1 A review of the scientific achievements

1.1 Introduction

Now, at the beginning of the 21st century it is appropriate to summarize the scientific achievements in the field of S Dor variables (or LBVs: Luminous Blue Variables) and to make an inventory of them in the Galaxy and the Magellanic Clouds. When Humphreys & Davidson (1994) wrote their review paper on S Dor variables entitled: "Astrophysical Geysers-The Luminous Blue Variables'', the Galaxy numbered 5, the LMC 6 and the SMC 1 "confirmed'' of these variables. The list of "candidates'' numbered 4, 4 and 0 stars, respectively. A few years later, Parker (1997) listed 6 new candidates for the Galaxy and 2 confirmed S Dor variables and 1 candidate for the LMC. The list presented by Bohannan (1997) is very similar. Apart from a concise description on the various aspects of S Dor variables (as I will call them throughout this paper, see Sect. 1.2), a list is presented of 34 confirmed members (including 8 so-called ex-/dormant members, see Sect. 1.2), 12 candidate members and 3 former candidates. Of the 46 objects (leaving out the 3 non-members) 21 belong to the Galaxy, 4 to the SMC and 21 to the LMC. They have been divided into four categories (defined in Sect. 2.1). For each category three tables are given listing a number of photometric and physical parameters, the reddening and the distance (all have been selected and/or have been made as homogeneous as possible), time scales and light amplitudes of the various types of instabilities, and whether ejecta are present. Each entry is accompanied by non-exhaustive reference numbers decoded in a separate table. It is not professed to be complete, after all, other references can be found in the quoted ones. Further, for 18 objects a schematic light curve is presented, giving an impression of the past and present light variations. A few brightness estimates of LMC objects made in the 19th century are partly based on a compilation by Thackeray (1974) and partly on other sources such as the HD and HDE catalogues (the last one dated 1925). The ptm (photometric) and ptg (photographic) magnitudes of the HD catalogue are, depending on the declination, based on visual magnitudes of the Bonner Durchmusterung dated around 1850, of the Cordoba Durchmusterung and of the Cape Photographic Durchmusterung (both dated at the end of the 19th century) by applying a colour index correction if necessary (see the introduction to the HD catalogue). A short discussion is devoted to a possible evolutionary connection between S Dor variables and the variable yellow hypergiants and some attention is paid to the present status of $\eta$ Car. The structure of the S Dor (SD)-area in the theoretical HR-diagram is analyzed for the four categories mentioned above. Finally, a discussion is presented on the total numbers of estimated S Dor variables in the three stellar systems.

1.2 Nomenclature and general characteristics

S Dor variables are a separate class of massive and very evolved stars. They are subject to a number of instabilities, often at the same time. Their origin is still largely a mystery, although there are a number of presumptions based on theories and models. Three types of photometrically observable instabilities belong to the "SD-phenomenon'', two others to the microvariations. One of the latters is typical for all variable super- and hypergiants: the $\alpha$ Cyg variables (thus including the S Dor variables, see Sect. 1.6). I prefer to call them "S Dor variables'' and not "LBVs'', because this is the traditional designation given by Kukarkin et al. (1974), (to be more specific: "hot S Dor variables'', since it is not excluded that also cooler supergiants can be subject to similar type of instabilities, see Sect. 3.2.5; de Jager & van Genderen 1989; van Genderen 1991a; Stahl et al. 1990). In this way confusing names like "yellow LBVs'' can be avoided. An even more important reason not to call them LBVs is that all evolved massive stars are (micro-)variables, thus, also the blue ones, but only a very small fraction belongs to the S Dor variables. The preference to keep the original name memorized, has been brought into practice by introducing the concept "S Dor (SD)-phase'' for the cyclic phases of brightening on a time scale of years to decades and light amplitudes up to a maximum of (van Genderen et al. 1997a,b; Sect. 3.4 of the present paper). It should be avoided to call these cyclic SD-phases "eruptions'' or "outbursts'', because they suggest a period with violent mass ejections, which, as we know nowadays, is not the case (Sect. 1.5). The main cause of SD-phases are stellar radius and temperature variations. Sometimes, but not always, they are accompanied by a denser wind (Sects. 1.5 and 3.2.1). The few cases which showed genuine eruptions, called "SD-eruptions'' and witnessed the last few centuries (Sect. 1.4), are P Cyg (17th century), $\eta$ Car (19th century), perhaps HD5980 (1993-1995) in the SMC and a few in other galaxies (Humphreys 1999). Humphreys (1999) suggested to name the just mentioned objects "$\eta$ Car-like variables'', not only because of the eruptions, but also because of an excess luminosity during the eruption (see for $\eta$ Car: van Genderen & Thé 1984; for P Cyg: Lamers & de Groot 1992, de Groot & Lamers 1992; for V12 in NGC2403 and for SN1961V: Humphreys & Davidson 1994). After these eruptive periods, the four variables showed a post-maximum plateau, a second, lesser eruption and subsequently a strong obscuration by circumstellar dust (Humphreys et al. 2000). That these eruptive periods are fundamentally different from the SD-phases, which in the case of $\eta$ Car are visible as small-amplitude light oscillations (several 0 $.\!\!^{\rm m}$1) on a time scale of a few years, became obvious from a photometric analysis in 1984 by van Genderen & Thé (1984: Sects. 9.2 and 9.6), see also Whitelock et al. (1983) and van Genderen et al. (1999: Sect. 4.1). Since many S Dor variables seem to suffer from such eruptive periods at least once in their life time (Sect. 1.8), I believe that a separate name for stars like $\eta$ Car, P Cyg, etc., is not yet necessary, unless their light curves are really unique, i.e. when it will be shown in due course that other S Dor variables exhibit eruptive light curves different from those just mentioned. The eruptive light curve of the candidate S Dor variable HD5980 in the SMC (in 1992 and 1993) looks quite different indeed (see for references Tables 11, 12 and 13). That e.g. the variable star hidden in $\eta$ Car behaves as a normal S Dor variable also, is demonstrated by the 26yr (1974-2000) of multi-colour photometry undertaken by our group. It shows typical SD-phases with at times superimposed microvariations, although, often disturbed by a variable non-stellar light source (with especially in the near-UV peculiar periodicities). This light source could perhaps be a luminous accretion disk/hot spot system: see Sects. 3.2.2 and 3.2.6 and Tables 4, 5 and 6; van Genderen et al. 1994, 1995, 1999; 2001; de Groot et al. 1997a; Sterken et al. 1996b, 1999a,b).

