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Astron. Astrophys. 337, 393-402 (1998)

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4. Discussion and conclusions

We have investigated the photometric characteristics of four [FORMULA] Cyg variables. Two of them belong to the LMC: R 85, an emission-line object and suspected LBV, and R 110 an active LBV. According to the photometry R 85 is a true and active LBV also, but not so spectacular. Two other stars are SMC members: R 42 and R 45. For both the search for a period was troublesome, which even becomes worse if the time base is made longer (say from 3 to 5 y). This could mean that the multi-cyclic oscillations are disturbed by strong stochastic noise (Sect. 4.5).

4.1. R 85 = HDE 269321

No detailed spectroscopic analysis exists for R 85. Its spectrum is B5 Iae (Feast et al. 1960). The suspicion that R 85 could be an S Dor variable with a small range was expressed by Stahl et al. (1984). Our new photometry confirms that classification and it appears that R 85 is subject to the two types of SD-phases defined by van Genderen et al. (1997a,b). Thus, there is a VLT (Very-Long Term)-SD phase with an estimated time scale of 4 decades and an amplitude of 0:m 3, and, only occasionally, a normal SD phase with a time scale of 400 d and an amplitude of 0:m 12.

The microvariations show a mix of the two types normal for active LBVs (van Genderen et al. 1997b): the [FORMULA] Cyg-type and the 100 d-type variation. Time scales lie between 15 and 180 d with an amplitude of 0:m 3. There exists a preference for time scales of the order of 83 d, 67 d and 40 d. The ratio between the second and first amounts to 4/5 and between the third and second to 3/5. Such ratios, if not accidental, often occur among multi-mode pulsating stars.

The likely explanation for the mix of the two types of microvariations mentioned above is that, presumably R 85 just has the transition temperature somewhere between 10 000 K and 15 000 K ([FORMULA] 14 000 K). Note that R 85 is the second LBV where both types were seen together; the other one is HR Car (van Genderen et al. 1997b).

4.2. R 110 = HDE 269662

This LBV had a spectacular behaviour during our photometric campaign 1989-1994: it showed a steep rising branch and a maximum (van Genderen et al. 1997b). The spectrum changed from late B to G. The microvariations have time scales of 50-100 d and their colour behaviour is mixed, while, considering the relatively long time scales, one expects them in general to be red in the maxima and blue in the minima. Probably, the star's position in the HR-diagram (extremely low temperature and luminosity) compared to other LBVs (Stahl et al. 1990) giving it a different structure, have something to do with the mixed colour behaviour. (It must be noted that the latter characteristic is roughly similar to that of S Dor's microvariations in maximum light: van Genderen et al. 1997a).

4.3. R 42 = HD 7099

R 42 is an abnormal [FORMULA] Cyg variable with a total light amplitude of 0:m 19, which is even larger than for hypergiants and is often exhibited by LBVs in quiescence. Colours are usually blue in the maxima and red in the minima as they should, but the ranges of the colours are twice as large as for other variables of the same spectral type. The search for a period was troublesome, probably due to a complicated type of multi-cyclicity and the contribution of stochastic secondary processes. Most surprising is that the strongest cycle in the power spectrum is so long: [FORMULA] 128 days. This is quite abnormal for such an early spectral type (B2.5 I)-that is, unless it represents the rotation period of the star which is of the same order as for a number of later BA-type supergiants investigated by Kaufer et al. (1996, 1997). These authors suggest the presence of co-rotating weak magnetic surface structures as the source for the rotationally modulated H[FORMULA] line-profile variability originating in the lower wind region. If the 128 d period in the brightness of R 42 is indeed caused by rotational modulation, perhaps too long for such an early spectral type, it might mean that magnetic fields and star spots are present. Therefore, it is recommended that a detailed spectroscopic study should be made to establish the true nature of the variability of R 42.

4.4. R 45 = HD 7583

The A0 hypergiant R 45 is visually the brightest star of the SMC (after the maximum stage of the LBV R 40, van Genderen et al. 1997b). Wolf (1973) has done a model atmosphere analysis and derived physical parameters, showing that the atmosphere is near the limit of instability. There are striking similarities with HD 33579, the A3-hypergiant in the LMC. He also found strong indications that emitting material of the chromosphere is falling back to the star's surface. Stellar wind properties were derived by Stahl et al. (1991), and Humphreys et al. (1991) considered R 45 a "normal" A-type hypergiant as opposed to those with an enhanced He abundance due to their post-red supergiant evolutionary stage. R 45 should then be a post-main sequence star evolving to the red, similar to HD 33579 (Nieuwenhuijzen et al. 1998).

Its variability in light as well as in colour is normal with respect to other [FORMULA] Cyg variables (hypergiants) of roughly the same spectral type. The search for a period was troublesome, probably due to multi-cyclicity and the contribution of stochastic secondary processes.

4.5. Instabilities in theoretical models

Evidence is now accumulating that the intricate photometric variability of [FORMULA] Cyg variables, among which the LBVs, is caused by multi-cyclic oscillations combined with a stochastic component (van Genderen et al. 1997b; Sterken et al. 1997, 1998; Paper I and the present paper).

