1 Introduction

This is the third detailed study on cyclicities in the light variations of a selection of well-monitored S Doradus variables. The two previous papers dealt with $\zeta^1$ Sco in the Galaxy and R40 in the SMC (Sterken et al. 1997a, 1998, respectively).

S Doradus stars - also known as Luminous Blue Variables (LBVs) - are found in the upper left-hand corner of the Hertzsprung-Russell diagram. They are photometrically variable with a large range of amplitudes (several hundredths of a magnitude to magnitudes) and on a vast range of time scales (hours, over decades, to centuries). The amplitudes of the variations seem to increase with the time scales at which they occur. Considering the presence of circumstellar ejecta, about 40% of the S Dor stars seem to have suffered an $\eta$ Carinae-type outburst in the past. For an extensive review of the light curve properties of S Dor stars, we refer to van Genderen (2001), who classified P Cyg as a weak-active (w-a) S Dor variable (because it was weak-active in the 20th century).

P Cygni (HR7763 = HD193237) is a notorious S Dor star of the $\eta$ Carinae type, with giant eruption(s), S Doradus phases and microvariability (for a detailed discussion, see de Groot 1969, and for a recent review see Israelian & de Groot 1999). According to Stothers (1999a), P Cyg is in a "state of marginal dynamical instability'' and de Jager (2001), studying its photosphere, used the following expression: "it finds itself at most at the fringe of instability''. Dynamical instability means that the outer layers are subject to a steady expansion or contraction, and in the first case eject matter vigorously. A discussion of the periodicity of the radial velocity and light variations of P Cyg was given by van Gent & Lamers (1986), see also van Genderen (1991) and van Genderen et al. (1992). A long time scale spectroscopic study of the H$\alpha$ emission line was compared with simultaneous photometry from different sources by Markova (2000, 2001) and Markova et al. (2001a, 2001b). These authors found various correlations with different time scales between the equivalent width of the H$\alpha$ line and the photometric behaviour. This is the first time that such a study of an S Dor variable has been made.

P Cygni is one of the very few hypergiants that have a well-documented light history. Discovered by Willem Jansz Blaeu on 18th August 1600 as a third-magnitude star, it was only the second so-called "nova'' after Tycho's "new'' star of 1572. This, and the invention of the telescope at about the same time, ensured a long series of observations of P Cygni, starting in 1600 and still continuing today. Though the observations of the first three centuries suffer from the fact that they were done visually, by different observers using different comparison stars, and in the absence of an agreed magnitude scale, it has still been possible to recover P Cygni's photometric history. An investigation of the characteristics of the light curve after 1700 has led to the conclusion that we are witnessing photometric changes due to stellar evolution (de Groot & Lamers 1992; de Groot et al. 2001).

In this paper we present the analysis of a unique set of new photometric measurements of P Cyg covering almost two complete decades, combined with archival data from the literature.