The Non-Parametric Model for Linking Galaxy Luminosity with Halo/Subhalo Mass: Are First Brightest Galaxies Special?

We revisit the longstanding question of whether first brightest cluster galaxies are statistically drawn from the same distribution as other cluster galaxies or are "special", using the new non-parametric, empirically based model presented in Vale&Ostriker (2006) for associating galaxy luminosity with halo/subhalo masses. We introduce scatter in galaxy luminosity at fixed halo mass into this model, building a conditional luminosity function (CLF) by considering two possible models: a simple lognormal and a model based on the distribution of concentration in haloes of a given mass. We show that this model naturally allows an identification of halo/subhalo systems with groups and clusters of galaxies, giving rise to a clear central/satellite galaxy distinction. We then use these results to build up the dependence of brightest cluster galaxy (BCG) magnitudes on cluster luminosity, focusing on two statistical indicators, the dispersion in BCG magnitude and the magnitude difference between first and second brightest galaxies. We compare our results with two simple models for BCGs: a statistical hypothesis that the BCGs are drawn from a universal distribution, and a cannibalism scenario merging two galaxies from this distribution. The statistical model is known to fail from work as far back as Tremaine&Richstone (1977). We show that neither the statistical model nor the simplest possibility of cannibalism provide a good match for observations. Our CLF models both give similar results, in good agreement with observations. Specifically, we find <m_1> between -25 and -25.5 in the K-band, sigma(m_1)~0.25 and <Delta_12> between 0.6 and 0.8, for cluster luminosities in the range of 10^12 to 10^13 h^-2 L_sun.