\journalname
Astronomy&AstrophysicsReview These tracks are also shown in Fig. \ref{aiphe} (dashed lines) and now match the secondary very well (lower curve), but not the primary – as expected for a non-optimised mixing length parameter. The derived ages differ by 0.08 Gyr (1.6%) for the Yonsei-Yale models, and by 0.20 Gyr (5%) for the experimental Victoria models (cf. the 1% age differences shown with asterisks in Fig. \ref{aiphe}). Because overshooting increases the main-sequence lifetime, but accelerates the crossing of the subgiant branch, the constraints provided by AI Phe will remain valuable for the next version of the models in which the mixing length parameter, overshooting, and He diffusion will be tuned together to match all the available observational constraints.
Two aspects deserve mention in this discussion: (i): What makes AI Phe so valuable for stellar evolution is the tiny error of the masses (only 0.4%); with mass errors of 3% the test would be far less conclusive. And (ii): The Yonsei-Yale models yield a mean age for AI Phe of 5.0 Gyr, while the experimental Victoria models give 4.1 Gyr – a non-negligible uncertainty in the context of age determinations for nearby solar-type stars. The still-uncertain features of stellar evolution models that can be usefully tested with the best binary data are therefore not just of purely academic interest, but have significant implications for Galactic research as well.

Current topics in stellar evolution models

Convective overshooting.
A91 discussed the comparison of stellar models with the binary data presented in that paper, with special focus on the then much-debated subject of overshooting from convective cores. A reasonable consensus that the phenomenon is indeed real developed in the following decade, and some formulation of convective overshooting is now incorporated in most models for the evolution of stars above \(\sim\)1.15 \(M_{\odot}\) that have been published since then.
More recently, attention has turned to the physical description of overshooting and calibration of the parameter(s) describing its extent in stars of different mass and metallicity \citep[see, e.g.,][]{Claret:07}. The mass range 1.1–1.5 \(M_{\odot}\) is of special interest here, as the convective core is small and overshooting potentially relatively important. Stars in this mass range are also those that are used as age tracers in the range of interest for Galactic evolution studies, 1–10 Gyr. The effects of slight changes in the amount of overshooting or the detailed elemental composition of the stars are most evident in the detailed morphology of the main-sequence turnoff, which is more clearly revealed by well-populated cluster sequences \citep{davb07} than by the point probes provided by binary systems (but note the discussion of AI Phe above). Accordingly, recent stellar evolution models have tended to calibrate their overshooting prescription from studies of stellar clusters – see, e.g., \cite{davb06}. The ongoing programmes to obtain accurate data for eclipsing binaries that are members of well-studied clusters will offer particularly strong constraints on the next generation of models by combining the power of both approaches – see, e.g., \cite{2008A+A...492..171G}.
Current discussions of stellar models also focus on the applications of asteroseismology, which led to the direct demonstration of the gravitational settling of He in the outer layers of the Sun. One of the reasons for the recent spectacular success of helioseismology is, in fact, that models are also constrained by the accurate values for the solar mass, radius, luminosity and chemical composition. Asteroseismology of other stars is, however, rarely performed on eclipsing binaries, hence on the stars with the most accurate masses and radii. While there are obvious practical reasons for this, the information content of the comparison of asteroseismic models with data for single stars is limited by our uncertain knowledge of their masses and radii.
Activity in low-mass stars.
Recent results on G-K-type eclipsing binaries have demonstrated unambiguously that stars with masses just below that of the Sun and in short-period binary orbits exhibit major discrepancies from standard stellar models that provide satisfactory fits to similar stars in long-period orbits, hence with slower rotation \citep{popper, JVC, v1061cyg}. The effect is even more obvious for M stars \citep{yygem, cucnc, guboo}. In short, these stars are up to 10% larger than their slowly-rotating counterparts – a huge effect when compared to observational errors of \(\sim\) 1% – and up to \(\sim\)400 K cooler. The two effects combine to yield the same luminosity as normal stars, indicating that this is a surface phenomenon. Early hints of similar discrepancies go back at least 30 years \citep{hoxie73, lacy77}, but the recent accurate results have removed any remaining observational ambiguity.
A shown convincingly by \cite{v1061cyg}, \cite{L-M}, \cite{morales}, and others, these effects are caused by significant surface activity (spots) on the faster-rotating stars. This is evident not only in the light curves, but also in the emission cores of the Ca II H and K lines and sometimes in X-rays as well. The accepted cause is strong surface magnetic fields, which inhibit efficient convection; and indeed, models with artificially low values of the mixing-length parameter in the outer convective zone (i.e., less efficient convection) fit the observations considerably better \citep{v1061cyg, chabrier, v636cen}. Metallicity has been discussed as an additional cause \citep{berger, L-M}, but would not be expected to affect fast and slow rotators differently.
It would appear that progress in observational accuracy has revealed a class of mildly-active binary stars, intermediate between ordinary inactive stars and the more extreme class of RS CVn binaries, but with properties clearly different from normal single stars. It remains to be seen whether a continuum of properties exists between these classes of stars, but new models are clearly needed which take these phenomena into account in a physically realistic way. Some headway on this front has already been made \citep[see, e.g.,][]{dantona, mullan, chabrier}.