SIMBAD references

The mass function of galaxy clusters is a powerful tool to constrain cosmological parameters, e.g. the mass fluctuation on the scale of 8h^–1 Mpc, σ₈, and the abundance of total matter, Ω_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 σ₈(Ω_m_/0.3)^α = β and find out the parameters of α = 0.40-0.50 and β = 0.8-0.9, so that σ₈= 0.8-0.9 if Ω_m= 0.3. Our σ₈ 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.