4 Discussion and conclusions

Our spectroscopic analysis of P Cygni revealed the presence of four kinds of line-profile variability: LT variability in HI and HeI lines of relatively high optical depth; red emission-wing variability; DAC-induced variability in the troughs of optical lines of low and intermediate excitation (such as NaI, CaII, HI, HeI and FeIII) and "swaying'' variability in the troughs and lobes of lines of intermediate and high excitation.

The LT variability consists of a very slow pattern of variation in both the velocity of the absorption cores and the strength of the emission peaks of the strongest HI and HeI lines. Variations in velocity are anti-correlated with changes in the strength of the emission peak. The LT variability is localized only in the outer part of the wind ( $V \geq 0.82V_{{\rm inf}}$): neither weaker lines of HI and HeI nor lines of higher-excitation ions showed LT variation in velocity or strength. The nature and origin of this kind of variability are still unknown. Recently, Markova et al. (1998) have reported evidence for a LT variation in the brightness and temperature of P Cygni. The relationship between the LT wind variability and the LT photospheric variability (if any) is the subject of another study (Markova et al. 2000a).

The red-emission-wing variability affects the high-velocity part of the P Cygni-type profiles, $+90 \leq V \leq +230/250$ km s^-1. This variability seems to be caused by low-intensity bumps whose position varies with time. The properties of this phenomenon are still largely unknown. A similar phenomenon may have been observed by Kuss & Duemmler (1995) who suggested that the bumps are due to light echos from outward-moving dense shells that produce different DAC sequences. Unfortunately, our set of photographic data is not very extended and has large gaps that do not allow any correspondence between the two phenomena to be established.

4.1 On the nature of DACs

Our analysis reveals the presence of systematic wind activity in optical lines of low and intermediate excitation (such as NaI, CaII, HI, HeI and FeIII), which takes the form of blueward-migrating DACs. We found evidence of at least one DAC episode in 1990. The same episode was also traced by Israelian et al. (1996) in UV FeIII and FeII lines. The properties of this DAC event are quite similar to the properties of other DAC events at earlier epochs, thus indicating that the mechanism that causes the appearance of DACs in both the UV and optical regions of the spectrum has not changed and was still at work in 1990 as it had been in earlier years. The fact that Stahl et al. (1994) failed to detect any DACs in their 1990 CCD spectra is most likely due to the fact that most lines showing DACs were situated outside the spectral region covered by their observations.

In spite of the great number of observational studies devoted to DACs in P Cygni, our knowledge of the mechanism that causes the phenomenon is still poor. The properties of the DAC events, such as duration, width in velocity space, acceleration, and absorption strength (Markova 1986b; Israelian et al. 1996, present study), indicate that the components are due to large-scale, time-dependent structures in the wind. Applying the well-known InglisTeller relation to the last visible Balmer line with and without line-splitting, we found that the density inside the structures producing the DAC event in 1990 was very high - about one order of magnitude higher than in the ambient wind. At such density the excitation/ionization of the matter is expected to be low. Indeed, our observations showed that the behaviour of the lines with lowest energy in the optical, namely the resonance lines of NaI (Sect. 3.4) and CaII (Markova 1991), was completely governed by the appearance and evolution of DACs. No evidence for variation different from the DAC-induced variability was found for these lines.

It seems that the most-frequently invoked model for interpreting the appearance of DACs in P Cygni has been that of outward moving, extended, dense shells (Markova 1986b; Lamers et al. 1985; Van Gent & Lamers 1986; Israelian et al. 1996). However, since one would expect to observe an increasing emission-line strength due to shell expansion, and since the quotient spectra of our sample did not reveal variations in emission in connection with those in absorption (Sect. 3.1), one is tempted to conclude that the material producing DACs does not seem to exist as a shell. It might well be however that this result has no physical meaning but only reflects the competition between the LT variability and the DAC-induced variability, whose effects on the emission lobes of the lines are contrary to each other (during the period studied). Thus we conclude that DACs in P Cygni may originate from outward moving dense shells.

Alternatively, DACs might be caused by material confined in discrete geometric units, "blobs'', "puffs'' or "spirals'', situated just in front of the stellar disk. Although the hypothesis of moving blops received strong support from radio (Skinner et al. 1997), spectral (Barlow et al. 1994), interferometric (Vakili et al. 1997) and polarimetric (Taylor et al. 1991) observations it meets invincible difficulties in interpreting the properties of the DAC phenomenon. In particular, the apparent regularity of the DAC events, with a quasi-period of about 200 days (Markova 1986b; Israelian et al. 1996), is hardly consistent with the idea of randomly-distributed regions of excess density inferred from polarimetric observations (Taylor et al. 1991). Thus we conclude that DACs in P Cygni are not due to outward moving blobs.

