Halo model analysis of cluster statistics
/ Authors
/ 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 satellite galaxies assigned to a cluster. Such a survey can strongly constrain {sigma}{sub 8} ({delta}{sigma}{sub 8}{approx_equal}0.05), the power law index {alpha} where =(m/M{sub 1}){sup {alpha}} ({delta}{alpha}{approx_equal}0.03), and perhaps even the Hubble parameter ({delta}h{approx_equal}0.07). We find cluster abundances and bias are not well suited for constraining {omega}{sub m} or the amplitude M{sub 1}. We also find that without bias information {sigma}{sub 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.
Journal: Physical Review D