Astron. Astrophys. 324, L25-L28 (1997)

4. Discussion

Our analysis of the Lyman lines covered by the ORFEUS spectrum results in a new temperature determination for the WD in V471 Tau: =35 125 1275 K which, regarding the error ranges, is in agreement with the earlier result from Guinan & Sion (1984) mentioned above and with a combined IUE Ly /EXOSAT EUV analysis by Vennes (1992) who arrived at =34 000 K and =8.40, although the latter parameters are located outside of our 3 error ellipse. We are confident that our result is of superior reliability because of the better quality of observations. We can now proceed and use our model flux and observed absolute flux in order to calculate the WD radius R from

where denotes the energy flux at Earth and is the (astrophysical) energy flux at the stellar surface. Reading f (1100Å) from Fig. 1 and taking the respective flux from our model atmosphere F (1100Å) (units: erg/cm² /s/Å) and adopting the distance pc results in the radius R , where the error range regards the 3 error of the spectral fit and the relative error in the distance, which are both of similar order. This value agrees with the astrometric result which yields R between 0.009 and 0.01 R (Cester & Pucillo 1976, Ibanoglu 1978).

We could now go on and determine the WD mass M from our gravity determination via

where G is the gravitational constant. However, our error in results in a large uncertainty for the mass (factor 1.7). Instead, the mass determination from the astrometric analysis (Bois et al. 1988) is most probably more exact. From their derived mass function we find the mean value M , assuming a K2 dwarf mass of 0.8 M . The error margin given here reflects the uncertainty in the mass function and the inclination angle. We can in turn infer from the above equation using R and M . This gives =8.35, which is compatible with our spectroscopic result.

In a recent examination Schmidt (1996) summarized the pre-HIPPARCOS situation of the empirical mass-radius relation using spectroscopic determinations of and and best values of parallaxes and gravitational redshifts. The data show a large scatter due to observational errors, which means that the theoretical mass-radius relation cannot be confirmed. Only a handful of DA white dwarfs in binaries allows the derivation of parameters precise enough to show the expected correlation. Although the situation has improved considerably by HIPPARCOS parallax measurements of 20 white dwarfs (Vauclair et al. 1997), it is still of considerable interest to analyze individual objects with highest possible accuracy. Fig. 3 shows the position of V471 Tau in the M-R diagram, together with other binary DA white dwarfs. Also shown are the theoretical zero temperature relation of Hamada & Salpeter (1961) and the evolutionary models of Wood (1994) for a carbon white dwarf with a thick hydrogen layer and =30 000 K. According to the formal errors V471 Tau is in agreement with the theoretical Hamada-Salpeter M-R relation but not with Wood's models, however, the discrepancy appears to be rather small. A more deviating result has been obtained recently by Provencal et al. (1997) in the case of Procyon B. From HST UV photometry they derive a radius which is even smaller than the two values found by previous analyses (Schmidt 1996). Provencal et al. suggest that Procyon B has a heavier core than carbon and call into question the assumption of carbon core composition commonly used for white dwarf stars. The deviation of V471 Tau from the Wood M-R relation is much less spectacular and we do not want to make a similar suggestion here.

Fig. 3. Mass and radius of the DA in the binary V471 Tau. The astrometric mass is combined with the radius determined from the comparison of the observed FUV flux with models. Also shown are other binary DA white dwarfs with masses and radii derived in a similar manner (from Schmidt 1996). For Procyon B the latest result by Provencal et al. (1997) is shown. Curves display the Hamada & Salpeter (1961) zero temperature relation and the evolutionary models of Wood (1994)

Finally, the observed 555 s period and the radius determined above imply a rotational speed of v =76 km/s for the WD. This value is markedly higher than the upper limits of the projected rotational velocity v sin i derived from high resolution H spectroscopy for six other (isolated) Hyades white dwarfs by Heber et al. (1997), which ranges between 21 and 35 km/s. As a matter of fact the present mass of the V471 Tau white dwarf is well within the mass range of the six other WDs (0.66-0.80 M ), but it is worthwhile to note that the initial mass of the isolated Hyades WDs is in the mass range between 2.5 and 3 M (Weidemann et al. 1992), whereas in contrast the V471 Tau primary has evolved from a 5 M main sequence star (Eggen & Iben 1988). However, the rotation of V471 Tau is not detectable in our spectra because of insufficient resolution. In addition interstellar absorption and incomplete removal of geocoronal emission masks rotational broadening of the innermost Lyman line cores.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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