XMM-Newton/Sloan Digital Sky Survey: Star Formation Efficiency in Galaxy Clusters and Constraints on the Matter-density Parameter

It is believed that the global baryon content of clusters of galaxies is representative of the matter distribution of the universe, and can, therefore, be used to reliably determine the matter-density parameter Ω_m. This assumption is challenged by the growing evidence from optical and X-ray observations that the total baryon mass fraction increases toward rich clusters. In this context, we investigate the dependence of stellar and total baryon mass fractions as a function of mass. To do so, we used a subsample of 19 clusters extracted from the X-ray flux-limited sample HIFLUGCS that have available Sloan Digital Sky Survey Data Release 7 data. From the optical analysis we derived the stellar masses. Using XMM-Newton we derived the gas masses. Then, adopting a scaling relation we estimate the total masses. Adding the gas and the stellar mass fractions we obtain the total baryonic content that we find to increase with cluster mass, reaching seven-year Wilkinson Microwave Anisotropy Probe (WMAP7) prediction for clusters with M ₅₀₀ = 1.6 × 10¹⁵ M _⊙. We observe a decrease of the stellar mass fraction (from 4.5% to ~1.0%) with increasing total mass where our findings for the stellar mass fraction agree with previous studies. This result suggests a difference in the number of stars formed per unit of halo mass, though with a large scatter for low-mass systems. That is, the efficiency of star formation varies on a cluster scale that lower mass systems are likely to have higher star formation efficiencies. It follows immediately that the dependence of the stellar mass fraction on total mass results in an increase of the mass-to-light ratio from lower to higher mass systems. We also discuss the consequences of these results in the context of determining the cosmic matter-density parameter Ω_m.