The Stellar Population Histories of Early-Type Galaxies. II. Controlling Parameters of the Stellar Populations

We analyze single-stellar-population (SSP) equivalent parameters for 50 local elliptical galaxies as a function of their structural parameters. These galaxies fill a two-dimensional plane in the four-dimensional space of [Z/H], log t, log $\sigma$, and [E/Fe]. SSP age and velocity dispersion can be taken as the two independent parameters that specify a galaxy's location in this ``hyperplane.'' The hyperplane can be decomposed into two sub-relations: (1) a ``Z-plane,'' in which [Z/H] is a linear function of log $\sigma$ and log t; and (2) a relation between [E/Fe] and $\sigma$ in which [E/Fe] is larger in high-$\sigma$ galaxies. Cluster and field ellipticals follow the same hyperplane, but their ($\sigma$,t) distributions within it differ. Nearly all cluster galaxies are old; the field ellipticals span a large range in SSP age. The tight Mg--$\sigma$ relations of these ellipticals can be understood as two-dimensional projections of the metallicity hyperplane showing it edge-on; the tightness of these relations does not necessarily imply a narrow range of ages at fixed $\sigma$. The relation between [E/Fe] and $\sigma$ is consistent with a higher effective yield of Type II SNe elements at higher $\sigma$. The Z-plane is harder to explain and may be a powerful clue to star formation in elliptical galaxies if it proves to be general. Present data favor a ``frosting'' model in which low apparent SSP ages are produced by adding a small frosting of younger stars to an older base population. If the frosting abundances are close to or slightly greater than the base population, simple two-component models run along lines of constant $\sigma$ in the Z-plane, as required. This favors star formation from well-mixed pre-enriched gas rather than unmixed low-metallicity gas from an accreted object. (Abridged)