1.3 Criteria for S Dor-membership

The criteria, or signatures for SD-membership are extensively discussed by Humphreys & Davidson (1994). Supplemented with new insights, they can be summarized as follows:

a)

visible ejecta (although only 40% of the present compilation has visible ejecta, Sect. 1.8), likely caused by (an) SD-eruption(s);

b)

spectroscopic (variable) characteristics indicating a high luminosity, a high mass loss rate ($\sim$ $10^{-5}\,M_{\odot}$yr^-1), an extended atmosphere and ejecta containing CN or CNO processed material. This type of chemistry as well as the dust composition, is consistent with a RSG (red supergiant) origin (Sect. 1.7);

c)

a photometric variability of up to 2 $.\!\!^{\rm m}$5 on a time scale of years to decades and even to centuries, the so-called SD-phases (Sects. 1.5 and 3.4). One of the typical characteristics is that the light variations show a large variety. The colour variations are crucial for the detection of the SD-phases and therefore a very strong diagnostic tool: due to the excursions on the HR-diagram at a more or less constant luminosity, the colour indices become red when the star (if hotter than $\sim$ 7000K) brightens and blue when the star becomes fainter. This habit appears to be easily detectable, even if the light ranges of SD-phases are as small as 0 $.\!\!^{\rm m}$1 or even smaller, thus, they should not be confused with the microvariations which have much shorter time scales (Sect. 1.6). In this way a number of candidates could be classified as genuine S Dor variables.

Spectroscopically suspected S Dor variables turned out to fulfil without any exception the photometric criteria, if enough multi-colour photometric observations were made. Therefore, if spectroscopic observations, as well as a proof for ejecta are (still) lacking, I applied the reverse reasoning to identify S Dor variables only based on the photometric multi-colour behaviour. Ofpe/WN9 stars will not be considered as suspected or candidate S Dor variables (such as S9), unless they show an N-enriched spectrum and stellar ejecta such like S61 (= Sk-69 266, see Tables 8, 9 and 10). To cite Bohannan (1997): "...$\,$Ofpe/WN9 stars have been proposed as quiescent LBVs. As appealing as that is, this call cannot be made on spectroscopic features alone''. Therefore, the stars studied spectroscopically in the UV by Smith Neubig & Bruhweiler (1999), although showing SD-characteristics in the UV, are not included in the present list of candidates, unless they were already identified as genuine S Dor variables by other criteria.

