The Mass–to–light Function of Virialized Systems and the Relationship between Their Optical and X-ray Properties

We compare the B-band luminosity function of virialized halos with the mass function predicted by the Press-Schechter theory in cold dark matter cosmogonies. We find that all cosmological models fail to match our results if a constant mass–to–light ratio is assumed. In order for these models to match the faint end of the luminosity function, a mass–to–light ratio decreasing with luminosity as L is required. For a ΛCDM model, the mass–to–light function has a minimum of ∼ 100h 75 in solar units in the B-band, corresponding to ∼ 25% of the baryons in the form of stars, and this minimum occurs close to the luminosity of an L galaxy. At the high-mass end, the ΛCDM model requires a mass–to–light ratio increasing with luminosity as L. This scaling behavior of the mass–to–light ratio appears to be in qualitative agreement with the predictions of semi-analytical models of galaxy formation. In contrast, for the τCDM model, a constant mass–to–light ratio suffices to match the high-mass end. We also derive the halo occupation number, i.e. the number of galaxies brighter than L∗gal hosted in a virialized system. We find that the halo occupation number scales non-linearly with the total mass of the system, Ngal(> L ∗ gal) ∝ m 0.55±0.026 for the ΛCDM model. We find a break in the power-law slope of the X-ray-to-optical luminosity relation, independent of the cosmological model. This break occurs at a scale corresponding to poor groups. In the ΛCDM model, the poor-group mass is also the scale at which the mass-to-light ratio of virialized systems begins to increase. This correspondence suggests a physical link between star formation and the X-ray properties of halos, possibly due to preheating by supernovae or to efficient cooling of low-entropy gas into galaxies. Subject headings: cosmology: large-scale structure of the universe — cosmology: dark matter — galaxies: clusters: general — galaxies: halos — galaxies: luminosity function, mass function — X-rays: general