Ages and metallicities of early-type galaxies in the Sloan Digital Sky Survey: new insight into the physical origin of the colour-magnitude and the Mg2–σV relations

We exploit recent constraints on the ages and metallicities of early-type galaxies in the Sloan Digital Sky Survey (SDSS) to gain new insight into the physical origin of two fundamental relations obeyed by these galaxies: the colour-magnitude and the Mg2–σV relations. Our sample consists of 26,003 galaxies selected from the SDSS Data Release Two (DR2) on the basis of their concentrated light profiles, for which we have previously derived median-likelihood estimates of stellar metallicity, light-weighted age and stellar mass. Our analysis provides the most unambiguous demonstration to date of the fact that both the colour-magnitude and the Mg2–σV relations are primarily sequences in stellar mass and that total stellar metallicity, α-elements-to-iron abundance ratio and light-weighted age all increase with mass along the two relations. For high-mass ellipticals, the dispersion in age is small and consistent with the error. At the low-mass end, there is a tail towards younger ages, which dominates the scatter in colour and index strength at fixed mass. A small, but detectable, intrinsic scatter in the mass-metallicity relation also contributes to the scatter in the two observational scaling relations, even at high masses. Our results suggest that the chemical composition of an early-type galaxy is more tightly related to its dynamical mass (including stars and dark matter) than to its stellar mass. The ratio between stellar mass and dynamical mass appears to decrease from the least massive to the most massive galaxies in our sample.