  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 $L^{-0.5\pm 0.06}$ is required. For a $\Lambda$CDM model, the
mass-to-light function has a minimum of $\sim 100 h^{-1}_{75}$ in solar units
in the $B$-band, corresponding to $\sim 25%$ 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 $\Lambda$CDM model requires a mass-to-light ratio
increasing with luminosity as $L^{+0.5 \pm 0.26}$. We also derive the halo
occupation number, i.e. the number of galaxies brighter than $\lgal^*$ hosted
in a virialized system. We find that the halo occupation number scales
non-linearly with the total mass of the system, $N\sbr{gal}(>\lgal^*) \propto
m^{0.55\pm0.026}$ or the $\Lambda$CDM 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 $\Lambda$CDM 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.
