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Astron. Astrophys. 341, 480-486 (1999)

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Appendix A: Calibration of log g

Fig. A1 shows [FORMULA] on the [FORMULA] plane for the effective temperature range of early B stars. The solid and dashed lines (integer and half-integer values of [FORMULA], respectively) are from Smalley & Dworetsky's (1995) grid. The filled and open circles represent early-B components of binary systems for which empirical [FORMULA] values are known, and the plus sign is 12 (DD) Lac. These points were plotted using observed [FORMULA] indices and the photometric effective temperatures, derived from [FORMULA] and [FORMULA] via the calibration of Napiwotzki et al. (1993), mentioned in Sect. 2.1. In order of decreasing [FORMULA], objects with known [FORMULA] are CW Cep AB (Crawford & Barnes 1970, Giménez et al. 1990, Clausen & Giménez 1991), [FORMULA] Vir A (Sterken & Jerzykiewicz 1993), QX Car AB (Andersen et al. 1983, Giménez et al. 1986), 16 Lac (Sterken & Jerzykiewicz 1993), V539 Ara A (Crawford et al. 1971, Gronbech & Olsen 1976, 1977), CV Vel AB (Clausen & Gronbech 1977, Balona 1994) and HR 2680 (Gronbech & Olsen 1976, 1977). The references in parentheses contain the uvby and [FORMULA] photometry we used. For the binaries with nearly equal components, denoted AB, we used combined light photometry. For [FORMULA] Vir A, V539 Ara A and HR 2680, we corrected the observed indices for the light of the fainter component; in the case of HR 2680, these duplicity corrections were very small. No corrections were required for 16 Lac. Note that in this figure 12 (DD) Lac is plotted with its photometric [FORMULA].

[FIGURE] Fig. A1. Lines of constant [FORMULA] in the [FORMULA] plane from Smalley & Dworetsky's (1995) grid of synthetic [FORMULA] indices. Dashed lines represent half-integer values of [FORMULA]. Also shown are early-B components of seven binary systems (filled and open circles) and 12 (DD) Lac (plus sign), plotted using the photometric [FORMULA] values and the observed [FORMULA]. The binary systems are identified in the text

For the binary systems, the [FORMULA] values read off Fig. A1, which we shall refer to as "photometric," can be compared with the empirical ones. For components of the SB2 eclipsing binaries CW Cep, QX Car, V539 Ara and CV Vel (filled circles), the empirical [FORMULA] values have been listed by Andersen (1991). For the primary component of Spica (the leftmost open circle), [FORMULA] can be derived from the mass and radius obtained by combining the spectrographic and interferometric orbits and the angular diameter (Herbison-Evans et al. 1971). Finally, for the primary components of the SB1 eclipsing binaries 16 Lac and HR 2680 (the other two open circles), the empirical values have been determined by Jerzykiewicz (1994). In the latter two cases, a mass had to be assumed to obtain [FORMULA], but the results were insensitive to the assumed mass. Taking straight means for the nearly equal-components binaries CW Cep, QX Car and CV Vel, we present the comparison in Fig. A2, where the difference between the empirical and photometric [FORMULA] values is plotted as a function of the photometric effective temperature. The error bars were plotted using standard deviations of the empirical values. For 16 Lac and HR 2680, the standard deviations are equivalent to changing the assumed mass by 2 [FORMULA]. The solid straight line was derived by the method of least squares. Equal weights were given to the points in the least-squares solution because the scatter in Fig. A2 is clearly not correlated with the standard deviations of the empirical [FORMULA] values.

[FIGURE] Fig. A2. The difference between the empirical and photometric [FORMULA] values for the binary systems shown in Fig. A1, plotted as a function of the photometric [FORMULA]. The error bars represent standard deviations of the empirical values. The solid straight line was fitted to the points by the method of least squares

The photometric [FORMULA] value of 12 (DD) Lac read off Fig. A1 is equal to 3.87. Taking into account the difference "empirical minus photometric," implied for [FORMULA] by the straight line in Fig. A2, we correct this to [FORMULA], where the standard deviation is that of the least-squares fit to the [FORMULA] differences. Adopting this standard deviation we assume that the scatter in Fig. A2 is caused mainly by errors of the photometric indices.

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© European Southern Observatory (ESO) 1999

Online publication: December 4, 1998
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