Annu. Rev. Astron. Astrophys. 2006. 44: xxx-xxx Copyright © 2006 by Annual Reviews. All rights reserved

2. SYNTHETIC STELLAR POPULATIONS

The ETGs treated in this review can only be studied in integrated light, hence the interpretation of their photometric and spectroscopic properties needs population synthesis tools. Pioneering unconstrained synthesis using "quadratic programming" (e.g., Faber 1972), was soon abandoned in favor of evolutionary population synthesis, whose foundations were laid down by Beatrice Tinsley in the 1970s (Tinsley & Gunn 1976, Tinsley 1980, Gunn, Stryker & Tinsley 1981). Much progress has been made in the course of the subsequent quarter of a century, especially thanks to the systematic production of fairly complete libraries of stellar evolutionary sequences and stellar spectra.

Several modern population synthesis tools are commonly in use today, including those of Worthey (1994), Buzzoni (1995), Bressan, Chiosi, & Tantalo (1996), Maraston (1998, 2005), Bruzual & Charlot (2003), Fioc & Rocca Volmerange (1997, PEGASE Code), Vázques & Leitherer (2005, Starburst99 Code), Vazdekis et al. (2003), and González Delgado et al. (2005). Though far more reliable than earlier generations of models, even the most recent tools still may suffer from incomplete spectral libraries (especially at high metallicity and for nonsolar abundance ratios), and poorly calibrated mass loss in advanced stages, such as the asymptotic giant branch (AGB). Yet, there is fair agreement among the various models, with the exception of those for ages around ~ 1 Gyr, when the contribution by AGB stars is at maximum, and Maraston's models (calibrated on Magellanic Cloud clusters) give appreciably higher near-IR fluxes than the other models.

Only a few "rules of thumb" regarding population synthesis models can be recalled here, which may be useful in guiding the reader through some of the subtleties of their comparison with the observations.

No evolutionary population synthesis code is perfect. Evolutionary tracks are not perfect and stellar libraries are never really complete. So, any code deficiency will leave its imprint on the results, generating a distortion of the age/metallicity grids used to map plots of one observable versus another. Inevitably, such distortions will leave their imprint in the results, and to some extent may lead to spurious correlations/anticorrelations when reading ages and metallicities from overplotted data points.

Ages derived from best fits to simple stellar populations (SSPs, i.e., single burst populations) are always luminosity-weighted ages, and in general are more sensitive to the youngest component of the real age distribution. SSP ages should be regarded as lower limits.

Spectra and colors of SSPs are fairly insensitive to the initial mass function (IMF), because most of the light comes from stars in a narrow mass interval around the mass of stars at the main sequence turnoff.

The time evolution of the luminosity of a SSP does depend on the IMF, and so does the mass-to-light ratio (M / L). For example, a now fashionable IMF that flattens below ~ 0.6 M (e.g., Chabrier 2003) gives M / L ratios a factor of ~ 2 lower than a straight Salpeter IMF.

Stellar ages and metallicities are the main quantities that the analyses of colors and integrated spectra of galaxies are aimed to determine. Yet, for many observables, age and metallicity are largely degenerate, with a reduced age coupled to an increased metallicity conjuring to leave the spectral energy distribution nearly unchanged. This results primarily from the color (temperature) of the main sequence turnoff, e.g., (B - V)^TO, (the true clock of SSPs) being almost equally sensitive to age and metallicity changes. Indeed, from stellar isochrones one can derive that (log t / [Fe/H])_{(B - V)^TO} -0.9 -0.35[Fe/H], and a factor of 2 error in estimated metallicity produces a factor ~ 2 error in age (Renzini 1992). Red giant branch stars are the major contributors of bolometric luminosity in old stellar populations, and their locus shifts to lower temperatures with both increasing age and metallicity, further contributing to the degeneracy. Thus, from full SSPs, Worthey (1994) estimated that a factor of 3 error in metallicity generates a factor of 2 error in age when using optical colors as age indicators, the so-called 2/3 rule. Several strategies have been devised to circumvent this difficulty and break the age-metallicity degeneracy (see below).

There are occasionally ambiguities in what is meant by the M / L ratio in the tabulated values. The mass M can be defined either as the mass of gas that went into stars, or the mass of the residual population at age t, including the mass in dead remnants (i.e., the original mass diminished by the mass lost by stars in the course of their evolution), or even the mass of the surviving stars, i.e., without including the mass in remnants. Caution should be paid when using tabular values, as different authors may adopt different definitions.

The power of stellar population diagnostics stems from the opportunity to age-date the stellar content of galaxies in a fashion that is independent of cosmological parameters. Then, once a cosmology is adopted, ages derived from observations at a lower redshift can be used to predict the properties of the stellar populations of ETGs at a higher one, including their formation redshift. Thus, ages derived for the local elliptical galaxies imply a well-defined color, spectral, and luminosity evolution with redshifts, which all can be subject to direct observational test. The extent to which a consistent picture of ETG formation is emerging from low- and high-redshift observations is the main underlying theme of this review.