4 Conclusions

It was my intention to give a concise overview of the current knowledge on S Dor variables up to the beginning of the 21st century, complemented with an inventory of all confirmed and suspected members and members in quiescence. I also felt the need to put much emphasis on the photometric achievements of the various types of instabilities, because usually not enough light is shed thereon and besides a number of misunderstandings, continuously wandering through literature, needed clarification and correction. S Dor variables exhibit a number of instabilities which, together with their precise evolutionary state, are highly of interest, but badly understood. None are strictly periodic like Cepheids and the like. The instabilities comprise:
1. the rare SD-eruptions (Sect. 1.4). Is stochastic resonance a cause, as tentatively suggested by Sterken et al. (1997a), possibly in connection with the dynamical ionization-induced dynamical instability discovered by Stothers & Chin (1996)?
2. the frequent SD-phases (Sect. 1.5) consisting of two types with different time scales (t < 10yr and yr, the short (S)-SD- and long (L)-SD phases, respectively) which are often superimposed on each other (Sect. 1.5.1). Is there any connection between these two and the SD-eruptions? Where and how do they originate and how should the multi-periodic character of the SD-phases of e.g. AG Car be explained (Sects. 1.5.2 and 1.5.3)? Presumably, the SD-phases, the "secular cycles'' according to Stothers & Chin (1995, see Sect. 1.5.1 of the present paper) originate deeper in the stellar interior than the microvariations, otherwise the latters should not remain so imperturbably present on the ongoing SD-phases;
3. the two types of microvariations (Sect. 1.6) with different timescales (weeks: near minimum light, and about 100d: near maximum light). Within a certain temperature interval (20000-10000K) they can be seen superimposed on each other. This suggests that they originate in different layers. Subsequently, e.g. when the SD-phase is on its way to maximum light, the short one quickly disappears (within a few months or shorter), the longer one continues. This must be due to changing physical conditions of the outer layers by the expansion. Thus, it appears that S Dor variables form a well-equipped laboratory for a number of photospheric and atmospheric pulsations and instabilities, but theoretically they are still badly understood. To cite Stothers (2000, priv. comm.): "A great difficulty right now seems to be the problem of correlating what the stellar models predict with what the observations show. This will continue to be a problem until theoretical models can be produced that are more sophisticated''. Therefore, the modeling should continue, with the emphasis on the explanation for the photometric phenomena and to answer the question: will all $\alpha$ Cyg variables pass through a blue S Dor-stage? Topics as well are the origin, the chemical and dynamical characteristics of their circumstellar ejecta which are usually much better understood. It appears that the chemistry and the dynamics of the ejecta are important for the interpretation of the evolutionary stage of S Dor variables: in most cases they point to a post-RSG stage, even for the most luminous variables. The inventory is complemented with physical and photometric parameters (made as homogeneous as possible) and other characteristics for all members and suspected members, collected from literature. Attention was given to errors in temperature and luminosity, of crucial importance for the interpretation of their position on the theoretical HR-diagram. The inventory contains 46 SDor variables among which 12 candidates and additionally it contains 3 rejected candidates. It is differentiated into four categories according to the size of the maximum light amplitude of the SD-phases exhibited in the 20th century. It appears that the strong-active S Dor variables obey the relation, called the SD-minimum strip:

$$\log L/L_{\odot} = 1.37\,\log T_{\rm eff} - 0.03.$$

The other categories obey the same relation, but with more scatter which is twice as large on the blue side than on the red side. This could point to evolutionary effects, or high rotation velocities. The occasional specimens even show a substantial and significant deviation from the narrow S Dor area (R4 in the SMC, R149 and HDE326823 in the LMC). Thus, according to the observations, the S Dor stage occupies only a small portion of the blue part of the evolutionary tracks of massive stars. In Sect. 3.2.5 a short discussion is given of the possible evolutionary connection between S Dor variables and the variable yellow hypergiants. These may be proto-low-luminous S Dor variables. In Sect. 3.2.6 the present status of $\eta$ Car is discussed (see also Sect. 1.8). It has been confirmed that the reliability of the radial velocity curve on which the existing binary models were based, is highly questionable. It would be a misunderstanding to believe that all S Dor variables are, or should be, spectacular during most of their lifetime. The majority appears to be low-amplitude (< 0 $.\!\!^{\rm m}$5) variables, or are close to the minimum state. It is estimated that for more than 70$\%$ of their lifetime as a hot S Dor variable, they are not spectacular at all. It was the happy few, like $\eta$ Car, P Cyg, S Dor, AG Car, etc., which gave the S Dor variables their famous reputation. The estimated total number of S Dor variables in the Galaxy amounts to $\sim$200. It seems that the frequency of S Dor variables in the Galaxy, the LMC and the SMC is more or less equal, although the frequency in the SMC is based on low-number statistic. All reseachers interested in these variables should look eagerly forwards to surprises which the unpredictable S Dor variables have instore for us in the 21st century.

Note added in proof: It is quite well possible that P Cyg is yet slightly instable in view of the possible very low-amplitude SD-phase with a time scale of about 8y (Table 6). Very recent research by Markova and collaborators has demonstrated that for this variation a correlation excists between brightness, temperature and radius, similar to those of other S Dor variables during SD-phases. Further, it appeared that the massloss rate increased with increasing radius (like R71 and S Dor) (Markova, N. 2000, ASP Conf. Ser., 204, 117; Markova, N. 2001, ASP Conf. Ser. on P Cyg, Armagh, in press; Markova, N., Morrison, N., Kolka, I., & de Groot, M. 2001, in press; Markova, N., Scuderi, S., de Groot, M., & Panagia, N. 2001, A&A, in prep.).

This 8y variation and a 500d variation are possibly cyclic, at least spectroscopically (Markova, N., Morrison, N., Kolka, I., & de Groot, M. 2001, in prep.).

Further, it appeared that the 100d microvariation of P Cyg (Table 6) has a counterpart in the wind variability (Markova, N., 2000, A&AS, 144, 391; Markova, N., Scuderi, S., de Groot, M., & Panagia, N. 2001, in prep).

The inner nebula within a few arcsec from HR Car (see Table 1) has been studied by Hulbert, S., Nota, A., Clampin, M., et al. 1999, IAU Coll., 169, 103, and White, S. M. 2000, ApJ, 539, 851.

R143 (see Table 1) appears to have a clump of material which is definitely ejected by an SD-eruption according to Smith, L. J., Nota, A., Pasquali, A., et al. 1998, ApJ, 503, 278.

A dust model for the ejected nebula of G79.29+0.46 (see Table 11) has been presented by Trams, N. R., van Tuyll, C. I., Voors, R. H. M., et al. 1999, IAU Coll., 169, 71, and more proof of its membership as an S Dor variable has been offered by Voors, R. H. M., Geballe, T. R., Waters, L. B. F. M., et al. 2000, A&A, 326, 236. Both references suggest for the central star $\log L/L_{\odot} \sim 5.48$ and $\log T_{\rm eff}\sim 4.26$, thus, different from the values listed in Table 11.

A bipolar shell has been discovered recently around G25.5+0.2 (see Table 11) by Clark, J. S., Steele, I. A., & Langer, N. 2000, ApJ, 541, L67.

Acknowledgements

I am much indebted to the following colleagues for their invaluable remarks and comments: Drs. R. B. Stothers, C. de Jager, C. Sterken, I. Salamanca and B. Wolf. I am also very grateful to Dr. J. K. Katgert-Merkelijn for improving the language.