Cosmological Constraints from the SDSS maxBCG Cluster Catalog

TL;DR

This study demonstrates that optical cluster abundances, when combined with weak-lensing mass measurements, can yield cosmological constraints competitive with X-ray cluster studies. Using a Bayesian self-calibration framework, the authors jointly constrain the matter fluctuation amplitude and density while simultaneously mapping the richness of clusters to their mass. The fiducial maxBCG data produce a robust constraint on a combined parameter; when paired with WMAP5 priors, they give precise values for the matter density and fluctuation amplitude that align with X-ray constraints, strengthening the case for cluster abundances as a precision cosmology tool. The dominant systematics arise from weak-lensing mass calibration and the scatter in the richness–mass relation, and the work outlines concrete paths—better mass calibration and improved richness estimators—to further tighten these constraints while leveraging additional cluster observables.

Abstract

We use the abundance and weak lensing mass measurements of the SDSS maxBCG cluster catalog to simultaneously constrain cosmology and the richness--mass relation of the clusters. Assuming a flat \LambdaCDM cosmology, we find σ_8(Ω_m/0.25)^{0.41} = 0.832\pm 0.033 after marginalization over all systematics. In common with previous studies, our error budget is dominated by systematic uncertainties, the primary two being the absolute mass scale of the weak lensing masses of the maxBCG clusters, and uncertainty in the scatter of the richness--mass relation. Our constraints are fully consistent with the WMAP five-year data, and in a joint analysis we find σ_8=0.807\pm 0.020 and Ω_m=0.265\pm 0.016, an improvement of nearly a factor of two relative to WMAP5 alone. Our results are also in excellent agreement with and comparable in precision to the latest cosmological constraints from X-ray cluster abundances. The remarkable consistency among these results demonstrates that cluster abundance constraints are not only tight but also robust, and highlight the power of optically-selected cluster samples to produce precision constraints on cosmological parameters.

Figures (15)

• Figure 1: Observed (diamonds) and modeled (solid line) cluster counts as a function of richness in our best-fit model described in Section \ref{['sec:results']}. The model counts are computed using the best fit model detailed in Section \ref{['sec:results']}, and are a good fit to the data.
• Figure 2: Mean weak lensing mass of maxBCG clusters as a function of richness. The diamonds with error bars correspond to our data, while the solid line shows the values predicted from our best-fit model (see Section \ref{['sec:results']} for details). We note the error bars are correlated, and the model is a good fit to the data.
• Figure 3: Mass selection function of the maxBCG algorithm. The nine solid curves represent the probability that a halo of the corresponding mass falls within each of the nine richness bins described in Table \ref{['tab:abundance_bins']}. The dashed line is the sum of all the binning functions, and is the probability that a halo of a given mass is assigned a richness $N_{200}\in [11,120]$, i.e. it is the mass selection function of the maxBCG algorithm over this richness range. These binning functions are all estimated using our best-fit model parameters, which are detailed in Section \ref{['sec:results']}.
• Figure 4: Confidence regions for each pair of parameters that were allowed to vary in our fiducial analysis (described in § \ref{['sec:analysis']}). Contours show $68\%$ and $95\%$ confidence regions. Plots along the diagonal show the probability distributions for each quantity marginalized over the remaining parameters. The probability distribution for the mass bias parameter $\beta$ also shows the prior $\beta=1.00\pm0.06$ assumed in the analysis.
• Figure 5: Constraints on the $\sigma_8-\Omega_m$ plane from maxBCG and WMAP5 for a flat $\Lambda\hbox{CDM}$ cosmology. Contours show the $68\%$ and $95\%$ confidence regions for maxBCG (solid), WMAP5 (dashed), and the combined results (filled ellipses). The thin axis of the maxBCG-only ellipse corresponds to $\sigma_8(\Omega_m/0.25)^{0.41}=0.832\pm 0.033$. The joint constraints are $\sigma_8=0.807\pm 0.020$ and $\Omega_m=0.265\pm 0.016$ (one-sigma errors).