5. Comparison with the semiempirical Infrared Flux Method
It is of the utmost importance that as a large number as 327 ISO standard stars have their temperatures well determined by the semiempirical narrowband IRFM and by the actual empirical broadband near-infrared approach, since comparisons between the independent results can be done at the best level of available accuracies. One best compares diameters rather than temperatures, since any detectable difference between the results is enhanced by a factor two and the suitable reference can rely on the observational correlation of Fig. 3 independent of absolute flux calibrations. Fig. 9 displays the percentage difference between the individual angular sizes predicted according to the semiempirical narrowband (BL) and empirical broadband (MI) near-infrared photometry for all the ISO standard stars of Class V and III. The diagram clearly indicates two remarkable differential effects.
The first most relevant effect is an average systematic difference % over the colour range including the A-type stars. Such an inconsistency has been already stressed in other investigations (Mégessier 1988; Napiwotzki et al. 1993) and can be now revisited. Since it is unlikely that the correlation be responsible for the observed deviation, taking into account that the photometric angular diameters are closely matched to the most accurate measurements available from interferometry techniques, I have searched for systematic errors in the semiempirical IRFM. The relevant sources of errors which can affect determinations by the IRFM are related to the bolometric flux measurements including the absolute calibration of the observed magnitudes, to the absolute calibration of the near-infrared reference flux and to the model-atmosphere monochromatic flux. First, there seems to be unlikely that bolometric fluxes be responsible for the observed deviations, taking into account the very consistent results of Table 6. In fact, only a flux discrepancy as large as that of Lyr would lead to the average shift observed for all A-type stars. Second, a significant error induced by the absolute calibration of the reference flux is also unlikely. Indeed, the comparison of the actual large deviation with the much smaller average value of % derived for dwarfs over the colour range , would provide the most convincing result that the absolute flux calibration could shift the data by no more than 1 %. Therefore, only the infrared monochromatic fluxes of A-type stars from the new LTE line-blanketed model atmospheres adopted by BL seem to be likely responsible for the observed systematic deviations. In this respect, notice the significant improvement between empirical and semiempirical estimates observed over the F-G-K spectral range.
The second effect is an intrinsic dispersion as large as about 2 % regardless the spectral classification of the stars. By assuming that the bolometric flux measurements and the broadband near-infrared colours be responsible for the observed scatter, it would imply flux errors as large as 4 %, not detected, however, in the correlations of Fig. 4. Then, we are compelled again to investigate for random errors arising in the narrowband photometric data and/or the monochromatic model fluxes adopted by the IRFM. A valuable test for assessing the observed dispersion is drawn in Fig. 10, where angular sizes predicted by two different versions of the IRFM are differentially compared with the actual broadband data. The BG version of the IRFM derives the near-infrared reference flux according to data just using Johnson broadband K magnitudes, whereas the BL version for the subset of stars in common is currently adopting specific narrowband filters. For self consistent comparisons, the BG bolometric fluxes should be multiplied by the average correction factor 0.958 derived from the subset of stars in common as reported in the upper part of the diagram. Then, the lower diagram shows the BL data with a dispersion nearly close to those of Fig. 9, as expected. In contrast, the BG data no longer display the high level of scatter as the BL results. Assuming that the LTE line-blanketed and MARCS code model atmospheres adopted by BL and BG, respectively, give rise to consistent results with a small dispersion, according to the BL investigation, there would be evidence for a significantly larger component of random errors arising in the narrowband near-infrared data of the IRFM compared to the version using broadband photometry.
The diagrams of Fig.s 9 and 10 can be readily exploited to assess systematic and random errors affecting the semiempirical narrowband temperatures by the IRFM, since the bolometric fluxes were assumed to be the same in both semiempirical and empirical methods. The significant systematic shift makes the IRFM temperatures of A-type stars too low by 2.33 % (SD = 0.9 %), whereas the average shifts of 0.17 % (SD = 0.9 %) and - 0.93 % (SD = 1.1 %) for dwarfs and giants, respectively, indicate much more consistent results over the F-G-K spectral range. Of course, this fair good agreement between the independent results gives also the most valuable and strong support to the reliability of temperature determinations at the target accuracy of 1 % required for the ISO standard stars.
© European Southern Observatory (ESO) 1998
Online publication: October 22, 1998