## 4. Consistency checks with other observational factsWe now check whether further observational facts that were not included in the simultaneous analysis, such as line ratios, Strömgren indices, and period change, are consistent with the model produced by the least-squares solution.
## 4.1. The spectral line ratio of He i 438.7 nmAs the components have almost equal temperatures (with ) and similar surface gravities the line-strength ratio should compare well with the luminosity ratio . Popper (1981) reproduced microphotometer tracings of the spectra of 26 OB eclipsing binaries in the wavelength range 430-450 nm. The BF Aur spectrogram illustrated in his Fig. 7 corresponds to phase 0:p70, i.e., the component eclipsed at primary minimum is receding. Lines of both stars are clearly present, the redshifted components all being the weaker ones. From and He i 438.7, Kallrath & Kämper (1992) estimated a line ratio of roughly , in agreement with the statement made already by Mammano et al. (1974) (but ignored by later investigators) that the spectroscopic component 2 is the one being eclipsed at primary minimum, i.e., corresponds to the photometric primary. Thus, KK accepted only solutions with line ratios close to that value. Their B solutions (KK Table 1 and Table 2) had a line ratio of about 1.2. The line ratios of our new spectroscopic data were evaluated at four quadrature phases for the He i line at 438.7 nm, and lead to the line-depth ratio (primary/ secondary) of (rms) as measured from the residual intensities in the respective line cores. A double-Gaussian fit with the routines supplied by the NOAO/IRAF data-reduction package yields an equivalent-width ratio of (rms) in good agreement with above value. The individual equivalent widths for the star with the stronger lines are between 402-376 mÅ and for the star with the weaker lines between 360-290 mÅ. The average internal rms error from the two-Gaussian fits was 8 mÅ. Fig. 1 shows a representative spectrum near quadrature. Note that the line profiles are never completely blend free and the internal rms error is thus likely underestimated. Let us now compare these observational facts with the computational
results summarized in Table 8 which shows the ratio
as a function of phase
and the mass ratio
Compared to the observational values, the values in Table 8 slightly indicate a preference for the solution, for which the computational light ratio are just within the error bounds of the observational line ratios. For the solution corresponding to the computational values are slightly out of the error bounds of the observational values. In Table 3 we note that solutions for have and that these solutions are thus not consistent with the observed line ratios. ## 4.2. The influence of the reflection effect on the solutionThe influence of the reflection effect, and in particular how significant multiple reflection is in the BF Aur system, has been analyzed by KK and by Van Hamme (1993b). For the solution in Table 3, we confirm again that multiple reflection is not significant in the BF Aur system, i.e., does not change the estimated parameters at all. ## 4.3. Additional information from Strömgren indicesStrömgren indices for BF Aur measured at five phases are available from the survey by Hilditch & Hill (1975). Because the components have almost equal temperature and similar surface gravities, their colors will be similar and we may take the indices measured as representative of either component, after correction for interstellar extinction. The indices measured can be dereddened with Crawford's (1978) intrinsic color relations for B-type stars. Taking the slope of the reddening line in the vs. diagram to be 1.5, one gets a color excess , and thereby , , , . From the color excess, we estimate the total visual absorption . This gives the combined visual magnitude corrected for interstellar extinction as , and for the mean component we get . From Moon's (1984) empirical calibration of the intrinsic color index in terms of the visual surface brightness parameter , defined as (Barnes & Evans 1976), we then derive and . Various temperature calibrations with Strömgren indices lead to closely concordant results summarized in KK. E.g., the -calibration of Davis & Shobbrook (1977) for luminosity class V-III, in conjunction with Code et al.'s (1976) (, )-relation gives K, . From interpolation in the theoretical grids of Lester et al. (1986) we get K and . Finally, a photometric spectral type may be derived from the position in the plane, which is that of an evolved B4-5V star. © European Southern Observatory (ESO) 2000 Online publication: October 24, 2000 |