The impact of the secondary dependence is determined by (1) the scatter in the observable-mass relation and (2) the correlation between observable and secondary variables. We find that for optical surveys, the secondary dependence does not significantly influence an SDSS-like survey; however, it may affect a DES-like survey (given the high scatter currently expected from optical clusters) and an LSST-like survey (even for low scatter values and low correlations). For an SZ survey such as SPT, the impact of secondary dependence is insignificant if the scatter is 20% or lower but can be enhanced by the potential high scatter values introduced by a highly correlated background. Accurate modeling of the assembly bias is necessary for cluster self-calibration in the era of precision cosmology.
Minimizing the scatter between cluster mass and accessible observables is an important goal for cluster cosmology. In this work, we introduce a new matched filter richness estimator, and test its performance using the maxBCG cluster catalog. Our new
estimator significantly reduces the variance in the L_X-richness relation, from sigma_{ln L_X}^2=(0.86pm0.02)^2 to sigma_{ln L_X}^2=(0.69pm0.02)^2. Relative to the maxBCG richness estimate, it also removes the strong redshift dependence of the richness scaling relations, and is significantly more robust to photometric and redshift errors. These improvements are largely due to our more sophisticated treatment of galaxy color data. We also demonstrate the scatter in the L_X-richness relation depends on the aperture used to estimate cluster richness, and introduce a novel approach for optimizing said aperture which can be easily generalized to other mass tracers.
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 le
nsing 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.
