6 Discussion

In a number of aspects, P Cygni is an exceptional case amongst the S Dor variables. During the last two decades (1982-1999) it showed the two types of microvariations ($\sim$0 $.\!\!^{\rm m}$1 and $\sim$0 $.\!\!^{\rm m}$2) on top of a very weak S Dor variability ($\sim$0 $.\!\!^{\rm m}$1). In what follows we discuss these three types of instabilities:

1.

The microvariability ($\sim$0 $.\!\!^{\rm m}$1) shows a quasi-period of 17 $.\!\!^{\rm d}$3 that is remarkably stable over 6.5 years. Yet, strictly speaking, one cannot call this a "period'' because the individual cycle lengths usually hover between 10 and 25 d, apart from the highly-variable shape of the cycles. The total absence of a significant single peak at the frequency of the 17 $.\!\!^{\rm d}$3 period in the amplitude spectrum is, therefore, understandable. Normally, cycle length variations of this type of microvariation (called the $\alpha$ Cyg-type by van Genderen et al. 1997a) are much smaller, resulting in at least a marginally significant peak in the amplitude spectrum. The weak-active S Dor variable R85 in the LMC is to some degree similar to P Cyg considering its mixture of oscillations of different duration (van Genderen et al. 1998), while the normal $\alpha$ Cyg variable (thus no S Dor variable) WRA977 also shows a stable quasi-period like P Cyg, over a time interval of 17 years (van Genderen & Sterken 1996). The stability of the 17 $.\!\!^{\rm d}$3 oscillation of P Cyg is reflected by the linear ephemeris for the epochs of its extrema. Obviously, its engine is periodic, but its effect on the photospheric light is of a highly quasi-periodic character. One could speculate that this is due to travel-time disturbances from the source in the interior to the surface by a stronger and longer time-scale rolling wave moving there and back.

Some systematic behaviour in the photospheric response due to the 17 $.\!\!^{\rm d}$3 oscillations is suspected because of a certain pattern in the O-C diagrams, but the evidence is still weak (de Groot et al. 2001). With this quasi-period, P Cyg fits very well the grid of P= constant lines for $\alpha$ Cyg variations in the H-R diagram (van Genderen & Sterken 1996);

2.

The long-term presence of the 17 $.\!\!^{\rm d}$3 oscillations on top of the 100d-type microvariations ($\sim$0 $.\!\!^{\rm m}$2) is outstanding. Only two other S Dor variables showed this, but only for a few months (Sect. 1.6 in van Genderen 2001). Could the quasi-periodicity of the shorter one be caused by the longer one? We did not find any relationship between the O-C values and the place within the 100d-type cycles.
These 100 d-type cycles show a highly variable duration as well: between 60 d and 130 d, but this is not abnormal. Israelian et al. (1996) suggested a correlation between the visual changes to a maximum (using part of the photometry presented here) and the ejection of recurrent shells deduced from the so-called discrete absorption components (DACs) as seen in IUE spectra. They estimated the frequency of the shells between 150 d and 250 d. However, this could well be an upper limit since the IUE observations show large gaps in time series. The analysis by van Gent & Lamers (1986), on the other side, revealed 60-70 d but this was also based on scattered spectrocopy.
Markova et al. (2001a) found an anti-correlation between these 100 d-type oscillations and the equivalent width of the H$\alpha$ emission line. Kolka (1999) discussed a 100 d-type cyclicity in the main spectroscopic features due to moving opacity enhancements (the DACs). He suggested as causes expanding density shells, or - inspired by the fact that the probable rotation period is roughly 100 d - corotating spiral density waves in the wind. We presume that the 100 d-type cyclicity in the spectrum and of the shells is somehow related to the 100 d-type light variations. The relatively long duration of many light maxima (also $\sim$100 d) rather suggests that we are dealing with a global or nearly global phenomenon, rather than with say, a large corotating hot spot. The long duration of the maxima is presumably an argument against an origin in the wind.
Since a light variation of $\sim$0 $.\!\!^{\rm m}$2 means a variation of $\sim$20% in L (assuming that the complete energy distribution varies more or less by the same amount), the 100 d-type light variations could be caused by a radius change of 10% (at constant T) in case of a radial pulsation, or by a T variation of 5% (at constant radius, thus no radial pulsation). The latter case is not likely because of the inconsistency with the observations (red colour in the maxima), see further.
Could they be explained by a larger than 10% increase of the radius and with a simultaneous slightly decreasing T and vice versa? This would imply a mean radial velocity variation of the photosphere amounting to $\sim$1 kms^-1 adopting $R=75~R_{\odot}$ (Najarro et al. 1997). This effect is too small to be detectable. If P Cygni were much cooler, one could suspect that the source of such a pulsational behaviour could be the low-amplitude ($\sim$0 $.\!\!^{\rm m}$2 in L!) oscillations due to the $\kappa$-mechanism found by Stothers & Chin (1995, 1996) and Stothers (1999b, 2000) in their models for yellow supergiants, called relaxation oscillations, with a time scale of months! It has been speculated before that the 100d-type light variations, usually present around the maxima of the S Dor phases, when the star is coolest, could be related to these oscillations (van Genderen 2001). However, in view of P Cygni's high temperature, the relaxation oscillations would have been much shorter, perhaps in the order of days.
The bi-stability mechanism proposed by Pauldrach & Puls (1990) is able to explain some of the observed characteristics of the shell ejections, while the light variation should then only be due to photospheric T variations by backscattering from the shell, i.e. T increases if the high mass-loss episode starts and vice versa. However, the light maxima should then become bluer, while the opposite is observed. An explanation for this inconsistency might be offered by the fact that shells are denser than the wind and if cooler than the photosphere, could weaken to some extent the flux at the shorter wavelengths relative to the longer ones.
But how does this shell creation start in the first place? We hypothesize that the cause is the source of the 100 d-type light oscillations. After all, P Cygni's wind is - according to Pauldrach & Puls' (1990) model - very unstable with respect to small changes in the luminosity (>3%) and/or the radius (>1.5%) of the star;

3.

The very weak S Dor cycles - between 1982 and 1999 - have a range of $\sim$0 $.\!\!^{\rm m}$1 on a time-scale of $\sim$4 y. It is quite possible that the observations in the nineteen nineties represent a cycle about twice as long (Fig. 5 and de Groot et al. 2001). Support for this longer one is given by Markova et al. (2001a, 2001b). They show that the H$\alpha$ emission line is possibly cyclic on a time-scale of that order ($\sim$7 y) and in phase with the brightness: maxima in 1985 (JD $\sim$ 2446300) and 1992 (JD $\sim$ 2448800), and minima in 1988 (JD $\sim$ 2447500) and in 1995 (JD $\sim$ 2450000). Besides, they demonstrate that it probably represents an S Dor phase as tentatively suggested by van Genderen (2001). They find that during the light maximum the radius increased by 7% and the temperature decreased by 10%. It should be noted that the SD cycles need not be periodic. Consecutive cycles can appreciably differ in duration and range from cycle to cycle, see e.g. R71 in Sterken et al. (1997b) and other S Dor variables (van Genderen et al. 1997a, 1997b).
The simultaneous H$\alpha$ spectroscopy by Markova et al. (2001a, 2001b) suggests that the short (S)-SD phase (short, because it is <10 y, van Genderen 2001) is likely accompanied by changes in the properties of the wind, i.e. an increase in the mass-loss rate and a decrease in the velocity field. These conclusions are based on the relative large optical depth of the wind, which led them to conclude that P Cyg likely has a permanent pseudo-photosphere with $\tau_{\nu}=2.30$.