\journalname
Astronomy&AstrophysicsReview The significant effects of both stellar evolution and abundance differences are well seen in the close-up of the deceptively tight mass-luminosity relation of Fig. \ref{logLlogM} that we show in Fig. \ref{logLlogMz}. Making the error bars visible highlights the fact that the scatter is highly significant and not due to observational uncertainties. The open symbols show – not surprisingly – that the stars classified as giants are more luminous than main-sequence stars of the same mass, but the more subtle effects of evolution through the main-sequence phase are also clearly seen.
But evolution is not all, as seen by comparing either star in VV Pyx with the primary of KW Hya (nos. 42 and 46 in Table \ref{tableMR}). The stars are virtually identical in mass and radius (or \(\log g\)), hence in very similar stages of evolution, but their temperatures are quite different and the luminosities differ by nearly a factor of two. Clearly, the two systems are expected to have different compositions, with KW Hya likely more metal-rich than VV Pyx. Unfortunately, no actual determination of [Fe/H] is yet available for either system to test this prediction.

Fitting individual systems

\label{sysfit}
The most informative comparison of stellar models with real stars is obtained when the mass, radius, temperature, and [Fe/H] are accurately known for both stars in a binary system. If the stars differ significantly in mass and degree of evolution, fitting both stars simultaneously for a single age provides a very stringent test of the models. We have calculated individual evolutionary tracks for the observed masses and metallicities of the systems in Table \ref{tableMR}, setting [Fe/H] = 0.00 if the metallicity is unknown. In most cases, a respectable fit is achieved, and any modest deviations can usually be explained in terms of uncertain temperatures, reddening and/or metallicity. Resolving the exceptional cases of large unexplained discrepancies will require detailed studies, perhaps involving additional observations, which are beyond the scope of this paper.
In nearly equal-mass binaries, the requirement for consistency between the two components is only a weak constraint on the models, at best. But the rare examples of significant differential evolution can be very informative, as shown in the classic case of AI Phe \citep{aiphe} – see Fig. \ref{aiphe}. With masses only 20% larger than that of the Sun and a metallicity only slightly lower, solar calibrations were adopted in that work for the helium content and mixing length of the Victoria models of the time, and a picture-perfect fit was obtained for both stars at exactly the same age.
In order to see how modern stellar evolution codes fare in this comparison, we show in Fig. \ref{aiphe} the observed properties of AI Phe together with tracks from the Yonsei-Yale code \citep{yi, demarque} for the measured masses and metallicity (solid lines). As seen, these models fit the primary (cooler) star well, but the track for the secondary (lower curve) is just outside the \(1\sigma\) error limit of the observations. Asterisks indicating \(\pm\)1% age differences show just how sensitive the fit is.
At our request, Dr. D. A. VandenBerg kindly computed new models for AI Phe with an experimental version of the Victoria code \citep{davb06}, which includes He diffusion in the outer layers; note that the adopted mixing length and overshooting parameters of these models have not yet been adjusted to match the solar and other constraints satisfied by the \cite{davb06} model series.