XMM-Newton/SDSS: 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 Omega_m. This
assumption is challenged by the growing evidence from optical and X-ray
observations that the total baryon mass fraction increases towards 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
nineteen clusters extracted from the X-ray flux limited sample HIFLUGCS that
have available DR-7 Sloan Digital Sky Survey (SDSS) 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 7-year Wilkinson Microwave
Anisotropy Probe (WMAP-7) prediction for clusters with M_500 = 1.6 x 10^{15}
M_sun. 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 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 Omega_m.
