Halo Model Analysis of Cluster Statistics

Abstract

We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass tracer is chosen to be the number of member galaxies assigned to a cluster. Such a survey can strongly constrain ${\sigma }_8$ ($\Delta {\sigma }_8\approx 0.05$), the power law index $\alpha$ where $<N_{gal}|m>=1+(m/M_1{)}^{\alpha }$ ($\Delta \alpha \approx 0.03$), and perhaps even the Hubble parameter ($\Delta h\approx 0.07$). We find cluster abundances and bias not well suited for constraining ${\Omega }_m$ or the amplitude $M_1$. We also find that without bias information ${\sigma }_8$ and $\alpha$ are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass tracer used in the survey.

27 pages, 11 figures, references added

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Cited by in corpus (9)

• Cosmological Constraints from the SDSS maxBCG Cluster Catalog
• A Weak Lensing Study of X-ray Groups in the COSMOS survey: Form and Evolution of the Mass-Luminosity Relation
• Towards a Concordant Model of Halo Occupation Statistics
• Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data
• Galaxy Occupation Statistics of Dark Matter Haloes: Observational Results
• Cosmology and the Halo Occupation Distribution from Small-Scale Galaxy Clustering in the Sloan Digital Sky Survey
• The Correlation Function of Optically Selected Galaxy Clusters in the Sloan Digital Sky Survey
• Cross-Correlation Lensing: Determining Galaxy and Cluster Mass Profiles from Statistical Weak Lensing Measurements
• Constraints on primordial non-Gaussianity from WMAP7 and Luminous Red Galaxies power spectrum and forecast for future surveys