The luminosities, sizes, and velocity dispersions of brightest cluster galaxies: Implications for formation history

The size-luminosity relation of early-type brightest cluster galaxies (BCGs), R-e proportional to L-0.88, is steeper than that for the bulk of the early-type galaxy population, for which R-e proportional to L-0.68. This is true if quantities derived from either de Vaucouleurs or Sersic fits to the surface brightness profiles are used. Contamination from an intracluster light component centered on the BCG, with parameters similar to what has been seen in some recent studies, is not able to account for this difference. In addition, although BCGs are hardly offset from the fundamental plane defined by the bulk of the early-type population, they show considerably smaller scatter. The larger than expected sizes of BCGs, and the increased homogeneity, are qualitatively consistent with models that seek to explain the colors of the most massive galaxies by invoking dry dissipationless mergers, since dissipation tends to reduce the sizes of galaxies, and wet mergers that result in star formation would tend to increase the scatter in luminosity at a fixed size and velocity dispersion. Furthermore, BCGs define the same g - r color-magnitude relation as the bulk of the early-type population. If BCGs formed from dry mergers, then BCG progenitors must have been red for their magnitudes, suggesting that they hosted older stellar populations than is typical for their luminosities. Our findings have two other consequences. First, the R-e-L relation of the early-type galaxy population as a whole (i.e., normal plus BCG) exhibits some curvature: the most luminous galaxies tend to have larger sizes than is expected from the R-e proportional to L-0.68 scaling-some of this curvature must be a consequence of the fact that an increasing fraction of the most luminous galaxies are BCGs. The second consequence is suggested by the fact that, despite following a steeper size-luminosity relation, BCGs tend to define a tight relation between dynamical mass R-e sigma(2)/G and luminosity. Although this relation is slightly different than that defined by the bulk of the population, the fact that their sizes are large for their luminosities suggests that their velocity dispersions are small. We find that, indeed, BCGs define a shallower sigma-L relation than the bulk of the early-type galaxy population. This shallower relation suggests that there may be a curvature in the correlation between black hole mass and velocity dispersion; simple extrapolation of a single power law M-center dot-sigma relation to large sigma will underestimate M-center dot.