7. Binary stars
One more constraint can be obtained from the stars of the sample which are component of a binary system having known orbit and masses. One of us (JF) has already used a few of the best known binaries in order to check the predictions of theoretical evolution computations (Fernandes et al. 1998). It is worth to see if, when known, the dynamical mass of the object confirms, or disproves, its location along the proper isochrone obtained above. The most interesting case is the binary µ Cas, the only metal-poor star, having a well determined mass.
7.1. µ Cas
Drummond et al. (1995) have derived the mass of µ Cas from its orbit, with the help of speckle interferometry to see its very faint companion (). The mass of µ Cas A, readjusted with the better distance provided by Hipparcos is 0.757 0.06 . The Alonso et al. (1996a) effective temperature for (A+B) is 5315 82 K, which corrected for the presence of the companion becomes 5339 85 K, in good agreement with Fuhrmann (1998) effective temperature of 5387 80 K. We obtain for µ Cas A from its parallax, and again correcting for the presence of the companion. The position of the star is plotted with respect to the uncorrected and corrected isochrones in Fig. 5. The evolutionary masses along the dot-dashed isochrone are shown with tick-marks. The location of µ Cas is near 0.8 , within the limits of the dynamical mass 0.757 0.06 . Unfortunately, the error bar on the mass is still a bit large to add an interesting new constraint. The influence of the uncertainties on the values of the various parameters of the models on the position of µ Cas in the HR diagram are documented in Table 2 (see Lebreton 1999for more details).
Table 2. budget of the impact of parameter variations on the position of a star like µ Cas in the HR diagram. The reference model has an age of 12 Gyr, a mass of 0.757 , Y = 0.245, [Fe/H] = -0.86, and [/Fe]= 0.3 dex
7.2. 85 Peg
Fernandes et al. (1998) showed that, using the data available on this object, there was no theoretical solution fitting the two components. Later on, Martin & Mignard (1998), have restudied several binaries from Hipparcos data, and shown that it is very difficult to escape the conclusion that the mass of the primary and the secondary are very similar, notwithstanding the fact that the secondary is 3.2 magnitude fainter than the primary. New determinations of the effective temperature of 85 Peg A by Thévenin & Idiart (1999) and C. Van't Veer (private communication, 1998) confirms that 85 Peg A has a metallicity very similar to that of µ Cas A, an effective temperature of 5550 100 K, and =5.22 0.06. Its location in the HR diagram (Fig. 5) is pratically on the same isochrone as µ Cas, and corresponds to a mass of 0.85 , higher than the mass given by Martin & Mignard (1998) (0.705 ), but below the mass given by Duquennoy & Mayor (1991) from the spectroscopic orbit. 85 Peg A does not deviate any more from the proper isochrone, once its high [/Fe] ratio, its true iron abundance corrected for NLTE effects, and sedimentation of heavy elements, are all taken into account. The problem is with 85 Peg B, which is too massive for its absolute magnitude. The colour of 85 Peg B can be derived from the V and K magnitudes of (A+B), V=7.75, K=3.94 (Johnson et al. 1968), the magnitudes = 5.81 and = 9.0, and assuming that from its effective temperature and Alonso calibration of versus (, [Fe/H]). The result is = 3.46 0.06, corresponding to about = 3950 K. The associated mass and absolute bolometric magnitude are respectively 0.54 (smaller than the dynamical mass of about 0.7 to 0.8 ) and 8.0. With a bolometric correction of -1.1 and the transformation from apparent to absolute magnitudes this gives VB = 9.57 too faint by 0.6 magnitude. One possibility is that 85 Peg B is a spectroscopic binary itself, but we shall leave this hot subject for another paper, this one having at least clarified the case of 85 Peg A.
Nothing really new, not already in Fernandes et al. (1998), can be said for this star. The fact that it is more evolved introduces one more parameter (age) and prevents to check the unevolved position of the star. The star is nevertheless identified in Fig. 2, and does not raise a particular problem.
© European Southern Observatory (ESO) 1999
Online publication: October 4, 1999