1.4 The S Dor (SD)-eruptions

The extremely powerful eruptions of a small number of S Dor variables mentioned in Sect. 1.2 released a total energy of 10^47.3-10^49.5ergs (Humphreys et al. 2000). There are different theoretical approaches to these SD-eruptions, although, to cite Davidson & Humphreys (1997): "Instabilities of this type are so complex that it is difficult to be sure that competing models are fundamentally different''. However, all authors agree that the L/M ratio is likely higher than for other stars at the same location on the HR-diagram, thus, they must have lost a lot of mass already. Humphreys & Davidson (1994) discussed all views and models giving the state of affairs up to 1994. They believe that the sub-photospheric instability models are most promising (outer layers below 2 10⁵K are dynamically isolated from the stellar interior because of the high opacity due to iron, and can easily become unstable). This is the hypothetical "modified Eddington limit'', in which "modified'' indicates that the opacity is temperature- and density-dependent. (The classical Eddington limit is an upper limit to the ratio L/M for a nearly static stellar atmosphere). Since then a number of other models and mechanisms were proposed: Langer et al. (1994) discussed a new scenario for the evolution of massive stars ( ) by introducing mass-loss in addition to the radiation-pressure driven wind, resulting in better agreement with the observations than previous scenarios. Cox et al. (1997) gave a summary of the mechanisms proposed to destabilize S Dor-envelopes up to 1996. Subsequently, Stothers & Chin (1997) interpreted e.g. $\eta$ Car as a star burning hydrogen in its core, while repeatedly encountering ionization-induced dynamical instability, with a time scale of 3-6yr on the average. This time scale for violent cycles agrees remarkable well with the observed frequency of $\sim$$1^{\rm m}$-peaks superimposed on the eruptive light maximum between 1827 and 1857. Note that the light curve (Fig. 11) shows a few gaps during this time interval of as long as $\sim$5yr, so that more peaks may have occurred. Then, two more peaks appeared: 13yr later in 1870, and again 20yr later in 1890. Also the other cases discussed by Humphreys et al. (2000), showed eruptive episodes characterized by a set of individual eruptions with a sharply declining frequency. Owocki & Galay (1997) suggested that when an evolving star responds to a super-Eddington condition, it will develop a convective outer layer which will be blown up mimicking a RSG. This envelope may then become detached, due to a density inversion, so that an S Dor variable is born. A quite different possibility has been proposed by Sterken et al. (1997) based on the high noise, extending over a wide frequency range exhibited by the light variations of the ex- or dormant S Dor variable $\zeta^{1}$ Sco. The presence of this noise, unpredictable, but to some degree in step with the microvariations, could from time to time amplify the regular long-term oscillations beyond expectation leading to an eruption. Such amplification of weak signals by associated noise, known as stochastic resonance, could lead to unexpected triggerings when combined with long-period oscillations, especially when the star is in a state of dynamical instability. In the proceedings of the IAU Coll. 169 held in Heidelberg in 1998, a number of papers were devoted to the instabilities in S Dor envelopes, in particular to the SD-eruptions (e.g. Guzik et al. 1999; $\O$degaard 1999) and all types of pulsations (the latter might play a role in the observed microvariations, see Sect. 1.6). During the workshop on $\eta$ Car, held in Montana 1998, special emphasis was given to its SD-eruption and the creation of the bipolar nebula. The model of Cassinelli (1999) includes binarity and that of Iben (1999) even a tertiary companion. These models describe with straightforward physics SD-eruptions leading to a bipolar nebula. However, other S Dor variables excist with bipolar nebulae without being a binary as far as we know. With hydrodynamical models of the evolution of bipolar ejecta, in particular that of $\eta$ Car, Langer et al. (1999) find support for the general conjecture that SD-eruptions occur when the stars approach the Eddington limit. Their models imply that initial stellar rotation rate and angular momentum have influence on the occurrence of SD-eruptions and that they are very important to the evolution of very massive stars. Stothers' (1999a) calculations show that rotation influences the hydrostatic structure as well, the course of the evolution and in an indirect way the star's L/M ratio and consequently the onset of dynamical instability, an appealing mechanism discovered by Stothers & Chin (1993, 1994, 1995, 1996). All these models do not consider any possible influence of the frequently occurring SD-phases (which are in fact slow pulsations, Sect. 1.5) and the microvariations (which are always present, Sect. 1.6) on the eruptive instabilities and on the production of ejecta. An exception so far with respect to $\eta$ Car, is the study of Stothers (2000). He examines the effect of the enormous stellar wind on the envelope structure, assuming that $\eta$ Car possesses a very massive hot main-sequence star, only slightly evolved. The high mass loss must dynamically perturb its outer envelope down to the two main iron convection zones of which the turbulent energy can be directly transformed into mass ejections. Besides, Stothers (2000) found that secular oscillations of the outer envelope, caused by the runaway mass loss, is potentially able to account not only for the cycles of visual brightenings (the SD-phases, Sect. 1.5), but also for the 1827-1857 eruptive period. Whatever the truth is about the SD-eruptions, they seem to occur rarely in view of the low number of ejecta per S Dor variable. There are even S Dor variables without any ejecta (Sect. 1.8).