During the last few years, dynamical strange-mode and mode-coupling instabilities were found in theoretical models of massive stars (Glatzel & Kiriakidis 1993; Kiriakidis et al. 1993; Glatzel 1997). A strong non-adiabaticity in the stellar envelopes is necessary for strange modes to occur (Zalewski 1993). Essential for pulsational instability in [FORMULA] Cyg variables is also a sufficiently high [FORMULA] ratio (e.g. Gautschy 1992) on which depends the radiation pressure. The envelopes possess three opacity peaks: one by metals (the Z-bump) and two by the partial ionization zones of He and H, which cause density inversions and, consequently, acoustic cavities giving rise to a rich unstable oscillation spectrum (Gautschy & Glatzel 1990; Glatzel 1997; see also the excellent review papers on stellar pulsations by Gautschy & Saio 1995, 1996).

It is therefore not unrealistic to suppose that such phenomena might result in intricate light variations of evolved massive stars because of linear superposition of many excited modes. There are no direct objections against presuming that these multiple excited modes appear superimposed on top of the S Dor phases (which have annual-to-decadal time scales) whether they are caused by the relaxation oscillations in the outer layers of LBVs-as theoretically discovered by Stothers & Chin (1993, 1994, 1995)-or by the pulsation cycles leading to "outburst" in the models of Cox et al. (1997) and Guzik et al. (1997). It is then also conceivable that LBVs near minimum should show an oscillation spectrum of a different kind then near maximum. The reason is that the radius of the star/envelope is small in the first case and large in the second case. The size has a direct impact on the physical structure. However, the physics of strange modes and their consequences on the continuum light is still not well understood. Based on our various monitoring campaigns we have indeed observed different kinds of microvariations (often with a multi-periodic character) on top of the SD phases. Guzik et al. (1997) find in their models oscillations with periods of 5-40 d, indeed typical for the [FORMULA] Cyg-type microvariations which we have found in LBVs fainter than the median magnitude (van Genderen et al. 1997a, b).

The LBV models of Stothers and Chin have achieved many points of detailed agreement with the observations of SD phases (Stothers & Chin 1996, 1997)-despite Glatzel's (1997) criticism. A recently described fact in favour of these models is that LBV nebulae often represent H-rich envelopes of RSGs ejected before the "blue LBV phase" (Nota & Clampin 1997; Smith 1997).

However, it is still a matter of debate what exactly pulsates: the outer envelope, or the underlying star (or perhaps both). Stothers & Chin predict envelope pulsations during the "blue LBV phase" (thus after the RSG stage) and characterize the accompanying slow cyclic light variations as "eruptions" with the expectations that thick shells are then ejected, "while the star moves hardly at all on the H-R diagram, the observable changes being produced primarily by the optically thick ejected cloud" (Stothers & Chin 1996; actually, this is similar to the "classical" interpretation of the observed light- and colour variations of SD phases independently proposed by Martini 1969 and van Genderen 1979, and that [FORMULA] stays more or less constant: Sect. 4.3 in the latter paper). While Stothers & Chin predict quasi-regular cycles of the annual-to-decadal time scales, which is the case indeed, we believe that ejections of that caliber do not occur because they have not been observed. We rather believe that after expansion the envelope contracts again wihout losing much of its mass. It is true that significant mass-loss variations exist in some LBVs, but no general correlation between mass loss and photospheric parameters has been found (Leitherer et al. 1992; de Koter et al. 1996) such as for the radius (Leitherer 1997). If during every SD cycle a thick shell were ejected, then e.g. AG Car and S Dor should have been enshrouded by conspicuous nearby clouds, caused by centuries, if not millennia, of SD phases with a time scale of 1-10 yr. That is also the reason not to call them "outbursts" (or "eruptions") as has been proposed by Lamers 1987, Leitherer et al. 1992 and van Genderen et al. 1997a. Guzik et al. (1997) define an "outburst" when the outward photospheric radial velocity suddenly becomes large, and the radii of outer zones monotonically increase during several "would-be pulsation periods". Quantitative information on the possible expelled mass is lacking; therefore, it is uncertain whether this definition is correct.

Others believe that the cyclic variations of LBVs, (with an annual-to-decadal time scale), the SD phases, are caused by the underlying stellar radius (Leitherer et al. 1989; de Koter et al. 1996; van Genderen et al. 1997a), although de Koter et al. (1996) conclude that they are induced by the combined effect of an increase of the stellar radius and a reduced effective gravity. A pseudo-photosphere in the wind is not likely to occur (de Koter 1997).

Perhaps, the truth on what pulsates, lies somewhere between these suppositions and depends also on the individual LBV.

However, considering the conspicious individuality of the photometric characteristics of LBVs, one is inclined to believe that most of the instability sources are seated in a somewhat less-bound outer envelope. (According to the models of Stothers and Chin the envelope is even nearly detached from the underlying star. Also in Maeder's (1992, 1997) "geyser model", the outer gaseous photospheric layers float upon a radiative layer, according to him a favourable situation for "giant outbursts").

After all, this could offer much freedom (intuitively) for the dynamical consequences and, thus, for the annual-to-decadal brightness variations and the significant mass-loss variations in some LBVs (see above).

On the other hand, spectroscopically as well as with regard to their morphology and physics of circumstellar or ring nebulae, LBVs show more homogeneity (e.g. Nota & Clampin 1997; Smith 1997; Hutsemékers 1997). Computations of the behaviour of circumstellar gas around such objects can be well modelled and predicted and provides a powerful tool for the investigation of the stellar mass-loss history (Garcia-Segura et al. 1996).

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© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998