In recent years the model of co-rotating spirals (known as the CIR model: Mullan 1984, 1986; Cranmer & Owocki 1996) has become popular for the interpretion of the recurrence of DACs in O-type stars (Kaper et al. 1997, 1998). This model seems to be capable of explaining most of the established properties of DACs in P Cygni as well. For example, a spiral-shaped structure would cut across a wide range of projected velocities thus explaining the relatively large width of the DACs in velocity space (about 70 km s^-1). Due to curvature of the spiral, such structure would also cause the appearance of a time lag for different velocities, a result that simply appears from a study of the time behaviour of the Balmer progression (Markova 1991). In addition, the established increase and subsequent decrease in the strength of DACs in Balmer lines (Markova 1986a) might also be readily interpreted in terms of a spiral-shaped DAC-forming region which rotates into and out of the line of sight. On the other hand, there are a few results that are not consistent with the CIR model. For instance, if DACs are due to spiral-shaped structures that co-rotate (or nearly co-rotate) with the star, then their character should be strictly periodic (even over a limited time interval) with a cycle length that is determined by both the rotational period of the star, $P_{{\rm rot}}$, and the number of co-rotating spirals and, thus, could be comparable to (or be an integer fraction of) $P_{{\rm rot}}$. The observations showed that the DAC-induced variability in P Cygni is not periodic - as one might be tempted to infer from the excellent agreement between the estimates reported in the literature for the recurrence of DACs: 200 $\pm$ 7days in 1981-83 (Markova 1986b, optical observations) and 206 $\pm$ 11days in 1985-90 Israelian et al. 1996, UV observations) - but occurs on a time-scale that varies from about 150 to about 250 days. Furthermore, from the radius, 76 $R_\odot$ (Pauldrach & Puls 1990), and the rotation velocity of the star, 40 km s^-1 (Israelian 1995), we derive an upper limit to the rotation period of 96 days. Hence, the time-scale of the DACs is longer than the estimated maximum rotation period, $P_{{\rm rot}}$(max). All this indicates that rotation does not seem to play a fundamental role in determining the recurrence of the DACs in P Cygni.

The recurrence of DACs over an interval of more than 50 years (Markova 1986b) suggests that the structures producing DACs are not a transient feature of the wind but persist over many flow times and are more likely maintained by photospheric processes. This assumption seems also to be supported by the finding that on a few occasions the appearance of a new DAC was accompanied by an increase in the stellar brightness (Israelian et al. 1996). Spectral observations, however, indicate that the structures producing DACs do not seem to be directly linked to the photosphere but originate somewhere up in the wind: no DACs with velocities lower than 90 km s^-1 have ever been detected (Markova 1986b; Israelian et al. 1996, present study). Thus we conclude that the source of large-scale structures in the wind is more likely coupled with the stellar photosphere but because of some unknown reasons these structures do not develope in the inner part of the wind.

Finally, we note that the longevity of the DAC events, which lasts more than 100 radial flow times of the wind (the characteristic radial flow time of P Cygni's wind is about 2.8 days), suggests that the structures producing DACs might not represent single mass-conserving features but rather might arise from slowly evolving perturbations through which wind material flows.

In summary, DACs in P Cygni presumably originate from large-scale, time-dependent, enhanced-density (lowexcitation) perturbations, which develop in the outer part of the wind, $V \geq 0.41V_{{\rm inf}}$), but appear to be maintained by photospheric processes. The geometry of the structures is still not clear. It could be either spherically symmetric or curved, like kinks. The recurrence of the DACs does not appear to be related to the stellar rotation.

4.2 On the nature of the modulations

The observations showed that the "swaying'' variability occurs over a broad range of velocities (negative and positive) within the profile. This variability manifests itself by modulations (like fluctuations above and below a mean level) in the position and intensity of the absorption cores and emission peaks of most lines in the spectrum. Simultaneous variations in emission and absorption-line strength (i.e. EW) were also established.

