Uncertainties in the Modeling of Old Stellar Populations

We compare three recent models of the spectral evolution of stellar populations to assess the origin of serious discrepancies in the colors predicted for ≳ 1 Gyr old populations of the same input age and metallicity. To isolate the source of these discrepancies, we investigate separately the two main characteristics of each model: the underlying stellar evolution prescription and the spectral calibrations used to transform the theoretical Hertzsprung-Russell diagram into observables A 0.05 mag discrepancy in B - V color is caused almost entirely by a known limitation of theoretical spectra. Differences in spectral calibrations are found to account for only a small fraction of the 0.25 mag discrepancies in V - K color and of the 25% dispersion in mass-to-visual light ratio among the models considered here. The main source of disagreement for these quantities in the underlying stellar evolution prescription. For idealized galaxies containing a single generation of stars and no dust, properties derived from broadband colors using population synthesis models are found to be accurate by roughly, ±35% in age at fixed metallicity, 25% in metallicity at fixed age if the heavy-element mixture is assumed to be scaled-solar, and 35% in mass at fixed metallicity and fixed initial mass function. These indicative uncertainties are based on the dispersion in the predictions of the models investigated here. There appear to be persistent problems in virtually every ingredient of population synthesis models. The most serious are the lifetimes and luminosities of stars in post-main-sequence evolutionary stages; the temperature of the red giant branch and color-temperature relation for cool stars; and the lack of accurate libraries of stellar spectra, especially for cool stars and for nonsolar metallicities. These problems have profound causes. The main one is the high sensitivity of stellar evolution models on the efficiency of several critical factors which are either not sufficiently understood or cannot yet be determined uniquely from comparisons with observations (opacities, heavy-element mixture, helium content, convection, diffusion, mass loss, rotational mixing). Other major limitations are the difficult spectral modeling of cool stars and the unavailability of calibration stars for metal-rich populations and populations with altered chemical mixes.