Appendix C
Metallicity Calibration and the V - K Color

As previously discussed, a change in mean metallicity is the most likely explanation for the UVK color-aperture and color-luminosity effects found in early-type,galaxies. In this Appendix we shall attempt to estimate quantitatively the implied variation in metallicity, as measured by Fe/H (Fe/H)_obs / (Fe/H).

The UVK colors of a stellar ensemble composed of a single generation of stars will become bluer with decreasing metallicity because of three reasons: First, the ultraviolet line blanketing will decrease; second, the horizontal branch will shift to the blue; and third, the giant branch will steepen. Now it is well known that the position of the horizontal branch does not correlate perfectly well with metal abundance. Furthermore, Peterson (1976) has shown that changes in CN band strength, through variations only in the nitrogen abundance, can alter the U - V color by several tenths of a magnitude, for the same value of Fe/H. Thus, we expect the V - K color, which depends primarily on just the giant branch morphology, to be a superior indicator of mean metallicity than the U - V color. Recent infrared observations of globular clusters (Malkan, Aaronson, and Kleinmann 1977; Aaronson and Malkan 1977) have in fact demonstrated that as an accurate measure of metallicity, the V - K color is comparable to the best purely optical techniques.

We shall thus use the V - K color as our metallicity indicator. It is first necessary to determine the ratio log(Fe/H) / V - K. Using the luminosity function of M3, and theoretical evolutionary tracks of Rood (1972), Strom et al. (1976) found that log(Fe/H) / V - K 1.2, with V - K 3.15 as the solar abundance value. The globular cluster observations of Aaronson and Malkan (1977) provide a strictly empirical calibration. Preliminary results indicate that log(Fe/H) / V - K 2., with V - K = 3.0 as the solar abundance value.

In Paper I the mean V - K color at log A / D₀ = - 0.6 in elliptical galaxies was found to vary from 3.15 to 3.33, for a change in absolute magnitude of from -19 to -23. The calibrations discussed above imply a concomitant change in Fe/H of 1.6 - 2.3. This result is completely consistent with the work of Faber (1973), who estimated a factor of 2 change in Fe/H was required to explain the change in optical line indices between her group 2 and group 5 galaxies, which cover about the same magnitude range as the Paper I sample. (It was in fact shown in Paper I that the UVK colors correlate quite well With Faber's CN₀ - Mg₀ index.) Furthermore, the V - K colors suggest a mean value of Fe/H of 1 to 2 at M_V = - 19, and-2 to 4 at M_V = - 23, amounts again consistent with Faber's estimates.

A mean radial color change V - K / logA / D(0) of ~ 0.1 was found for elliptical galaxies in Paper I and for the bulges of early-type spirals in this paper. This suggests a typical change in Fe/H of 1.5 to 2 over a range of -0.3 to -1.3 in log A / D₀, a value that appears to be within the limits of the theoretical collapse models discussed by Larson (1974, 1975, 1976).

We caution that the above estimates depend on linear extrapolation of calibrations based on metal-poor galactic globular clusters to seemingly metal-rich composite galaxian systems. Better knowledge of the end points of giant star evolution coupled with detailed synthesis models which include chemical evolution may be needed to confirm the validity of this assumption.