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<div class="ltx_p">Astronomy&amp;AstrophysicsReview
Accordingly, we have attempted to model first the radii of the stars in Fig. \ref{logRlogT} by fitting a ZAMS relation, then fitting the deviations from that relation as functions of \(\log g\), with small additional terms in [Fe/H]. That strategy was quite successful, as illustrated in Fig. \ref{deltaR}, which shows the correlation between \(\log g\) and the deviation of the observed radii from a global polynomial fit including terms in \(T_{\rm eff}\) and [Fe/H] only (i.e. not just a ZAMS fit to Fig. \ref{logRlogT}). Note that stars below 0.6 \(M_{\odot}\) and pre-main-sequence stars (open circles) do not fit this relation and are excluded from the following discussion.</div>


<div class="ltx_p">We therefore proceeded to perform a full fit to \(M\) and \(R\), expressed as the simplest possible polynomials in \(T_{\rm eff}\), \(\log g\) and [Fe/H]. The resulting equations are given below and the coefficients listed in Table \ref{tableCoef}, with one extra guard digit.</div>


<span class="ltx_Math">\begin{eqnarray}
\log M &amp; = &amp;  a_{1}+a_{2}X+a_{3}X^{2}+a_{4}X^{3}+a_{5}(\log g)^{2}+a_{6}(\log g)^{3}+a_{7}{\rm[Fe/H]}\nonumber  \\ 
\log R &amp; = &amp;  b_{1}+b_{2}X+b_{3}X^{2}+b_{4}X^{3}+b_{5}(\log g)^{2}+b_{6}(\log g)^{3}+b_{7}{\rm[Fe/H]}~{},\nonumber \\
 \end{eqnarray}</span>
<div class="ltx_p">where \(X=\log T_{\rm eff}-4.1\). The scatter from these calibrations is \(\sigma_{\log M}=0.027\) and \(\sigma_{\log R}=0.014\) (6.4% and 3.2%, respectively) for main-sequence and evolved stars above 0.6 \(M_{\odot}\). The larger error in the mass, which varies over a smaller range than the radius, suggests that mass may depend on the input parameters in a more complex way than that described by these equations (see also below).
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