2 The implementation of the IRFM

In principle, stellar effective temperatures can be determined in a fundamental way by measuring both the angular diameter and the bolometric flux of stars. In practice, this direct approach is limited to very bright stars confined to the close solar neighbourhood. If, as in the present programme, we are interested in extending the temperature determination to other target stars, then we are compelled to use indirect methods. Among the latter, the InfraRed Flux Method (Blackwell et al. 1990) has proven its reliability and non-critical dependence on models for spectral types earlier than late K and/or M. A detailed description of the implementation of the IRFM adopted in the present work is given in Paper I. For the sake of self-consistency we provide below a brief outline of it.

The determination of $T_{\rm eff}$ is obtained by comparing the quotient between the bolometric flux ($F_{\rm Bol}$) and the monochromatic flux at a chosen infrared wavelength of the continuum ($F(\lambda_{\rm IR})$) both measured at the top of the Earth's atmosphere ($R_{\rm obs}$), with the outputs of models ($R_{\rm theo}$). Therefore, the basic equation of the IRFM is:

$$\begin{eqnarray} R_{\rm obs}=\frac{F_{\rm Bol}}{F(\lambda_{\rm IR})}= \frac{\sig... ...ber \\ =R_{\rm theo}(\lambda_{\rm IR},T_{\rm eff},{\rm [Fe/H]},g),\end{eqnarray}$$ (1)

where the dependence of models on metallicity, surface gravity, and $\lambda_{\rm IR}$ is explicitly taken into account. The monochromatic fluxes are obtained by applying the relation

 

$$F\!(\lambda_{\rm IR})\!=\!q(\lambda_{\rm IR},\!T_ {\rm eff},... ...},g)\! [F_{\rm cal}(\lambda_{\rm IR})10^{-0.4(m-m_{\rm cal})}],$$ (2)

where m and $m_{\rm cal}$ are, respectively, the magnitudes of the problem and standard star, $\lambda_{\rm IR}$ is the selected wavelength at the infrared, $F_{\rm cal}(\lambda_{\rm IR})$ is the absolute flux of the standard star at $\lambda_{\rm IR}$, and $q(\lambda_{\rm IR},T_{\rm eff},{\rm [Fe/H]},g)$ is a dimensionless factor which corrects the effect of the different curvature of the flux density distribution, across the filter window, between the standard and the problem stars.

The separation of observational and model inputs is easily obtained by substituting relation (2) in Eq. (1) as follows:

$$\begin{eqnarray} \frac{F_{\rm Bol}}{F_{\rm cal}(\lambda_{\rm IR})10^{-0.4(m-m_{\... ...e/H]},g)R_{\rm theo}(\lambda_{\rm IR},T_{\rm eff},{\rm [Fe/H]},g).\end{eqnarray}$$ (3)

Once [Fe/H] and $\log(g)$ are known for a certain star, the observational quantities on the left-hand side of Eq. (3) determine the star's effective temperature by comparing with the theoretical values obtained from models on the right-hand side. An outline of the practical application of the IRFM is shown in Fig. 1.

  

Figure 1: Outline of the IRFM as implemented in the present work