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Astron. Astrophys. 335, 605-621 (1998)

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6. The nature of the pulsations

6.1. Strange-mode instabilities?

Kiriakidis et al. (1993) have suggested that the variability of LBVs could be due to strange-mode instabilities. They have calculated the location in the HR-diagram where this instability occurs using the OPAL opacities for various metallicities: [FORMULA], 0.02 and 0.03. The location depends very strongly on the metallicity. This is shown in Fig. 5, where we plot the regions where the strange-mode instability occurs for two values of the metallicity: Z=0.004 and 0.03. The location of our program stars is also indicated. The LMC stars are compared with the prediction for [FORMULA] (although this metallicity is lower than the LMC value of [FORMULA]) and the Galactic stars are compared with the [FORMULA] predictions. The values of [FORMULA] of LBVs is varying. In this figure we used the mean value of log [FORMULA] at the epoch where we measured the microvariations.

[FIGURE] Fig. 5. The location of the strange-mode instabilities in the HR-diagram (shaded area) for [FORMULA] and [FORMULA] (from Kiriakidis et al. 1993). The location of our LMC program stars at the time of the observed variability are compared with the predictions of [FORMULA] and the Galactic stars are compared with [FORMULA]. The left full line indicates the location of the main sequence.

The temperature range in the HRD where the strange-mode instability occurs is very sensitive to the metallicity. The LMC stars are outside the instability region for [FORMULA]. However, the instability region for [FORMULA] (not predicted) might cover the location of the LBVs of the LMC. Of the Galactic stars, AG Car is in the predicted instability region, but the other two program stars are outside the region. They are too faint by about 0.2 dex. However, given the uncertainty in the stellar parameters and in the location of the edges of the strange mode instability region, the disagreement between predictions and observations might not be significant.

It is very unlikely that the strange-mode instability is responsible for the microvariations of most of the LBVs. The reason is simple: the microvariations of LBVs are very similar to those of normal supergiants (where it is sometimes called [FORMULA] Cyg variability). The only difference is that the amplitudes and periods of the LBVs are larger than for normal supergiants by about a factor two. All early type supergiants, from types O through A, show these microvariations. This is not in agreement with the predicted limited location of the strange-mode instability in the HRD.

We now investigate if the microvariations of the two LBVs for wich we found a much larger Q-value, i.e. S Dor and AG Car, could be due to strange modes.

AG Car
The luminosity of AG Car suggests an initial mass of about 70 [FORMULA]. The calculations of Kiriakidis et al. (1993) show the results for a model with an initial mass of 60 [FORMULA] and a metallicity of Z=0.02. The temperature of AG Car was about [FORMULA] K during the epoch for which we derived the period. For this temperature range the predictions show one unstable model with a period of [FORMULA] with [FORMULA], which corresponds to a period of only 0.3 days. This is much shorter than the observed periods by about a factor [FORMULA].

S Dor
Kiriakidis et al. (1993) did not publish the results for [FORMULA] which would be applicable to the pulsations of S Dor in the LMC. However they show the results for [FORMULA]. The luminosity of S Dor suggests that the initial mass was about 50 [FORMULA]. The nearest model in Kiriakidis et al. is for [FORMULA]. The predicted models of this star do not show unstable modes in the temperature region of [FORMULA] K, which is the temperature of S Dor at the time of the measured microvariations. However, since the location of the instability is very strongly dependent of Z, let us assume that a model with [FORMULA] is unstable. In that case we can use the eigen frequency calculations of Kiriakidis et al. to find the expected period. For a model with [FORMULA] [FORMULA] and [FORMULA] K the predicted period of the lowest order strange-mode instability is 4.4 days. This is a factor 30 to 50 shorter than the observed periods.

We conclude that the microvariations of the LBVs cannot be explained by strange-mode instabilities.

6.2. The similarity to Slowly Pulsating B-stars: non-radial g-modes?

We compare the microvariations of the LBVs with those of the Slowly Pulsating B-stars (hereafter: SPBs, Waelkens 1991). Pamyatnykh (1998) recently predicted a continuous extension of gravity mode instability due to the [FORMULA]-mechanism from the SPB- domain in the HR-diagram towards large stellar masses. The observational findings of Waelkens et al. (1998) with respect to the position in the HR diagram of variable supergiants discovered by Hipparcos are fully compatible with Pamyatnykh's theoretical prediction. The main period of the variation of the supergiants derived from the Hipparcos photometry also suggests an extension of the SPB instability domain. This can be seen on Fig. 3 of Waelkens et al. (1998): the position of all the supergiants suggests that they exhibit g-modes similar to those excited in SPBs.

Since the microvariations of the LBVs are very similar to those of the normal B-type supergiants (with the exception of AG Car and S Dor, see Sect. 5.2) this suggests that the microvariations of the LBVs are also due to pulsation in g-modes.

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998