Physical Properties of
Be Stars in Open Clusters

For the data coming from a Be object to be properly used, it is mandatory to separate the combined spectrum into its two main components: central star + envelope. Usually the methods to perform this separation try to adjust the absorption wings of some line (H for instance) to existing atmosphere models. The parameters of the corresponding model atmosphere (log T_eff and log g) are then chosen as representative for the underlying photosphere and this allows to isolate the emission spectrum from the envelope.

Open clusters represent a wonderful tool to asses this problem. We have an homogeneous set of Be stars of similar age and composition whose loci in the temperature - luminosity diagram can be well represented by the isochrone. The peculiar positions of Be stars in these diagrams is due to the contamination of the photometric indices by the circumstellar emission. The fact that Be stars in an 'off-emission' phase occupy positions indistinguishable from the normal B-type stars of the cluster, support this assumption (Fabregat et al. 1994).

We have developed an observational program where simultaneous uvby photometry and spectroscopy are combined to yield general properties of Be stars and physical properties of their circumstellar envelopes. In the (b-y)₀-M_V plane, Be stars deviate to redder positions with respect to the non-emission B stars due to additional reddening caused hydrogen free-free transitions in the envelope, which modify the slope of the Paschen continuum. In the c₀-M_V plane we have found two different behaviours: Be stars earlier than B5V show smaller (bluer) c₀ values due to free-bound transitions in the envelope, which reduce the Balmer jump, while late type Be stars seems to show regular or even larger c₀ values (in spite of the emission levels at H) indicating absorption at the Balmer discontinuity of circumstellar origin (Fabregat et al. 1996).

We developed a uvby calibration to obtain the intrinsic radiative parameters of underlying B stars. This was based on the existence of linear relationships between the equivalent widths of the Balmer emission lines and the photometric anomalies. We realized that the best relationship was attained between the circumstellar excess in Strömgren's c₁ index and the equivalent width of the H emission line. The photometric index is a measure of the H line equivalent width. This allowed to find the equations to correct the radiative parameters in terms of the photometric indices alone (Fabregat & Torrejón, 1998). On the other hand, the calibration is only valid for spectral types earlier than B5. There seems to be no correlation at all for late type Be stars.

It should be noted however that the number of stars upon which these results were obtained are few in number. We are currently involved in a larger scale study employing CCD photometry of Be stars in clusters. Particular attention is being paid to the -not yet solved- problem of standard transformation and the rejection of other emission-line stars as Herbig Ae/Be type objects, Blue Stragglers, etc. This will allow us to refine the calibration and investigate more deeply the case of late type Be stars which appear to deviate systematically from the relationships derived for their early type counterparts.

This calibration has been used to correct the spectra for the underlying absorption. Indeed, once the intrinsic photometric indices has been obtained, one can use the standard calibrations (Balona 1994) to obtain the physical parameters of the central star log T_eff and log g. This is just what you need as imput for the model atmospheres. This method is not sensitive to whether or not H line wings are in absorption.

In our study, average physical properties of the envelopes are inferred from an investigation of Balmer decrements. Following the works of Dachs et al. (1990) and Slettebak et al. (1992) we have plotted in Fig.1 a two decrement plot for a sample of Be stars in clusters.

Fig.1 Two decrement plot for early type Be stars. Stars are denoted either by open squares (low emission) or triangles (high emission). Bottom line links the centroids for high and low emission stars respectively, being parallel to the upper theoretical line.

From the inspection of Fig.1 it is clear that Be stars with large envelopes (high emission) lie closer to the predicted nebular values under Case B conditions {Case B assumes a low density nebula optically thick to Lyman radiation but completely transparent to Balmer radiation.}. Our D₃₄ and D₅₄ values are consistent with those computed by Drake & Ulrich (1980) for a gas at T_e ~ 10⁴K, ground state ionization ratio R_1C=3s^-1 and optical depth = 10⁵ and for and electron density in the range N_e ~ 10¹¹ to 10¹³. However stars with smaller envelopes deviate from the Case B conditons. This can be explained if small envelopes have higher electron densities due to higher average envelope temperatures. Indeed, their observed D₃₄ and D₅₄ values are consistent with those computed by Drake & Ulrich (1980) for a gas at T_e ~ 2 x 10⁴K, ground state ionization ratio R_1C = 3s^-1 and optical depth = 10⁵. For a gas in thermal equilibrium the increase in temperature produces a displacement in the two-decrement plot in the same direction. The general departure from the case B conditions is justified by the fact that Balmer lines are found to be optically thick {The computed optical depth for the adopted grid (cf. Drake & Ulrich, 1980) lies around ~ 4. Poeckert & Marlborough (1979) have found ~ 10² to 10⁴ at the line centers.}. The fact that the smaller envelopes are hotter can be understood in terms of the luminosity conservation in the envelope (Torrejón & Fabregat, 1999). These results are in full agreement with those obtained in previous works for field stars.

Finally, open clusters offer a invaluable tool to assess the problem of the evolutionary status of Be stars. From the study of our photometric data in clusters as well as from search in the literature, we have found the following relevant aspects:

1. The clusters with the highest frequency of Be stars h & Per, NGC 663 and NGC 3766) occupy a very narrow age interval (14-24 Myr).

2. Very young open clusters have no (or very few) Be stars.

3. Older clusters have lower frequencies, being seldom observable in clusters with log t = 8.0 (Mermilliod, 1982).

4. Clusters with Cep stars have no (or very few) Be stars and vice versa.

Points number 1 and 2 were presented for the first time in Torrejón (1997) on the basis of photoelectric photometry. Our CCD survey will provide more insight into these points.

The picture that emerges from the above observational facts is that a Be needs a minimum time to form and hence a Be star can not be a very young object. This need for a minimum time would be fulfilled by a B + evolved companion binary system following the mass transfer phase. The evolved companion would be, on the grounds of close binary evolution view (Pols et al. 1991) a He star, a white dwarf or a neutron star. The first two would lead to 'isolated' Be stars while the third one would lead to Be-X ray type systems. In view of subsequent studies, with negative results in the search for evolved companions (Meurs et al. 1992) this case remains open.

References

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