\journalname
Astronomy&AstrophysicsReview

Testing stellar models

\label{models}
Comparison with stellar evolution models is one of the most prominent uses of accurate binary data \citep[see, e.g.,][]{Pols:97, Lastennet:02, Hillenbrand:04} and features in most modern papers on binary system parameters. An extensive discussion on the subject was given in A91, with a focus on what information can be obtained from data of increasing degrees of completeness. Only a few main points will be repeated here, with a summary of recent developments.
The key point of the A91 discussion was that, while even the best data can never prove a set of models right, sufficiently accurate and complete data can reveal significant deficiencies in the physical descriptions in stellar models: When the (preferably unequal) masses and identical composition of two binary components are known, and the age of the model of one star is fixed from its radius, requiring the model to match the observed radius of the other star at the same age is a non-trivial test. Matching the observed temperatures as well provides additional constraints, e.g., on the helium content and mixing length parameter of the models. AI Phe, as shown in A91, probably remains the best textbook example (but see Sect. \ref{sysfit}).
In the following, we briefly review the ways that accurate and increasingly complete binary data can be used to constrain stellar model properties. We begin with some general considerations of the possible tests, then discuss fits to individual systems, and finally review recent progress of more general interest.

General considerations

Information from \(M\) and \(R\) only.
The change in radius with evolution through the main-sequence band is clearly seen in the mass-radius diagram of Fig. \ref{logRlogM}. In the absence of significant mass loss, evolution proceeds vertically upwards in this diagram, and a line connecting the two stars in a given binary system indicates the slope of the isochrone for the age of the system.
The level of the ZAMS (zero-age main sequence) and the slope of young isochrones in this diagram depend on the assumed heavy-element abundance \(Z\) of the models, the ZAMS models having larger radii at higher \(Z\). Thus, any point below the theoretical ZAMS curve in Fig. \ref{logRlogM} would be interpreted as that star having a lower metallicity than that of the models, and a binary with a mass ratio sufficiently different from unity can constrain the range in \(Z\) of acceptable models. Obviously, the smaller the observational errors, the stronger the constraints on the models \citep[see, e.g.,][]{uoph}. But unless \(Z\) (i.e. [Fe/H]) has actually been observed, one cannot check whether the model \(Z\), and hence the derived age, is in fact correct. And there is still no constraint on the helium abundance and mixing length parameter of the models.
Information obtainable with \(M\), \(R\), and \(T_{\rm eff}\).
Adding \(T_{\rm eff}\) to the known parameters allows one to go a step further. E.g., in the temperature-radius diagram (Fig. \ref{logRlogT}), models for the accurately known mass of every star have to match not only the two observed radii for the components of each binary system at the same age, but also the two values of \(T_{\rm eff}\). A match can often be obtained by adjusting the metal and/or helium abundance (equal for the two stars) and/or the mixing-length parameter (also the same unless the stars have very different structures), and plausible numbers will usually result, but the test is weak without a reality check on these numbers.
Tests using \(M\), \(R\), \(T_{\rm eff}\), and [Fe/H].
Having the complete set of observable data allows one to make truly critical tests of a set of stellar models: \(M\) and [Fe/H] fix the basic parameters of the model of each star (assuming a value for the helium abundance \(Y\), which normally cannot be observed directly, and/or for the mixing-length parameter). A model for the stars in a binary is then only successful if the temperatures and radii (or luminosities) of both stars are fit within the observational errors at a single age -- a non-trivial requirement.