Testing the accuracy of synthetic stellar libraries

One of the main ingredients of stellar population synthesis models is a library of stellar spectra. Both empirical and theoretical libraries are used for this purpose, and the question about which one is preferable is still debated in the literature. Empirical and theoretical libraries are being improved significantly over the years, and many libraries have become available lately. However, it is not clear in the literature what are the advantages of using each of these new libraries, and how far behind models are compared to observations. Here we compare in detail some of the major theoretical libraries available in the literature with observations, aiming at detecting weaknesses and strengths from the stellar population modelling point of view. Our test is twofold: we compared model predictions and observations for broad‑band colours and for high‑resolution spectral features. Concerning the broad‑band colours, we measured the stellar colour given by three recent sets of model atmospheres and flux distributions, and compared them with a recent UBVRIJHK calibration which is mostly based on empirical data. We found that the models can reproduce with reasonable accuracy the stellar colours for a fair interval in effective temperatures and gravities. The exceptions are (1) the U-B colour, where the models are typically redder than the observations, and (2) the very cool stars in general (V-K≳ 3). Castelli & Kurucz is the set of models that best reproduce the bluest colours (U-B, B-V) while Gustafsson et al. and Brott & Hauschildt more accurately predict the visual colours. The three sets of models perform in a similar way for the infrared colours. Concerning the high‑resolution spectral features, we measured 35 spectral indices defined in the literature on three high‑resolution synthetic libraries, and compared them with the observed measurements given by three empirical libraries. The measured indices cover the wavelength range from ~3500 to ~8700 Å. We found that the direct comparison between models and observations is not a simple task, given the uncertainties in parameter determinations of empirical libraries. Taking that aside, we found that in general the three libraries present similar behaviours and systematic deviations. For stars with T_eff≤ 7000 K, the library by Coelho et al.is the one with best average performance. We detect that lists of atomic and molecular line opacities still need improvement, specially in the blue region of the spectrum, and for the cool stars (T_eff≲ 4500 K).