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This paper commences a series of investigations into the stellar populations of local elliptical galaxies as determined from their integrated spectra. The goal of the series is to determine the star formation and chemical evolution histories of present-day elliptical galaxies. The primary galaxy sample analyzed is that of González (1993, G93), which consists of 39 ellipticals drawn primarily from the local field and nearby groups, plus the bulge of Messier 31. Single-stellar-population (SSP) equivalent ages, metallicities, and abundance ratios are derived from Hβ, Mg b, and Fe line strengths using an extension of the Worthey (1994) models that incorporates non-solar line-strength "response functions" by Tripicco & Bell (1995). These functions account for changes in the Lick/IDS indices caused by non-solar abundance ratios, allowing us to correct the Worthey (1994) models for the enhancements of Mg and other α-like elements relative to the Fe-peak elements.SSP-equivalent ages of the G93 ellipticals are found to vary widely, 1.5 ∼ < t ∼ < 18 Gyr, while metallicities [Z/H] and enhancement ratios, [E/Fe] are strongly peaked around [Z/H] = +0.26 and [E/Fe] = +0.20 (in an aperture of radius r e /8). The enhancement ratios [E/Fe] are milder than previous estimates, owing to the application of non-solar abundance corrections to both Mg b and Fe for the first time. While [E/Fe] is usually > 0, it is not the "E" elements that are actually enhanced but rather the Fe-peak elements that are depressed; this serves not only to weaken Fe but also to strengthen Mg b, accounting for the overall generally mild enhancements. Based on index strengths from the Lick/IDS galaxy library (Trager et al. 1998), C is not depressed with Fe but rather seems to be on a par with other elements such as Mg in the "E" group. Gradients in stellar populations within galaxies are found to be mild, with SSP-equivalent age decreasing by 25%, metallicity decreasing by [Z/H] = 0.20 dex, and [E/Fe] remaining nearly constant out to an aperture of radius r e /2 for nearly all systems.Our ages have an overall zeropoint uncertainty of at least ∼ 25% due to uncertainties in the stellar evolution prescription, the oxygen abundance, the effect of [E/Fe] = 0 on the isochrones, and other unknowns. However, the relative age rankings of stellar populations should be largely unaffected by these errors. In particular, the large spread in ages appears to be real and cannot be explained by contamination of Hβ by blue stragglers or hot horizontal branch stars, or by fill-in of Hβ by emission. Correlations between these derived SSP-equivalent parameters and other galaxy observables will be discussed in future papers.

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 (1999). 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, log σ, 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 sub-relations: (1) a "Z-plane," in which [Z/H] is a linear function of log σ 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 sub-samples 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 vs. 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 produce...

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