5 Refraction in connection with BVRI photometry

Many spectral and photometric classification methods (some examples were given above) provide MK spectral types and luminosity classes of stars. These data are necessary for accurate refraction calculations. As to photometric classification, it may only be realized with the use of filter combinations whose bands are narrower than 300 - 500 Å. However, photometries with band widths of the order of 1000 Å and more are performed. They may reach fainter stars and are very useful for many tasks. The most wide-spread photometry is the UBVRI photometry of Johnson ([1965]). In Fig. 5 their filter transmission curves are given together with the quantum efficiency of a CCD detector used in our study. Here we restrict ourselves with the BVRI range where the CCD detector is sensitive.

To assign photometric indices to the tabulated spectral energy distributions for different spectral types and luminosity classes (Sviderskiene [1988]) we use the mean relations of Schmidt-Kaler ([1982]) where the B-V indices are given as functions of MK spectral types, separately for dwarfs (luminosity class V), giants (luminosity class III) and supergiants (luminosity class I), respectively. For V-R and V-I indices we take the respective relations from Straizys ([1992]). In Figs. 6, 7 and 8 the dependencies of the calculated refraction on B-V, V-R and V-I indices respectively are given for different luminosity classes, one accuracy of refraction measurements (0.05 arcsec) is indicated. We conclude from these figures that in the case of the B-V index the luminosity effects are significant for K - M types; but for V-R and V-I indices these effects are small in comparison with the indicated accuracy of refraction measurements.

In Figs. 6, 7 and 8 the interstellar reddening effects are also given for B5 dwarf at different degrees of reddening. To get the E(V-R) and E(V-I) values for the corresponding E(B-V), the following reddening ratios taken from Taylor ([1986]) are used:

E(R-I)/E(B-V) = 0.838, (4)

E(V-R)/E(B-V) = 0.80. (5)

These ratios are valid for stars earlier than A0. In the case of B-V indices (Fig. 6) the reddening line is deviating significantly from the lines for unreddened dwarfs. The situation is quite different for V-R and V-I indices (Figs. 7 and 8, respectively) where the reddening lines are almost parallel or nearly coincide with the lines for unreddened stars. Judging on the last two figures we may suspect that there is no necessity to know E(B-V) as well as spectral types and luminosity classes in order to obtain the refraction from V-R or V-I indices with accuracies of 0.03 - 0.05 arcsec in refraction.

In this respect it is to the point to quote a remark of Straizys ([1992]) that in case of color indices at $\lambda \leq$ 5000 Å (it is close to the range of the CCD detector sensitivity) luminosity effects are small; reddening and temperature effects coincide. As a result, atmospheric extiction coefficient (discussed by Straizys) may be expressed by one linear function of color index. Similarily, refraction may be expressed by about a one-to-one function of V-R (or V-I) index for all spectral types, luminosity classes and reddenings. The V-I index seems to be the most preferable parameter for estimating refraction because at least for B5 dwarf the reddening line is almost non-distinguishable from the line for unreddened stars in Fig. 8 and the interval of measurements is large in comparison with accuracy of measurements (about $0\hbox{$.\!\!^{\rm m}$ }02$ in V-I, Johnson et al. [1966]).

To get more examples, we have also calculated the reddening line position for B5 supergiant in Fig. 8 and found that this line is also almost non-distinguishable from the respective line for B5 dwarf. We conclude that the possibility may exist to estimate mean refraction for a star from V-I index only with the accuracy of 0.05 arcsec or better; spectral type, luminosity class and interstellar reddening may be unknown. The V-I index is well known as the measure of $T_{\rm {eff}}$ (Straizys [1992]); in addition, its unsensitivity to metal abundance effects at least for F - G dwarfs has been detected (Malyuto [1969]; Alonso et al. [1996]).

The most correct approach to attack this problem is to calculate synthetic indices (by convolution of tabulated spectral energy distributions with the transmittance functions of BVRI filters) for different spectral types and luminosity classes and at different artificial reddenings. It should be compared with the calculated refraction in order to check the conclusion of present Section and to extend it to later spectral type intervals.