1.5 The S Dor (SD)-phases

The SD-phases (see also Sect. 1.3, c) are presumably largely phases of variable radius and temperature. This was first suspected by van Genderen (1982), and later confirmed by the study of Leitherer et al. (1989), while de Koter et al. (1996) showed that a reduced effective gravity should take part in the process. The luminosity stays more or less constant. One of the exceptions is S Dor; here the change in $M_{\rm bol}$ is close to $1^{\rm m}$ (van Genderen et al. 1997a). An SD-phase is apparently a kind of pulsation, especially by the envelope (see also Lamers et al. 1998: Sect. 5.3). It appears that there are two types: one on a time scale of years and another one on a time scale of decades (Sect. 1.5.1). The physical implications, amongst others with respect to the mass loss rate (see below) are still not understood (Schmutz 1997). His suggestion is that an SD-phase "is a sort of small giant eruption that never makes it to infinity''. Most likely we see the stellar photosphere all the time from minimum to maximum light (and not an expanding optically thick pseudo-photosphere as thought formerly, however, see Sect. 3.2.1). It is of interest to note that the S Dor-phases of $\eta$ Car seem to be more or less sensitive for tidal forcing of a supposed companion with an excentric orbital revolution of 5.5yr (van Genderen et al. 2001): around the periastron passages the light is in, or close to a maximum. Such a possibility has been suggested by Stothers & Chin (2000). It is doubtful whether the physical process of the SD-phases can be compared with a terrestrial geyser. This geyser model has been introduced by Maeder (1989, 1992). He elaborated the density inversion below the photospheres of cool supergiants (temperature below 9000K), discovered by Böhm-Vitense (1958), a probable cause of eruptive episodes. Although the S Dor variables discussed here are hotter, Humphreys & Davidson (1994) suggested that their characteristics allow the comparison with geysers. The duration of the quiescent period should be correlated with the size of the preceding eruption. However, the investigation of such a type of correlation for AG Car did not support that (van Genderen et al. 1997a). What we did find is that the durations of the SD-phases (on a time scale of years) appear to be linearly proportional to the visual light amplitude. The geyser model may be physically related to the dynamical unstable yellow/red SD-stage, as follows from the calculations of Stothers & Chin (1996) (see also Sect.  1.8 and the comments by Humphreys & Davidson 1994). Contrary to former beliefs, a positive correlation between the brightness variation due to the SD-phases and the mass loss rate appeared to be not always true (Leitherer et al. 1989, 1994; de Koter et al. 1996). Whether M increases or decreases during an SD-phase depends on the temperature change, the proximity to the Atmospheric Eddington Limit (AEL, Lamers 1997), and the bistability jumps (Pauldrach & Puls 1990; Lamers 1997).

1.5.1 Two types of SD-phases

The study of a century of photometric observations of AG Car and S Dor revealed the presence of two different SD-phases. If both are present simultaneously, the shorter one, time scale of years: t< 10yr, is clearly superimposed on the longer one, time scale of decades: yr (van Genderen et al. 1997a). The first one was called a normal (N)-SD phase, the second one a very long-term (VLT)-SD phase. So far, no SD-phases were found with cycle lengths between 10-20yr. After having studied so many S Dor variables in more detail, I want to introduce the more convenient names: short (S)-SD and long (L)-SD phase, respectively. SD-phases are probably caused by two different instability regions. This suspicion is based on the fact that amplitude and shape of the S-SD phases are clearly modulated by the ongoing L-SD phase (van Genderen et al. 1997a; Sterken et al. 1996a). So far, there is no theoretical support for this assumption. In the models of Stothers & Chin (e.g. 1995) the "secular cycles'' can perhaps be identified as the SD-phases, but their models do not predict a sharp physical (or even temporal) division between S- and L-SD phases. The actual length of a particular "secular cycle'' depends on the dynamical mass-loss rate. However, the observed S-SD cycle durations of the order of a year are too short to be attributed to the secular cycles (Stothers, priv. comm.). It is also possible that a period-modulation excists, i.e. that the L-SD phase influences the arrival times of the light maxima of the S-SD phases (Sects. 1.5.2 and 1.5.3). It appears that most of the S Dor variables are subject to both types of SD-phases, albeit not always simultaneously (see light curves presented by van Genderen et al. 1997b; van Genderen & Sterken 1996; Sterken et al. 1998).

