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

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5. The physical state of BF Aurigae

A change in period [FORMULA] days/cycle has been determined by a parabolic fit of the BF Aur O-C curve obtained by Demircan et al. (1997) which leads to the ephemeris


with [FORMULA], [FORMULA] and [FORMULA], and the integer-valued quantity E denoting the epoch (number of cycles measured from [FORMULA]). The period increase measured in days/cycle is equivalent to a weak period increase of [FORMULA]. which is of the same order as the value [FORMULA] obtained by Zhang et al. (1993) or the value [FORMULA] found by Simon (1999). Note however, that Fig. 8 in KK shows that the period has remained practically constant over more than 70 years of observational records.

Although the accuracy of the data is quite high, q is only weakly defined and at present the question whether q is larger or smaller than unity cannot be decided with certainty. So, the best we can do is discuss the possible scenarios and their implications on the astrophysical state of BF Aur.

Scenario 1 : The observed period change has the right sign for mass reversal if we get a solution with [FORMULA], [FORMULA] and [FORMULA] (implied by the stronger lines of the photometric secondary which is the spectroscopic primary and in agreement with the least squares results). The lower mass star fills or almost fills its Roche lobe. In that case we have conservative mass exchange (the system loses no mass), and mass reversal has just taken place. The period increases of BF Aur can be explained by the possible mass transfer from the less massive component to the more massive one as the case assumed in the most of Algol systems.

Scenario 2 : Here we have [FORMULA], [FORMULA] and [FORMULA]. Note that Schneider et al. (1979) used the WD code in mode 5 and got a semi-detached configuration with [FORMULA]. They point out that one should then expect BF Aur to be in the rapid phase of mass transfer from the more to the less massive component (proceeding on a thermal time scale) and thus to see a corresponding period decrease. This, however, is not observed; the period has remained practically constant over more than 70 years of observational records (see Fig. 8 in KK), and the newer results even indicate a period increase. The likely reason for this is that the period change due to mass transfer is proportional to [FORMULA], which probably is much smaller than thought before. It may be estimated that, if only 5-10% of the material lost by the primary is lost from the system (non-conservative case), a period decrease might be compensated or even turned into a period increase (see the discussion in by Wilson and Stothers (1995) related to the non-conversation of angular momentum, or transformation of orbital angular momentum into rotational angular momentum). Note that there is no problem being in the rapid phase past mass reversal. One should not assume that the rapid phase should stop when the masses equalize. Conservative mass transfer theory predicts that the rapid phase will continue far beyond the equal-mass point. For example, U Cep is widely believed to be in the rapid phase (or just coming to the end of it) although the mass donor is considerably less massive than the acceptor.


Table 9. Strömgren indices of BF Aur taken from the survey of Hilditch & Hill (1975). Reddening-free (bracketed) indices were computed as [FORMULA], [FORMULA], [FORMULA].
1) Measurements discarded from mean values.

Scenario 3 : We have [FORMULA], [FORMULA] and [FORMULA]; our light curve analysis suggests that BF Aur is still barely underfilling its Roche lobe so that mass transfer has not yet fully developed. The more massive star almost fills its Roche lobe. Since q is just above unity all arguments of scenario 2 apply as well. Let us now compare our results with respect to the mass-luminosity relation which we expect to be fulfilled for main-sequence components of close binary systems as long as mass transfer has not yet influenced their evolution. Taking [FORMULA], we should have [FORMULA]. A solution compatible with the mass-luminosity relation should fulfill [FORMULA] for equal temperatures. Since the ratio of radii is about [FORMULA] for all reasonable solutions, this indicates a mass ratio near 1.04. Fig. 5 in KK shows that the bolometric magnitude difference between the binary components, as predicted from the light curve solutions, is a flat function of q (which means that the observed spectral line ratios can only be used to solve the transit/occultation question but not to discriminate between mass ratios) while the mass-luminosity relation is a steep function of q. The intersection occurs at [FORMULA] which corresponds well to the solution [FORMULA] in Table 3.

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© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000