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Astron. Astrophys. 356, 913-928 (2000)

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6. Basic physical properties of 60 Cyg

To be able to comment briefly on possible causes of the different types of variations of 60 Cyg found here, we have to begin with some estimates of the basic physical properties of the object.

6.1. Radiative properties and spectrum synthesis

In order to obtain an at least approximate spectroscopic estimate of the effective temperature and gravity of 60 Cyg, we used the spectra obtained during its quiescent phase, i.e. without obvious emission, similarly as we have done for another Be star, 4 Her - c.f. Koubský et al. (1997). Using the computer code developed by Kubát (1994, 1996, 1997), we calculated a small grid of models of static plane-parallel NLTE stellar atmospheres consisting of hydrogen and helium. The atomic data and model atoms were identical to those used by Kubát et al. (1999). T he synthetic spectra were then calculated using the computer code SYNSPEC (see, e.g., Hubeny et al. 1994). The best fit of the observed profiles of H[FORMULA] and H[FORMULA] was found for the model corresponding to [FORMULA] = 27000 K, [FORMULA], and v sin i = 320 km s-1 (see Figs. 20, 21, 22, and 23). Our estimate of [FORMULA] agrees with an independent estimate by Prinja (1989) - cf. his Table 1 - and also with the dereddened UBV colours of the star for data outside Be phases, cf. Fig. 2 and 3.

[FIGURE] Fig. 20. Examples of rectified intensity H[FORMULA] profiles in the non-emission, intermediate and emission phase, respectively. The profiles are identified by HJD-2400000 on their right side. The synthetic profile (SYNT - [FORMULA], [FORMULA], and v sin i =320 km s-1) is also shown and the comparison of the observed and synthetic profiles is discussed in Sect. 6.1.

[FIGURE] Fig. 21. The same as Fig. 20, but for H[FORMULA].

[FIGURE] Fig. 22. The same as Fig. 20, but for He I 4471 Å.

[FIGURE] Fig. 23. The same as Fig. 20, but for He I 6678 Å.

Although we calculated a self-consistent hydrogen-helium NLTE model, we were not able to fit the He I lines consistently. We tried to use models with enhanced helium abundance in order to improve the fit. The best results were obtained for the abundance [FORMULA]. This gives a reasonable agreement both for He I 4388 Å and He I 4471 Å line profiles. However, the theoretical profile of He I 6678 Å is still shallower than the observed one (see Fig. 23). This difference disappears for even higher helium abundance, but the fit for He I 4471 Å then becomes much worse. Besides, a strong He I 4438 Å line appears in the theoretical spectrum. No such line is observed in the spectrum of 60 Cyg, so higher He abundance than [FORMULA] is not realistic.

It is conceivable that the abundance of helium is indeed enhanced in the atmosphere of 60 Cyg. However, as our analysis of secular changes of various observables showed, even the He I lines must partly originate in the envelope since their shape and width vary with time. We note that especially He I 6678 Å line is a very sensitive indicator of the presence of circumstellar matter. Quite possibly, the He I 6678 Å line appears deeper because it represents a superposition of the photospheric line with a broad shell line.

6.2. Radius, mass and rotational period

Perryman et al. (1997) derived a parallax of 60 Cyg: [FORMULA]. One has to use the observed brightness of the star from a period without emission to obtain an estimate of the stellar radius. From the character of long-term changes, we estimate [FORMULA]5[FORMULA]45. From Fig. 3, one can estimate [FORMULA]0[FORMULA]06, therefore [FORMULA]5[FORMULA]27. Using a bolometric correction corresponding to the effective temperature derived here from Code et al. (1976) and the observed parallax, one arrives at a radius of [FORMULA]5.2 [FORMULA] (4.0-7.1 [FORMULA]), where the quoted range is estimated from the parallax error and an estimated error of 1000 K in the effective temperature.

If one uses Harmanec's (1988) formulæ for normal radius and mass as functions of the effective temperature, based on accurate binary data, one obtains


The agreement of the radius estimated here from the parallax with a normal radius of a star with [FORMULA] = 27000 K is remarkable. In the absence of any direct determination, we therefore tentatively adopt also the above normal mass for 60 Cyg.

Using the above-derived extreme values of the mass and radius estimated from their error range and the v sin i derived by us earlier, one can assess the possible range for the rotational period of 60 Cyg after Harmanec (1991)


In other words, only the 0[FORMULA]2997 period - of all the possible periods of rapid changes reported here - seems to be safely enough out of the range of tolerable rotational periods of 60 Cyg. This shows how the lack of any direct knowledge of the stellar masses of Be stars makes any truly quantitative modeling of their observed variations ambiguous and uncertain.

6.3. Estimated parameters for the suspected 146[FORMULA]6 binary system

The RV variations of the H[FORMULA] emission wings and He I 6678 Å absorption with a period of 146[FORMULA]6 are quite reminiscent of the orbital motion of another, well-known Be binary, [FORMULA] Per (see Boi et al. 1995) which has an orbital period of 126[FORMULA]7. We are aware that the observed changes could also be caused by regularly changing asymmetry of the wings of the observed lines (see the upper profiles in Fig 4). However, the good agreement in the amplitude and mean RV for an absorption He I 6678 Å line and wings of H[FORMULA] emission, gives some credibility to the binary nature of 60 Cyg.

A formal orbital solution of the RV curve of H[FORMULA] emission leads to [FORMULA]10.8 [FORMULA] 0.1 km s-1, [FORMULA] = -13.4 km s-1 and f(m) = 0.0191 [FORMULA]. If one assumes that the rotational axis of the primary is perpendicular to the orbital plane, then the Keplerian rotation at the primary radius of 5.2 [FORMULA] sets the limits on the orbital inclination


The binary parameters for these two limits are the following:



This range of parameters also clearly shows that the antiphase RV curve of the H[FORMULA] central absorption (Fig. 5, middle panel) cannot represent the orbital motion of a secondary since this would lead to unrealistically low masses for both stars for any tolerable values of the orbital inclination.

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Online publication: April 17, 2000