1.5.2 Periodicities/cyclicities of S Dor variables

Important for the interpretation and modelling of the SD-phases is the fact that multi-periodicities/-cyclicities have been found in the S-SD phases of a number of S Dor variables (van Genderen et al. 1997a,b; Sterken et al. 1996b, 1997a, 1998). AG Car shows a very pronounced primary periodicity of 371.4d with beat cycles (Sect. 1.5.3). So far, no theoretical models predict two different types of SD-phases (Sect. 1.5.1), nor any (multi-) periodicity (e.g. Maeder 1989, 1992, 1997; Glatzel & Kiriakidis 1993; Cox et al. 1997, 1999; Guzik et al. 1997, 1999; Glatzel 1997). Stothers & Chin's (1995, 1996) models reveal a mechanism for dynamical instabilities. From their evolutionary models, "periods'' were predicted of the overall "secular cycles'' of $\eta$ Car, AG Car and S Dor (i.e. the cycles from hot to cool portions of the dynamical unstable stage and vice versa), which agree with the observed ones (S-SD phases) to within a factor of two. So far, no repetition of light curve characteristics has ever been found for the SD-phases. It seems that Dorfi & Feuchtlinger's (1998, priv. comm. to Guzik et al. 1999) models of S Dor-type envelopes exhibit regular pulsations.

Figure 1: From top to bottom: the (O-C)-, $\triangle t$- and the schematic light curve of AG Car from maximum No. 30 onwards (full line; the dotted curve represents the underlying L-SD cycle)

1.5.3 The multi-periodic character of AG Car

The primary period of the S-SD phases of AG Car appeared to have been stable during a century: P₀ = 371.4d $\pm$ 0.6d (m.e. = mean error). The oscillating O-C (= observed epochs of maximum light minus the computed epochs of maximum light) values suggested the presence of a first beat period $P_{\rm b\,1}$ = 21.6yr and a possible second beat period $P_{\rm b\,2}$ = 4.7yr (van Genderen et al. 1997a). New epochs of maximum light in 1995 and 1996 supported these results (Sterken et al. 1996a). The last and most reliable part of the 21.6yr beat cycle (represented by the O-C diagram, see below) appears to have a similar shape as the L-SD cycle. I believe that this is suspect. Therefore, it is possible that $P_{\rm b\,1}$ has been caused by the modulation of P₀ by the L-SD cycle ($\sim$20yr) instead of by a secondary period P₁ = 390d. This is explained in Fig. 1, from top to bottom: Panel 1: the O-C curve for the S-SD phases (numbers from van Genderen et al. 1997a and Sterken et al. 1996a), based on the linear ephemeris with P₀ = 371.4d starting with maximum 30. Panel 2: the trend of the duration $\triangle t$(d) between two successive maxima. It illustrates the secondary oscillations of Panel 1 more clearly, representing the possible beat cycle $P_{\rm b\,2}$ = 4.7yr. Each horizontal line piece, marked by the numbers of the two maxima has a length $\triangle t$(d). The estimated error amounts to $\pm$ 35d. It appears that $\triangle t$ hovers between 200d and 540d. Using the formula $1/P_{\rm b\,2} = \vert 1/P_{2} - 1/P_{0}\vert$ and depending on whether P₂ (its meaning is explained below) is shorter or longer than P₀, one finds P₂ = 305d and 475d, respectively. Panel 3: the schematic light curve from maximum 30 onwards. The dotted curve, touching most of the minima represents the shape of the underlying L-SD cycle on which the S-SD phases are superimposed. The rising trend in the O-C values (Panel 1) between e.g. maxima 34 and 38 means that the maxima arrive progressively later due to the accumulation of too long S-SD cycles, thus, too large $\triangle t$ values compared to the average $\triangle t$ (= P₀). The opposite appears for the subsequent steep decline after maximum 38. That the O-C curve in panel 1 and the dotted L-SD curve in panel 3 look similar is evident. This may not be accidental, and due to a modulation effect by the L-SD cycle on the periods P₀ and P₂. If this should be correct, the beat $P_{\rm b\,1}$ = 21.6yr has nothing to do with the interference of P₀ with a secondary period P₁ (= 390d). The latter is then obsolete, and P₂ (305d or 475d) should be called P₁. The ratio between these two, P₀ (= 371.4d) and P₁ (= 305d or 475d), amounts to approximately 4/5 (if 305d is used), or 5/4 (if 475d is used), a ratio which is often found among multi-periodic pulsating stars.

