3 Model inputs: the q- and R-factors

The use of broad-band photometry to obtain the IR monochromatic fluxes requires the application of the so-called q-factors introduced in Eq. (2) (See also Paper I). Ideally, q-factors should be determined from spectroscopic data, but in the absence of a complete data base of empirical IR spectra, we have to rely on a grid of models to compute q -factors. Note however that q-factors always imply small corrections in the range studied.

The theoretical flux density distributions from Kurucz's (1991, 1993) models have been used to calculate $R_{\rm theo}(\lambda_{\rm IR})$ and $q(\lambda_{\rm IR})$ factors, as defined in Eq. (1) and Eq. (2) respectively. The effective wavelengths of the bands J, H, K and L' for the application of the IRFM were computed by considering the instrumental response of the photometric system (Alonso et al. 1994b and Paper IV) and the atmospheric transparency of the site computed by using the PLEXUS code (Clark 1996). Then the closest wavelengths sampled by the models were adopted ($\lambda_{J}=1272.5\;{\rm nm}$, $\lambda_{H}=1635.0\;{\rm nm}$, $\lambda_{K}=2175.0\;{\rm nm}$ and $\lambda_{L'}=3690.0\;{\rm nm}$).

 

Table 1: Calibration of q- and R-factors versus metallicity, $\log(g)$ and effective temperature for $\lambda_{\rm eff}=1272.5~{\rm nm}$ (J band), computed using fluxes generated with Kurucz (1993) models

 

Table 2: The same as in Table 1 for $\lambda_{\rm eff}=1635.0~{\rm nm}$ (H band)

 

Table 3: The same as in Table 1 for $\lambda_{\rm eff}=2175.0 ~ {\rm nm}$ (K band)

Tables 1, 2, 3 and 4 contain the calibration of q- and R-factors generated with Kurucz's models as a function of temperature, metallicity and surface gravity. Effective temperatures cover the range 3500-6500 K, surface gravities cover the range $\log(g)=(0.0-3.5)$, and metallicities cover the range (0.5, -3.5).

3.1 Sensitivity of $q \times R$ to the effective temperature

The separation of terms in Eq. (3) (i.e. model information to the right-handside, and observational data to the left-handside) is useful to simplify the analysis of the influence of errors on the derived temperatures.

Among the four near-IR wavelengths considered in this work, the $q \times R_{J}$ factors are the least sensitive to temperature, especially under 5000 K. The $q \times R_H$ and $q \times R_K$ sensitivities are comparable, although temperatures lower than 4000 K derived using $q \times R_H$ are less reliable, due to the relative maximum of the flux associated with the minimum of the H^- opacity reached in this band. As a consequence, the value of q_H factors in this temperature range is significantly different from 1, so that the effect of any possible uncertainty in the H^- opacity or in other sources of opacity which now become more important is amplified. Finally, the highest sensitivity to $T_{\rm eff}$ is shown by $q \times R_{L'}$, however this sensitivity is counterbalanced by the difficult of measurement of fluxes in this band.

The variations induced by the change in metallicity or surface gravity are only important for $T_{\rm eff}$ lower than 4250 K. In particular, the variation of R-factors in the range $\log(g)=0-3.5$ for a fixed temperature and metallicity is almost negligible.

  

Figure 2: Top: Mean uncertainties in the IRFM temperatures derived from J, H, K and L' fluxes, induced by an error of 5% in the observational quotient $\frac{F_{\rm Bol}}{F_{\rm cal}(\lambda_{\rm IR})10^{-0.4(m-m_{\rm cal})}}$. Bottom: Maximum mean uncertainties of the IRFM temperatures induced by an error of 0.5 dex in [Fe/H] and $\log(g)$ respectively. Note the change in the scale of the ordinate axis with respect to the top figure

The values of $q \times R$ obtained from Tables 1-4 allow the errors induced by the uncertainties in the different input parameters of the IRFM on the derived temperatures to be derived easily (Fig. 2).
If we consider a variation of 5% in $q \times R$ --the theoretical counterpart to the quotient $F_{\rm Bol}/F(\lambda_{\rm IR})$-- the change in temperatures derived using the factors R_H, R_K and R_L' is practically constant over 4000 K: 1.6-2% for T_H and 1.6% for T_K and T_L'. The change of T_J varies from 8% at 4000 K to 2% at 7000 K. Hence, R_J is the poorest indicator of $T_{\rm eff}$ for the application of the IRFM, and we will consider only T_J temperatures over 5000 K in the average.
An uncertainty of 0.5 dex in metallicity causes, over 4000 K, a maximum average error of 0.5% in the mean temperatures derived applying the IRFM (Fig. 2). The influence of an error of 0.5 dex in $\log(g)$ is even smaller on the derived temperatures, reaching at most average errors of 0.3% over 4000 K.