\journalname
Astronomy&AstrophysicsReview
Fortunately, an external check of the distances (and hence of \(T_{\rm eff}\)) is provided by the Hipparcos parallaxes \citep{Perryman:97}, revised recently by \cite{vanleeuwen}. There are 28 systems for which the distances derived in Table \ref{tableMRsup} and from the revised Hipparcos parallaxes are both known to better than 10%. Fig. \ref{distcheck} shows the difference (in percent) between the two determinations, as a function of \(T_{\rm eff}\). Weighting these differences according to their errors, the mean difference and standard deviation are 1.5% and 8.2%, respectively, and no systematic trend is apparent. This comparison suggests that the adopted effective temperature scales are essentially correct and adds strong support to the use of binary stars as distance indicators. However, close attention to the determination of \(T_{\rm eff}\) and interstellar reddening is needed in every case.
\label{metallicity}Metal abundances.
Knowledge of the chemical composition of a star is needed in order to compute appropriate theoretical models for its evolution. Accordingly, we have searched the literature for [Fe/H] determinations for the stars in Table \ref{tableMR}; the 21 reliable values found are reported in Table \ref{tableMRsup}. Photometric metallicity determinations are subject to a number of uncertainties, including interstellar reddening, so we have elected to include only spectroscopic determinations here. In most cases, they refer to the binary itself, but we have included a few systems in open clusters with [Fe/H] determinations from other cluster members.
Most of the systems in Table \ref{tableMRsup} have metallicities close to solar, so a solar abundance pattern for the individual elements is expected \citep[see, e.g.,][]{edv93}. Hence, the \(Z\) parameter of stellar models should generally scale as [Fe/H].
\label{rotation}Rotational velocities.
Axial rotational speed is an important input parameter in light curve synthesis codes as it enters the computation of the shapes of the stars. In addition, the axial rotations and their degree of synchronisation with the orbital motion are direct probes of the tidal forces acting between the two stars \citep[e.g.,][]{mazeh}, as is the orbital eccentricity. Rotations are also needed to compute apsidal motion parameters for binaries with eccentric orbits (see Sect. \ref{apsidal}).
We have therefore collected the available direct spectroscopic determinations of \(v\sin i\) and its uncertainty for as many of the components of the stars in Table \ref{tableMR} as possible (81 systems); the results are reported in Table \ref{tableMRsup}. While the accuracy varies from system to system, it is usually sufficient to detect appreciable deviations from the default assumption of (pseudo-)synchronism.
\label{ages}Ages.
The age of a star can, in principle, be determined from theoretical isochrones when \(T_{\rm eff}\), \(\log g\) (or \(M_{V}\)), and [Fe/H] are known. Computing stellar ages and – especially – their uncertainty in practice is, however, a complex procedure fraught with pitfalls \citep[see, e.g., the extensive discussion in][]{GCS1}. Some of the original sources of the data in Table \ref{tableMR} discuss ages, but many are based on outdated models, and their origin is necessarily heterogeneous. Determining truly reliable ages for the stars in Table \ref{tableMR} would require (re)determination of effective temperature and [Fe/H] for many systems and a detailed comparison with models (see Sect. \ref{models}) – a major undertaking, which is well beyond the scope of this review.
Even a rough age estimate is, however, a useful guide to the nature of a system under discussion, e.g., when assessing the degree of circularisation of the orbit and/or synchronisation of the rotation of the stars. To provide such estimates on a systematic basis, we have computed ages for all but the lowest-mass systems from the Padova isochrones \citep{girardi}, taking our adopted values of \(T_{\rm eff}\), \(\log g\), and [Fe/H] as input parameters and setting [Fe/H] = 0.00 (solar) when unknown. For the lowest-mass systems and some of the more recent studies, we have adopted the ages reported in the original papers. All the age estimates are listed in Table \ref{tableMRsup}.
We emphasise that these values are indicative only: Errors of 25–50% are likely, and in several cases they will be larger. Any accurate age determination and realistic assessment of its errors would require a critical re-evaluation of the input parameters \(T_{\rm eff}\) and [Fe/H] – probably requiring new observations – and far more sophisticated computational techniques than are justified with the material at hand. For this reason, we deliberately do not give individual error estimates for the ages in Table \ref{tableMRsup}.