4.3. Correlations between stellar populations and structure

Correlations between stellar populations and structure provide some of the most important constraints on models for galaxy formation. The color-luminosity relation for elliptical galaxies has been known for more than three decades (Baum 1959; de Vaucouleurs 1961). A similar correlation exists for absorption-line strengths (Faber 1973), and has been interpreted as a metallicity-mass relation that is a natural consequence of galactic winds. Among giant ellipticals, metallicity indicators correlate more tightly with velocity dispersion than with luminosity (Terlevich et al. 1981; Burstein et al. 1988; Bower et al. 1992; Bender et al. 1993). Compact galaxies such as M32 and NGC 4486B have values of Mg₂ that are high for their luminosities, but entirely in keeping with their velocity dispersions.

Bender et al. (1993) examined the Mg₂- correlation for a large sample of galaxies that included dE's from the Local Group and the Virgo cluster. They found that the same correlation extends from giant ellipticals to the faintest local dwarf spheroidals, although that statement is somewhat dependent on the adopted metallicity-Mg₂ conversion and contradicts the earlier conclusion of Vader (1986). Residuals from the mean trend are most likely due to young or intermediate-age stars in a small fraction of the galaxies. Schweizer et al. (1990) showed that among the giants the residuals from the mean Mg₂- relation correlate with the ``fine structure'' parameter, a measure of the degree of morphological peculiarity. The data for the dwarfs are as yet too sparse to make the same test, but there are certainly examples of dE's with morphological peculiarities and evidence of young stars (e.g. NGC 205).

For giant ellipticals, the overall scatter in the Bender et al. (1993) Mg₂- relation is only slightly larger than that expected from observational uncertainties. This small scatter, and the lack of any detectable correlations with other parameters (ellipticity, isophotal shape, or velocity anisotropy) is of fundamental importance. For example, the small scatter in the color-luminosity relation indicates that giant ellipticals must either be very old (z_formation 2), or have formed in a coordinated event at lower redshift (Bower et al. 1992). For giant E's the rms dispersion in age or metallicity at fixed is less than about 15%. The rather limited data for dE galaxies allows variations of about 50%. Differences between nucleated and non-nucleated dE's have been sought (Caldwell and Bothun 1987; Evans et al. 1990), but not in a way that controls for the color-luminosity or color-velocity dispersion relations. Comparison of the colors of the nuclei and the envelopes show no systematic differences; however examples of both blue and red nuclei are known (Chaboyer 1994).

Dwarf ellipticals, with mean surface-densities of stars comparable to those of the outer parts of giant ellipticals, are useful for testing ideas for the origin of color and metallicity gradients. Such gradients (de Vaucouleurs 1961; Thomsen and Baum 1987; Gorgas et al. 1990) are not explained by the simplest models of galactic winds, which are typically one-zone models with a single criterion for ejection of gas from the galaxy (Arimoto and Yoshii 1987; Dekel and Silk 1986; Bressan et al. 1994), but can be produced naturally when variations in the star-formation feedback efficiency with radius are taken into account. Franx and Illingworth (1990) suggested that the local metallicity within ellipticals is determined by local escape velocity, consistent with models involving an extended period of gaseous infall, or localized ejection of the ISM by supernovae. They base their argument on the color profiles for 17 ellipticals that follow roughly the same relation in a color s. v_esc plot. However, the small data set, the lack of a detailed comparison of v_esc vs. other parameters such as surface-brightness or r / r_e in reducing the scatter among the color gradients, and the rather large zeropoint uncertainties in the Franx and Illingworth (1990) dataset allow room for other possibilities. Bender et al. (1993) suggest that stellar populations P are controlled by a combination of total mass M and the local stellar volume density as P = f (M ), translating for observed quantities into Mg₂ 0.33 log (M² <>) and B - V 0.037 log (M² <>).

That such relations must be missing part of the story can be seen by plotting local colors vs. local line strengths (Gonzalez 1993; Ferguson 1994). If stellar populations were determined entirely by galaxy structure, the different measures of age and metallicity should track each other closely. In actuality, the slopes differ from galaxy to galaxy, do not follow the trend expected for pure metallicity variation, and do not extrapolate to the colors and line-strengths observed for dE galaxies. It is not yet clear whether this is a second-order effect (e.g. due to the fact that the mix of metallicities must vary as a function of radius in galaxies due to projection), or whether something more fundamental is at work. The key question is whether the stellar populations of dE's resemble those in the outer regions of giant ellipticals, and whether the resemblance is closer if the comparison is made at constant surface brightness or constant velocity dispersion.

More precise measurements of dE stellar populations are desperately needed. The well-observed local dwarfs give us some hint of a universal metallicity-luminosity relation, but also strong indications that the simplest models for explaining such a relation (supernova winds during a single rapid star-formation episode) must be wrong. Available data on cluster dE's neither strongly support nor rule out a similar relation between luminosity and metallicity. Their similar morphologies suggest that cluster and Local Group dE's share a common origin, but the much higher dwarf/giant ratio and the spatial segregation of different dE types within clusters (see Sect. 6) argues otherwise. For cluster dE's, the key test will be to determine, for a large homogeneous data set, which of the many possible parameters (velocity dispersion, surface brightness, luminosity, position in a cluster, presence or absence of a nucleus, etc.) influence the global stellar populations.