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This paper analyzes single stellar population (SSP)-equivalent parameters for 50 local elliptical galaxies as a function of their structural parameters. The galaxy sample is drawn from the high-quality spectroscopic surveys of González (1993) and Kuntschner (1998). The basic data are central values of SSP-equivalent ages, t, metallicities, [Z/H], and ``enhancement'' ratios, [E/Fe], derived in Paper I, together with global structural parameters including velocity dispersions, radii, surface brightnesses, masses, and luminosities. The galaxies fill a two-dimensional plane in the four-dimensional space of [Z/H], logt, logσ, and [E/Fe]. SSP age, t, and velocity dispersion, σ, can be taken as the two independent parameters that specify a galaxy's location in this ``hyperplane.'' The hyperplane can be decomposed into two subrelations: (1) a ``Z-plane'', in which [Z/H] is a linear function of logσ and logt and (2) a relation between [E/Fe] and σ in which [E/Fe] is larger in high-σ galaxies. Velocity dispersion is the only structural parameter that is found to modulate the stellar populations; adding other structural variables such as I_e or r_e does not predict [Z/H] or [E/Fe] more accurately. Cluster and field ellipticals follow the same hyperplane, but their (σ,t) distributions within it differ. Most Fornax and Virgo cluster galaxies are old, with a only a small sprinkling of galaxies to younger ages. The field ellipticals span a larger range in SSP age, with a tendency for lower σ galaxies to be younger. The present sample thus suggests that the distribution of local ellipticals in the (σ,t) plane may depend on environment. Since the (σ,t) distribution affects all two-dimensional projections involving SSP parameters, many of the familiar scaling laws attributed to ellipticals may also depend on environment. Some evidence for this is seen in the current sample. For example, only Fornax ellipticals show the classic mass-metallicity relation, whereas other subsamples do not. The tight Mg-σ relations of these ellipticals can be understood as two-dimensional projections of the metallicity hyperplane showing it edge-on. At fixed σ, young age tends to be offset by high [Z/H], preserving Mg nearly constant. The tightness of the Mg-σ relations does not necessarily imply a narrow range of ages at fixed σ.

Although SSP parameters are heavily weighted by young stars, modeling them still places tight constraints on the total star formation history of elliptical galaxies. The relation between [E/Fe] and σ is consistent with a higher effective yield of Type II SNe elements at higher σ. This might occur if the IMF is enhanced in massive stars at high σ, or if more SNe II-enriched gas is retained by deeper galactic potential wells. Either way, modulating Type II yields versus σ seems to fit the data better than modulating Type Ia yields. 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 (assuming no change in σ). If the frosting abundances are close to or slightly greater than the base population, simple two-component models run along lines of constant σ 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.