\journalname
Astronomy&AstrophysicsReview To further explore the potential of our new calibrations, we have derived masses and radii for the 1,040 nearby F, G, and K stars studied by \cite{VF05} from their spectroscopic determinations of \(T_{\rm eff}\), \(\log g\) and [Fe/H]. Their masses and radii are derived in two ways: either directly, i.e., the radius from luminosity based on the Hipparcos parallax \citep{Perryman:97} combined with \(T_{\rm eff}\), then the mass from \(\log g\), or alternatively, \(M\) and \(R\) are derived from theoretical isochrones with the luminosity and spectroscopic \(T_{\rm eff}\) and [Fe/H] values as input parameters. Their results and our values are compared in Fig. \ref{CalibTest2}.
Two features are prominent: First, the masses and radii derived from isochrones by \cite{VF05}, and preferred by them, are indeed much more reliable than those derived directly from parallax, \(T_{\rm eff}\) and \(\log g\); in particular, implausibly large masses are found for the evolved stars in the latter case. Second, a small, but significant deviation (\(\sim\)5%) is seen for masses near \(1~{}M_{\odot}\), in the sense that our calibrations give slightly larger masses than the isochrones. Because the same effect is found for the Sun, as noted above, the isochrones are probably not the cause of this difference.
We have attempted to refine our mass calibration with higher-order terms, but without success. The number of systems with good [Fe/H] determinations is still too small to support a more sophisticated approach, so we prefer to retain the simple equations above, noting that the accuracy achieved is still very good and the equations far simpler to use than interpolating in isochrone tables.