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Astron. Astrophys. 362, 673-682 (2000)

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4. Consistency checks with other observational facts

We 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.


[TABLE]

Table 5. Parameters derived from the radial velocities and the light curves with the Levenberg-Marquart algorithm and free mass ratio. [FORMULA] and [FORMULA] denote the Roche potentials, [FORMULA] and [FORMULA] the filling factors indicating that BF Aur is detached. The second line specifies the standard deviations of the estimated parameters. The solution in this table is referred to as solution 1 .



[TABLE]

Table 6. Parameters derived from the radial velocities and the light curves with the Levenberg-Marquart algorithm and free mass ratio. [FORMULA] and [FORMULA] denote the Roche potentials, [FORMULA] and [FORMULA] the filling factors indicating that BF Aur is detached. The second line specifies the standard deviations of the eastimated parameters. The solution in this table is referred to as solution 2 .



[TABLE]

Table 7. Full parameter set describing the adopted light curve solution for BF Aur, together with estimated uncertaintities of the main parameters. [FORMULA] measures the relative difference of the mean effective temperatures, J is the surface brightness. [FORMULA] and [FORMULA] denote the fill-out parameter [FORMULA]. S and V denote surface area and volume. k is the ratio of the mean radii.


4.1. The spectral line ratio of He i 438.7 nm

As the components have almost equal temperatures (with [FORMULA]) and similar surface gravities the line-strength ratio should compare well with the luminosity ratio [FORMULA]. 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 [FORMULA] and He i 438.7, Kallrath & Kämper (1992) estimated a line ratio of roughly [FORMULA], 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 [FORMULA] (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 [FORMULA] (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 [FORMULA] as a function of phase [FORMULA] and the mass ratio q; these values were computed with Wilson's subroutine LC. The mass ratio [FORMULA] ([FORMULA]) corresponds to the solution in Table 5 (6).


[TABLE]

Table 8. This table shows the ratio [FORMULA] as a function of phase [FORMULA] and the mass ratio q; these values were computed with Wilson's subroutine LC. The mass ratio [FORMULA] ([FORMULA]) corresponds to the solution in Table 5 (6).


Compared to the observational values, the values in Table 8 slightly indicate a preference for the [FORMULA] solution, for which the computational light ratio are just within the error bounds of the observational line ratios. For the solution corresponding to [FORMULA] the computational values are slightly out of the error bounds of the observational values. In Table 3 we note that solutions for [FORMULA] have [FORMULA] and that these solutions are thus not consistent with the observed line ratios.

4.2. The influence of the reflection effect on the solution

The 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 indices

Strömgren 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 [FORMULA] vs. [FORMULA] diagram to be 1.5, one gets a color excess [FORMULA], and thereby [FORMULA], [FORMULA], [FORMULA], [FORMULA]. From the color excess, we estimate the total visual absorption [FORMULA]. This gives the combined visual magnitude corrected for interstellar extinction as [FORMULA], and for the mean component we get [FORMULA]. From Moon's (1984) empirical calibration of the intrinsic color index [FORMULA] in terms of the visual surface brightness parameter [FORMULA], defined as [FORMULA] (Barnes & Evans 1976), we then derive [FORMULA] and [FORMULA].

Various temperature calibrations with Strömgren indices lead to closely concordant results summarized in KK. E.g., the [FORMULA]-calibration of Davis & Shobbrook (1977) for luminosity class V-III, in conjunction with Code et al.'s (1976) ([FORMULA], [FORMULA])-relation gives [FORMULA] K, [FORMULA]. From interpolation in the theoretical grids of Lester et al. (1986) we get [FORMULA] K and [FORMULA]. Finally, a photometric spectral type may be derived from the position in the [FORMULA] plane, which is that of an evolved B4-5V star.

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© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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