The stellar clock is driven by the interior evolution, whose main determinants are the chemical composition, stellar mass, and the decline of mass with time. In addition, massive-star evolution depends rather critically on mixing processes which determine the relative efficiency of the convective vs. radiative energy transport. Since convection is the more efficient process, any mechanism in its favor (such as rotation), will increase the stellar temperatures in the Hertzsprung-Russell diagram (HRD) in comparison with a radiative model (Yi 2003). Despite remaining uncertainties, the overall evolution in the upper HRD is fairly well understood (Chiosi & Maeder 1986; Maeder & Meynet 2000).
Massive stars follow one of two major evolutionary channels. If their initial masses are below ~ 25 M (for solar chemical composition), the core-contraction is mirrored by an envelope expansion until they reach the Hayashi line in the red. Observationally, this evolution is identified as the sequence OB star blue supergiant red supergiant (RSG). More massive stars experience higher mass loss because of the strong luminosity dependence of radiatively driven winds (Kudritzki & Puls 2000). As a result, the He-rich cores are exposed before the RSG phase is reached, and the corresponding hotter surface temperatures lead to a reversal of the evolution back to the blue part of the HRD. The spectroscopic phases of this sequence are OB star blue supergiant Wolf-Rayet (W-R) star. A W-R population indicates younger, more massive stars than a RSG population.
Calibrating and verifying these predictions is non-trivial because of the scarcity of massive stars, their uncertain distances, and their generally elusive parameters. Therefore, the recent mass determination of the eclipsing spectroscopic W-R binary WR20a from an orbit analysis by Bonanos et al. (2004) and Rauw et al. (2004) is significant: the two components have masses of 83 ± 5 M and 82 ± 5 M, making them the most massive stars with direct mass determinations. Their properties agree with the predictions of stellar evolution theory.
Evolution models by themselves are of limited usefulness for comparison with observables because they lack detailed predictions of spectral features. Therefore they are usually linked to a spectral library, which can be either empirical or theoretical (e.g., Lejeune & Fernandes 2002). Recently, there has been a shift in preference away from empirical to theoretical libraries. The main reasons are the reliability of the latest generation of model atmospheres and the need to cover the full parameter space which is otherwise observationally inaccessible. Galactic stars have the chemical evolutionary history imprinted, and their spectra are therefore badly suited for comparison with those of, e.g., elliptical (Thomas et al. 2004) or Lyman-break galaxies (Mehlert et al. 2002).
Current theoretical efforts are reflected in the synthetic library of Martins et al. (2004) who computed ~ 1600 high-resolution stellar spectra, with a sampling of 0.3 Å and covering the wavelength range from 3000 to 7000 Å. The library was computed with the latest improvements in stellar atmospheres, incorporating non-LTE line-blanketed TLUSTY models (Lanz & Hubeny 2003) for hot, massive stars and spherical line-blanketed Phoenix models accounting for tri-atomic molecules (Hauschildt et al. 1999) for cool stars. The grid covers the full HRD for chemical abundances of twice solar, solar, half solar, and 1/10 solar. The replacement of the traditional Kurucz (1993) atmospheres at the hot and cool end is significant. Important age diagnostics such as the helium lines are strongly affected by non-LTE effects in O stars. LTE models predict too weak equivalent widths. An example of the corresponding improvement at low Teff is shown in Fig. 1. Phoenix models account for the overall energy distribution in a self-consistent way because of their extensive molecular line list. These molecular transitions are missing in the widely used Kurucz models. Lejeune et al. (1998) provided an empirical correction to the Kurucz models. This correction becomes obsolete with the new fully blanketed models.
Figure 1. Comparison of the fluxes predicted by the models of Kurucz (1993), Lejeune et al. (1998), and Hauschildt et al. (1999). The latter are based on Phoenix atmospheres and predict the overall shape in a self-consistent manner. Upper panel: supergiant; lower panel: dwarf (Martins et al. 2004).
Combining this (or any other suitable) library with evolution models allows the synthesis of any desired spectrophotometric quantity, a concept that dates back to Tinsley (1968). In the next section I will frequently rely on this technique for an age-dating of single stellar populations (SSP).