4.1. Metallicity Gradients
We now provide an overview of the abundance profile picture for spheroidal systems, especially elliptical galaxies. The principal techniques for measuring abundances in these systems involve the use of photometric indices of integrated starlight, since individual stars cannot be resolved. A brief description of these techniques is given in Appendix C. Elliptical galaxies look superficially like a fairly homogeneous class of galaxies, with muted star formation and no obvious cold gas and kinematically supported by almost randomly oriented orbits. Star formation can be seen in most ellipticals at some level, as can dust lanes and emission-line gas, but usually at a level below that of spirals. Ellipticals also exhibit regularity of colors and absorption feature strengths, with larger galaxies being redder and having stronger metallic absorption features than smaller ones. This has long been interpreted as a sign that the metallicity is higher in larger galaxies (see, e.g., Faber 1972).
To derive abundance profiles in stellar systems, colors and absorption feature strengths as a function of galactocentric radius are interpreted through population models. Some color gradient studies include Kormendy & Djorgovski (1989), Franx & Illingworth (1990), and Peletier et al. (1990). Most studies of optical absorption features have utilized one particular system of feature indices developed at Lick Observatory (described in Worthey et al. 1994 and references therein). The last few years have seen a rapid expansion of galaxy data available in this system. To measure an absorption feature in the Lick system, one creates a pseudocontinuum by bracketing the spectral feature of interest with flanking passbands. Flux in the flanking bands is measured and a straight line is drawn between the midpoints of the flanking bands to represent the (pseudo)continuum. The flux difference between the pseudocontinuum and the absorption feature is integrated and the result is expressed in Å of equivalent width (or magnitudes, depending on the specific index; see Worthey et al. 1994 and Worthey & Ottaviani 1997 for the details). Figure 10 illustrates the idea for a portion of the spectrum. There are 25 indices defined, five definitions measuring Balmer lines and 20 measuring various metallic absorption blends. The index system operates at a low resolution (~ 8 Å FWHM) necessitated by Doppler smearing from the substantial (up to = 350 km s-1) velocity dispersions of large elliptical galaxies, and most of the indices require corrections when velocity dispersions get large.
Figure 10. Mid-optical spectra of stars of differing spectral types are shown, with pseudocontinuum and central index passbands from the Lick index definitions shown. The hashed regions are the central passbands. Solid horizontal line segments mark the pseudocontinua on selected spectra. Dashed lines represent the "continuum" calculated by finding the average flux in the pseudocontinuum passbands and then drawing a straight line between pseudocontinuum midpoints. Indices are expressed either as equivalent widths, as in stellar spectroscopy, or as flux ratios in magnitudes, depending on the index. See Worthey et al. (1994) for the details.
While most of these 25 indices follow the log(Age) / log Z - 3/2 constant-index slope described in Appendix C, a few (the Balmer indices) are relatively age sensitive, with log(Age) / log Z - 1/2 to -1, while others, notably, a feature called Fe4668 whose main contributor is really molecular carbon, are relatively metal sensitive, with log(Age) / log Z -5 (Worthey 1994). Arrayed against each other, it seems possible to separate the effects of age and metallicity, in the mean.
To derive an abundance gradient in an elliptical galaxy, one compares observed colors or line strengths with model predictions, often assuming a constant age throughout the galaxy. For instance, Franx & Illingworth (1990) find a mean color gradient in 17 elliptical galaxies of (U-R) / log r = -0.23 ± 0.03 mag per decade in radius. Entering the Worthey (1994) models at age 12 Gyr, one finds that a change of 0.15 dex in Z gives the required (U-R), so the gradient assuming constant age is log Z / log R = -0.15 dex per decade. The same number is reached by considering the B-R gradient. Because of the very steep surface brightness dropoff of elliptical galaxies, projection effects are small and usually neglected. The steep dropoff also means that long-slit spectroscopy usually only reaches to 0.5-1.0 Re (the half-light radius), although color gradient studies and ultradeep spectroscopy can reach to several Re.
Color studies and line strength studies generally give a consistent picture of a gradient of about log Z / log R -0.2 dex per decade. There is probably a small correction to this number, however, due to age effects. Simultaneous mean-age, mean-Z estimates using the Balmer versus metal feature technique described above were derived for the González (1993) and Mehlert et al. (1998) samples of galaxies, about 60 early-type galaxies in a wide variety of environments, and the distribution of gradients is shown in Figure 11a. There are no trends of gradient strength with luminosity or velocity dispersion (unlike average Z, which is larger in larger galaxies). The average age gradient is younger toward the center by 0.1 dex decade-1 (a few Gyrs) and more metal rich by 0.25 dex decade-1. The scatter in the average seems mostly due to observational error, error in correcting for H emission fill-in, and variation in abundance ratio mixture, and the residuals scatter along the -3/2 age-metallicity slope (Fig. 11b) in the way expected for random errors in input index values.
Figure 11. (a) Gradients measured in early-type galaxies in two data sets: González (1993) nearby ellipticals and Mehlert et al. (1998) ellipticals and S0s in the rich Coma cluster. Gradients were derived using the H index vs. a mean abundance index called [MgFe], defined as (Mg b × <Fe>)1/2, where <Fe> is the arithmetic average of Fe5270 and Fe5335. Derived from this particular index combination and filtered through Worthey (1994) models, the mean age gradient is 0.1 dex decade-1 (younger toward the center) and the mean gradient in abundance is -0.25 dex decade-1 (more metal rich toward the center). Interestingly, the Mehlert gradients in both age and Z are a factor of 2 more shallow than the González gradients, but as of this writing it is not clear whether this is an aperture effect due to the greater distance of the Coma galaxies or a real environmental trend. (b) The correlation between age gradients and Z gradients. The correlation may have an astrophysical component, but errors from H emission corrections, abundance ratio effects, and observational error probably explain most of the elongation, which is close to the -3/2 degeneracy direction expected from a random error source.
This -0.3 gradient in dex decade-1 units corresponds to about -0.02 dex kpc-1 assuming an 8 kpc radius, which is a factor of 3 more shallow than the gradient found for the Milky Way disk and other nonbarred spirals (see Section 2.1). But such a value is well within the range of theoretical models for galaxy formation. For example, Larson's (1974) dissipative models predict log Z / log R = -1, while various Carlberg (1984) models range from -0.5 to 0.0. Pure stellar merging gives zero gradient, and in fact tends to erase preexisting gradients by roughly 20% per event, or even more via changes in radial structure of the galaxies (White 1980).
The gradient numbers seem fairly robust and consistent from data set to data set and from model to model. What about absolute abundances? These are trickier. The nuclei of large elliptical galaxies have mean [Z / H] in the range 0.0-0.4 dex as inferred from Balmer versus metal feature diagrams. In principle, the mean abundance can be known much more precisely, but there is an additional stumbling block beyond just the inaccurate models and the complication of age-metal degeneracy. The elemental mixture in elliptical galaxies is not scaled-solar. Abundances derived from lighter element lines like Mg b or Na D are much higher than those derived from heavier Fe or Ca lines, and this is the main cause for uncertainty in the absolute abundance (Worthey 1998).