1.6 S Dor variables as a subgroup of $\alpha$ Cyg variables. The two types of microvariations

All evolved massive stars, generally referred to as $\alpha$ Cyg variables, including the S Dor variables, show currently a photometric microvariability with light amplitudes  0 $.\!\!^{\rm m}$2. Note that the light amplitude of the microvariations can be larger than that of the S-SD phase (e.g. HD34664 = S22 in Fig. 16). The time scales, often called semi- or quasi-periods, are of the order of days (the hot members) to months (the cool members) (van Genderen 1989, 1991a; Sterken 1989; van Leeuwen et al. 1998; van Genderen & Sterken 1999 and references therein). Although the precise evolutionary connections and the physical differences between $\alpha$ Cyg variables and S Dor variables are still unclear, I tentatively considered the last ones as a small sub-group of the first ones (van Genderen et al. 1988). The photometric behaviour of the famous S Dor variable P Cyg seems to support this view. According to the models the star should be dynamically stable at present (thus no SD-phases, but see Note added in proof; Sect. 3.2.2), but it does show microvariations. It also appears that in the same temperature domain S Dor variables and normal $\alpha$ Cyg variables, show almost the same type of microvariations. Often, the microvariations of S Dor variables near minimum light show fewer secondary features, and the amplitudes (or the "maximum light amplitudes'': MLA) appear to be somewhat larger (van Genderen 1989, 1991a; van Genderen & Sterken 1996). Many S Dor variables near minimum light might still show very weak SD-phases which contribute to the MLA's. Analyzing the S Dor variables with a strong SD-activity, we noted a peculiar phenomenon. At or near minimum light they show $\alpha$ Cyg-type microvariations with quasi-periods of the order of days to weeks (like normal $\alpha$ Cyg variables). As soon as they pass a certain temperature domain on their way to maximum light, somewhere between 20000K and 10000K, another type of microvariation emerges rather abruply (within a few months), with a much longer time scale: the "100d-type'' variation. That is to say, the time scale is often of the order of 100d, but can range from 50d to 150d, of the same order as normal $\alpha$ Cyg variables (non-S Dor variables) of the same temperature. The amplitudes are still  0 $.\!\!^{\rm m}$2 (see references above). However, the colour behaviour of the 100d-type variations is often red in the light maxima instead of blue as for the shorter microvariations mentioned above (e.g. R40 in van Genderen et al. 1997b: Figs. 8-10) and often more chaotic (e.g. S Dor and R127 in van Genderen et al. 1997a and 1997b, respectively). I speculate that they could correspond to the oscillations found by Stothers & Chin (1995, 1996) in their models and called "relaxation oscillations'' (a kind of pulsation superimposed on a dynamical unstable structure) due to the kappa-mechanism. They occur during the cool part of the "secular cycles'' in the models as well as in the observed maxima of the SD-phases. The predicted periods are also in the order of months! Stothers' (1999c) idealized hydrodynamical models reveal very small bolometric light amplitudes, less than 0 $.\!\!^{\rm m}$2, which is likely to be generally true, even for realistic models. We found three S Dor variables where both types of microvariations were seen together: the short one superimposed on the long one. The first two are HR Car and R85 (Fig. 13), but only for a few months (van Genderen et al. 1990, 1997b, 1998b). The third is P Cyg, but here both oscillations, 18.3d and 100d-type, are already seen together for many decades up to the present day (de Groot et al. 2001). Obviously, the physical state of P Cyg is very close to the switching point for a long time. Apart from these two types of microvariations, P Cyg also shows a very low amplitude oscillation with a cycle length of $\sim$3000d (de Groot et al. 2001), which is presumably an S-SD phase (see Table 6), and an apparent brightness rise due to evolution to the red (Lamers & de Groot 1992; de Groot & Lamers 1992). Thus, in more than one respect P Cyg is an exceptional case (see also Sects. 1.7 and 3.2.2). Apart from the enigmatic way in which the two types of microvariations succeed each other, the 100d-type ones offer another riddle: it is quite peculiar that the time scales of e.g. R127 and HR Car, hardly changed during the brightness rise of $\sim$1$^{\rm m}$ in $V_{\rm J}$ (van Genderen et al. 1997b: Sect. 4.2). This creates a paradox if one wants to explain them as a result of stellar radial pulsations, non-radial pulsations offer an acceptable alternative. But how to explain the (temporarily) simultaneous excitation of both microvariations? So far, theoretical studies do not predict such a phenomenon. The switch from one to the other could be explained by physical changes, such as the density structure during expansion and contraction. However, this cannot offer an explanation for the simultaneous presence of both types of microvaraitions. There are different views on the cause and the physical background of microvariations. Amongst others, they were linked with the "strange-mode'' instabilities (oscillation modes recovered in linear, non-adiabatic calculations for stars with high L/M ratios), see e.g. Kiriakidis et al. (1993, 1997), Soukup et al. (1994) and Cox et al. (1995). See also the reviews by Gautschy & Saio (1995, 1996). Sterken (1989) was the first to suggest that the SD-domain on the HR-diagram is an extension of the instability domains of the non-radial (l>0) pulsators in the g-mode: $\beta$ Cep variables and SPBs (slowly-pulsating B-type stars) (see also Waelkens et al. 1998; Lamers et al. 1998). This seems to be supported by theoretical calculations (Pamyatnykh 1998) which also indicate that the above mentioned instability domain covers a much wider region than predicted for the strange-modes. Further, Lamers et al. (1998) found that the observed periods of the microvariations (often near minimum brightness) are much longer than those caused by the strange modes. According to Gäng's (2000) analysis of spectroscopic time series of HD160529, radial and non-radial pulsations are probably present.

