## 3. Simultaneous photometric and spectroscopic least-squares solutionIn agreement with the line-ratio discussion in Sect. 4.1 and the discussion of nomenclature in Kallrath & Milone (1999, Sect. 2.7), we refer to the primary component labelled by index 1 as the photometric primary (the star eclipsed at primary minimum). The photometric primary corresponds to the spectroscopic secondary star (the star with the weaker spectral lines). The spectroscopic primary is eclipsed at secondary minimum. To solve the light curves, we used the software package WD98, a successor of WD95 (Kallrath et al. 1998) based on the 1993 version of the WD code, and a further improved version, called WD98, based on the 1998 version of the WD code. The least-squares problem of parameter estimation is treated in the usual way described in Kallrath & Milone (1999, Chapter 4). We used all observations described in Sect. 2, with the following meaning: -
is a flux-dependent weight chosen proportional to the phase-dependent inverse flux of the binary system [for details, see Kallrath & Milone (1999, p.103], as appropriate for photon statistics in the nomenclature of Linnell & Proctor 1970); and -
is a curve-dependent weight accounting for the standard deviation of the data points in that curve.
The factors and
are described in detail in Wilson
(1979) and Kallrath & Milone (1999). Calculations were performed
either in mode 2 (cf. Wilson 1988), The strong correlation of the limb-darkening coefficients with other light-curve parameters and its negative influence on the numerical properties of the light curve is a well-known problem (see, e.g., Wilson & Devinney 1971, or Twigg & Rafert 1980). Only under exceptional circumstances (i.e. total eclipses) will it be possible to extract meaningful limb-darkening coefficients. In view of these difficulties it is perhaps the wisest to trust the coefficients derived from the best available model atmospheres. Therefore, we adopted the square root and, alternatively, in some additional test runs the logarithmic limb-darkening coefficients given by Van Hamme (1993a), which are based on the model-atmosphere grid of Kurucz (1979). For BF Aur as an early type system the square-root coefficients, and , seem to be more appropriate and we used Van Hamme's (1993a) interpolation software was used to derive these values. If the temperature of the secondary component changed in the course of the iterations, the limb-darkening coefficients were adopted accordingly. The albedos were fixed at the values appropriate for radiative envelopes, , corresponding to full reradiation. Gravity darkening exponents were chosen, corresponding to von Zeipel's law. Since the new observations are of high quality and are consistent
in time, a simultaneous analysis of both radial-velocity curves and
the
The fit including proximity effects (turned on by the control flags
ICORR1 and ICORR2 in the WD program set to 1) requires that the shapes
of the stars and the surface flux distribution are known. This was
achieved by adopting some of the parameters obtained in the
simultaneous analysis. Note that the fit and its standard deviation is
better and that the standard deviations of the estimated parameters
are smaller. Therefore, we continued to model the radial velocities
with the proximity effects. Note that the uncertainty in the mass
ratio prevents us from deciding
whether Since
For completeness, we give in Table 7 those values which can be derived from the finally adopted solution (surfaces , volumes , mean radii . Fig. 3 and Fig. 4 show the final solutions of the light curves and the radial velocity curves, respectively.
© European Southern Observatory (ESO) 2000 Online publication: October 24, 2000 |