Galaxies and Cluster of Galaxies as Peak Patches of the Density Field

Abstract: The mass function of galaxies and clusters of galaxies can be derived observationally based on different types of observations. In this study we test if these observations can be combined to a consistent picture which is also in accord with structure formation theory. The galaxy data comprise the optical galaxy luminosity function and the gravitational lensing signature of the galaxies, while the galaxy cluster mass function is derived from the X-ray luminosity distribution of the clusters. We show the results of the comparison in the form of the mass density fraction that is contained in collapsed objects relative to the mean matter density in the Universe. The mass density fraction in groups and clusters of galaxies extrapolated to low masses agrees very well with that of the galaxies: both converge at the low mass limit to a mass fraction of about 28\% if the outer radii of the objects are taken to be $r_{200}$. Most of the matter contained in collapsed objects is found in the mass range $M_{200} \sim 10^{12} - 10^{14} h^{-1}_{70} M_\odot$, while a larger amount of the cosmic matter resides outside of objects with radius $r_{200}$.