1.7 The evolutionary status

Most of the variable supergiants can be found on the blue side of the HR-diagram. This agrees with the various theoretical models (e.g. Lovey et al. 1984; Stothers & Chin 1994, 1995, 1996; Schaller et al. 1992; Langer et al. 1994; Vanbeveren et al. 1998). The excess of blue supergiants is possibly due to the widening of the main sequence and their longer lifetimes. S Dor variables are mainly concentrated in the blue part of the HR-diagram as well. According to Stothers & Chin (1994, 1995, 1996) this is due to their much longer lifetime in their second (blue) phase of dynamical instability ($\sim$10⁴yr) than in their first as a yellow supergiant ($\sim$10³yr). Supergiants on a blueward track, which are a small minority due to their faster evolution, should show processed material at their surface like presumably the $\alpha$ Cyg variable HD157038, a B1/2IaN-type star (Lennon & Dufton 1986, see for its photometric variability van Genderen et al. 1989). Indeed, most of the S Dor variables show He- and N-enriched and O-poor circumstellar ejecta, pointing to CNO-processed material (e.g. L. Smith 1997). Also the dust composition of a number of S Dor variables (e.g. AG Car, WRA751, R71) points to an evolutionary connection with RSG (e.g. Viotti et al. 1988; Robberto et al. 1993; L. Smith et al. 1997, 1998; Voors 1999), although evolutionary tracks of e.g. Schaller et al. (1992) of stars with M_i   40$M_\odot$ do not reach the RSG region at all, unless one introduces a mass loss in addition to the radiation pressure driven wind like Langer et al. (1994) did. Further support for a possible RSG-connection comes from the hydrodynamical models of the nebulae of e.g. P Cyg and AG Car by Garcia-Segura et al. (1996a,b), which imply that these stars evolved through what they call: a "blueward excursion''. Yet, P Cyg is the only S Dor variable which lacks any dust in its ejecta (Voors 1999). (It is however not clear whether they also mean an excursion starting right from the RSG domain. Their evolutionary track for a star with an initial mass of 60$M_\odot$, does show a returning point in the RSG domain). Initially, there was a discrepancy with regard to the H-content in mass (X) at the surfaces of S Dor variables amounting to $\sim$0.36 (see the compilation by Stothers 1999b), while post-RSG should have 0.10-0.20 (Maeder 1997), or $\sim$0.18 (Stothers 1999b). However, this seems to have been solved now by Stothers & Chin (2000). If one adopts the Schwarzschild (temperature-gradient) criterion for convection instead of the Ledoux (density-gradient) criterion, a fully convective (thus chemically homogeneous) zone develops just above the H-burning shell, with X approximately equal to 0.35. The star would then be in the second (blue) S Dor stage. On the other side, Maeder (1999) concluded that due to stellar rotation, some He- and N-enrichments at the stellar surface already occur during the MS-stage for not too high rotational velocities, thus it is not quite abnormal to find slightly enriched supergiants. Further, the computations indicate that rotation makes the star enter the WR-stage during the MS-stage, thus preventing an S Dor- and RSG-stage altogether. Also with respect to the scheme of evolution of all massive stars, there is still no consensus: different sequences of stellar types exist (see e.g. Langer et al. 1994; Stothers & Chin 1996; Vanbeveren et al. 1998).

