The optical luminosity function of virialized systems

We determine the optical luminosity function of virialized systems over the full range of density enhancements, from single galaxies to clusters of galaxies. The analysis is based on galaxy systems identified from the Nearby Optical Galaxy (NOG) sample, which is the largest all-sky catalog of objectively identified bound objects presently available. We find that the B-band luminosity function of systems is insensitive to the choice of group-finding algorithms and is well described, over the absolute magnitude range -24.5 less than or equal to M -5 log h(75) less than or equal to -18.5, by a Schechter function with alpha(s) = -1.4 +/- 0.03, M-s* -5 log h(75) = -23.1 +/- 0.06, and phi(s)* = 4.8 x 10(-4) h(75)(3) Mpc(-3), or by a double power law: phi(pl)(L-s) proportional to L-s(-1.45+/-0.07) for L-s < L-pl and φ(pl) (Ls) ∝ L-s(-2.35+/-0.15) for L-s > L-pl, with L-pl = 8.5 x 10(10) h(75)(-2) L., corresponding to M-s - 5 log h(75) = -21.85. The characteristic luminosity of virialized systems, L-pl, is similar to3 times that (L-gal*) of the NOG galaxies. Our results show that half of the luminosity of the universe is generated in systems with L-s < 2.9 L-gal* and that 10% of the overall luminosity density is supplied by systems with L-s > 30 L-gal*. We find a significant environmental dependence in the luminosity function of systems, in the sense that overdense regions, as measured on scales of 5 h(-1) Mpc, preferentially host brighter, and presumably more massive, virialized systems.