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 (CDM) 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-0.5 ± 0.06 is required. For a ΛCDM model, the mass-to-light function has a minimum of ~100 h 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+0.5 ± 0.26. This scaling behavior of the mass-to-light ratio seems to be in qualitative agreement with the predictions of semianalytical 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 hosted in a virialized system. We find that the halo occupation number scales nonlinearly with the total mass of the system, Ngal(>L) ∝ ℳ0.55 ± 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.