1.8 The number of stellar ejecta and their ages

In Tables 1, 4, 8 and 11 it is indicated whether circumstellar gas and/or dust nebulae have been detected. It appears that only 40$\%$ of the S Dor variables, including 8 candidates in these statistics for which the SD-membership is likely, possess with certainty one or more visible ejecta. (There is no statistically significant difference between the percentages of the different categories of S Dor variables defined in Sect. 2.1). It is not excluded that all have a neutral-H nebula, thus not easily detectable. Such nebulae are relics from previous evolutionary stages, such as e.g. a pseudo-RSG/super-Eddington phase with gentle ejections, as postulated by L. Smith et al. (1998). The visible ring nebulae around 25$\%$ of the WR stars, generally supposed to be partly the descendants of S Dor variables, or at least closely related to them, may be caused by the interaction of the fast WR wind with the slower winds of the RSG- and SD-mass loss episodes (Marston et al. 1994; Marston 1999). (It has also been suggested that the most luminous WNL stars may evolve into S Dor variables, rather than vice versa, after which they enter a second WR stage (Langer et al. 1994; Walborn 1989). Such a different history has consequences for the chemical composition of the WR nebulae, Garcia-Segura et al. 1996a,b.) The great homogeneity of the properties of the ejecta generally suggest an interacting wind scenario by non-isotropic outflows. Thus, they are created by an interaction of fast moving gas overtaking slow moving gas (e.g. Icke 1981; Garcia-Segura et al. 1996a,b; L. Smith 1997; Dwarkas & Balick 1998; Langer et al. 1999). The visible ejecta have dynamical ages between 10²yr and $7\,10^{4}$yr (e.g. Nota et al. 1995a; Nota & Clampin 1997; Smith et al. 1998). According to the dynamical evolution computations of Garcia-Segura et al. (1996a,b) visible ejecta have a lifetime of $\sim$10⁴yr, which is of the same order. The masses of the visible ejecta are at most a few solar masses (e.g. Nota & Clampin 1997), thus not sufficient to explain the current relatively low masses of the S Dor variables. According to Stothers & Chin's calculations (1996) the present blue phase of instability is also too short: 10³-10⁴yr, for a substantial mass loss. Thus, the major mass losses should have occurred during the preceding dynamical instability stage in the yellow- or RSG-stage as well as by the normal stellar wind since the MS-stage. The intervening stage from the RSG- to the blue SD-stage is expected to last $\sim\,6\,10^{4}$yr (Stothers & Chin 1996). In other words, most of the ejecta we observe today are presumably from the present blue SD-stage. Any ejecta formed in the yellow or red stage must have been dispersed into space. As far as we know, most visible ejecta are single. There are a few exceptions: AG Car has two ejecta (Nota & Clampin 1997) like R127 (Appenzeller et al. 1987; L. Smith et al. 1998), HR Car has at least three ejecta (e.g. Voors 1999), P Cyg has four ejecta (Barlow et al. 1994; Meaburn et al. 1996; Skinner et al. 1998; see also the review on P Cyg by Israelian & de Groot 1999). The differences in dynamical ages amount to from a few centuries to $5\,10^{4}$yr.

Figure 11: The schematic light curve (ptm, ptg and $V_{\rm J}$) versus date of $\eta$ Car between 1600 and 2000 (last observations made in February 2000). Note that the horizontal scale after 1900 is twice as large as before 1900. Dashed curve: the "secular rise'' due to the decrease of circumstellar extinction (mainly self-extinction of the Homunculus) according to the model of van Genderen et al. (1994, see also van Genderen et al. 1995, 2001). Dots are averages of time series and the oscillating curve represents a series of monitored SD-phases sketched on scale. See for further details the notes to Tables 4, 5 and 6

The largest conundrum of all: $\eta$ Car, with its bipolar Homunculus, 160yr old, and with N-rich fast moving knots and strings, must have been active on various occasions up to 1000yr ago (Walborn et al. 1978; Weis et al. 1999; Bohigas et al. 2000). A second, but older (a few 10³yr) bipolar shell has been found by Bohigas et al. (2000), but its chemistry shows no trace of chemical processing. The Homunculus has an onion-like structure, with sub-shells (Pantin & Le Mignant 2000). The light curve (Fig. 11) also suggests the occurrence of a series of $\sim\,1^{\rm m}$-eruptions between 1827 and 1857 with a repetition time  5yr. Apart from that there were also SD-eruptions around 1870 and 1890 (Sect. 1.4). However, it seems that their ejecta have another morphology (e.g. Davidson et al. 1997; N. Smith et al. 1998). It can be concluded that at least 40% of S Dor variables, suffer a small number of eruptive episodes during their present (second) blue lifetime. The observed eruptive episodes appear to last a few decades and consist of a set of distinct eruptions. These eruptions are visible as $\sim\,1^{\rm m}-3^{\rm m}$-peaks, in the beginning on top of an enhanced brightness. Subsequently the brightness drops, partly by circumstellar dust, and a few more eruptions occur (see light curves by Humphreys et al. 2000). The interval between such eruptive episodes may amount to a few centuries up to a few 10⁴yr. The overall impression is that S Dor variables lose most of their mass in previous evolutionary stages by the stellar wind and by eruptions caused by dynamical instabilities and not in their current lifetime as hot S Dor variables. The present visible ejecta are the relics of eruptive episodes from their present hot stage. S Dor variables which probably lack any ejecta, did not (yet) suffer from recent eruptions.