Mass Function of Rich Galaxy Clusters and Its Constraint on sigma_8

TL;DR

This paper uses galaxy cluster data from SDSS to determine the mass function and constrain sigma_8, finding values slightly higher than some previous estimates but consistent with weak lensing results.

Contribution

It introduces new scaling relations between cluster mass and observable properties, and applies them to SDSS data to refine cosmological parameter constraints.

Findings

Estimated sigma_8 = 0.8-0.9 for Omega_m=0.3

Derived the cluster mass function from SDSS data

Provided constraints on sigma_8 and Omega_m relationship

Abstract

The mass function of galaxy clusters is a powerful tool to constrain cosmological parameters, e.g., the mass fluctuation on the scale of 8 h^{-1} Mpc, sigma_8, and the abundance of total matter, Omega_m. We first determine the scaling relations between cluster mass and cluster richness, summed r-band luminosity and the global galaxy number within a cluster radius. These relations are then used to two complete volume-limited rich cluster samples which we obtained from the Sloan Digital Sky Survey (SDSS). We estimate the masses of these clusters and determine the cluster mass function. Fitting the data with a theoretical expression, we get the cosmological parameter constraints in the form of sigma_8(Omega_m/0.3)^{alpha}=beta and find out the parameters of alpha=0.40-0.50 and beta=0.8-0.9, so that sigma_8=0.8-0.9 if Omega_m=0.3. Our sigma_8 value is slightly higher than recent estimates from the mass function of X-ray clusters and the Wilkinson Microwave Anisotropy Probe (WMAP) data, but consistent with the weak lensing statistics.