Cosmology with the Space-Luminosity Distribution of Virialized Halos
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We derive the observed luminosity function of virialized systems. Coupling this statistic with the mass function predicted by CDM cosmogonies we obtain the functional behavior of the mass-to-light ratio over a wide dyna mical range in mass. We conclude that the mass-to-light ratio has a minimum close t o the luminosity of an L* galaxy halo. We also show how to derive in a self-consistent way the X-ray-to-optical luminosity ratio for galaxy systems. As a consequence, we predict a fundamental break in the auto-similar scaling behavior of fundamental correlat ions in going from the group to the cluster scales.