The properties of the studied lines, together with the trends we found, suggest that the "swaying'' variability of the troughs is not just due to the redistribution of a fixed amount of line absorption, as would occur if, e.g., the variability was caused by a macroscopic velocity field alone. Because variations in absorption EW do occur, the process or processes responsible for the observed phenomenon must also alter the number of absorbers, either through changes in the ionization/excitation or in the number density. Although changes in the excitation temperature of the wind, $T_{{\rm exc}}$, do occur - estimates derived in terms of a curve-of-growth analysis of 35 NII lines with excitation energies between 18.47 and 23.2 eV showed that the increase in velocity and strength of the lines between JD 2448017 and JD 2448052 (i.e. during the "swaying'' variation) was accompanied by a 15% decrease (about 3000 K) in $T_{{\rm exc}}$ - it seems unlikely that these variations govern the "swaying''variability of the wind. The fact that optical lines of different excitation and ionization show simultaneous increase/decrease in absorption EW clearly indicates that line-flux (strength) modulations are due to changes in the number density rather than to changes in the ionization/excitation of the wind. Therefore, we suggest that line-flux modulations in P Cygni's optical spectrum more likely originate from time-dependent enhanceddensity structures in the wind.

There are at least two pieces of evidence which indicate that the wind region affected by the modulations should be very extended. We found, first, that the "swaying'' variability affects all layers of the supersonic wind starting at its base and up to at least 14 R_* where the H$\alpha$ line forms and, second, that the modulations occur in both emission and absorption indicating that the structure producing the modulations should have significant azimuthal extent and could be either spherically symmetric (i.e. shells) or spiral-shaped. The hypothesis of spiral-shaped structures in the wind as a possible cause of the modulations implies a picture where spirals rooted in the photosphere co-rotate with the star. Strong evidence in support of this hypothesis would be therefore the establishment of a close relationships between the modulations and the stellar rotation.

It is not clear whether the "swaying'' variability of P Cygni's wind is related to the stellar rotation. The present data turned out to be insufficient and do not enable us to find out whether the established phenomenon is periodic or not. Nevertheless, the pattern of the "swaying'' variability appears to be qualitatively similar to the variability found at earlier epochs, thus suggesting that the phenomenon is stable over many years. The time-scale of the modulations, however, is different at different epochs. For example, the modulations in the velocity of the absorption cores of optical lines occurred on a time-scale of 100 to 120 days in 1981 (Markova 1993); of 50 to 60 days in 1982 and 1989 (Kolka 1989, 1991) and of about 100 days in 1990-1991 (present study). These results suggest that the "swaying'' variability is more likely caused by a photospheric process that is capable of reproducing itself on a different time-scale. Also, the fact that at some epochs, e.g. 1981, the time-scale of the modulations in velocity was longer than $P_{{\rm rot}}$(max) suggests that these modulations are probably not caused by co-rotationg structures. The lack of a time lag in the velocity variability of the lines seems to support this assumption, too. On the other hand, it is worthwhile emphasizing that the established line-flux (strength) modulations might be related to the rotation since their time-scale is shorter than $P_{{\rm rot}}$(max): in 1989 their time-scale was about 30 days (Kolka 1991) while in 1990 it was about 60 to 70 days.

It is a puzzling aspect of our analysis that the modulations in the velocity of the absorption cores are not obviously related to the modulations in the maximum absorption flux (strength). The two kinds of variations have one and the same pattern of behaviour but their timescales seem to differ. It appears that a similar situation was observed by Kolka (1991) who established variations in emission and absorption-line strength (i.e. EW) on a time-scale about two times shorter than the time-scale associated with simultaneous variations in the velocity of the absorption cores. These results, although rather uncertain due to the uncertainty in the relevant time-scale estimates, imply that the two sorts of modulations might have different origins.

Thus we see that the above results do not enable us to characterize the nature of the modulations completely. It is clearly important to perform a detailed time-series analysis of the modulations on a much more extended data set in order to obtain refined estimates of the relevant timescales and, thus, to make a more definitive assessment of the relationship between different kinds of modulations as well as between the modulations and the stellar rotation.

4.2.1 The modulations and the hypothesis of "photospheric connection''

In the previous subsection we have suggested, based on indirect evidence, that the modulations of P Cygni's wind might be caused by photospheric processes. The existence of (quasi-)simultaneous photospheric (Percy et al. 1996; Markova et al. 2000b) and spectral observations (Stahl et al. 1991, present study) allows us to test this hypothesis. Attempts to detect a direct coupling between stellarwind variability and photospheric variability have become known as the search for a "photospheric connection''.

Figure 11: Variations in the velocity of the absorption cores (lower panel, dots) and in the maximum absorption (upper panel, solid line) and emission (upper panel, dashed line) flux of selected lines formed in the deepest layers of P Cygni's wind, compared with variations in the V-band (open circles). All velocities are negative and measured with respect to the Sun (HRV = heliocentric radial velocity)

In Fig. 11 the "swaying'' variability in both the velocity of the absorption cores and in the maximum absorption and emission-line flux, $F_{{\rm max}}$(abs) and $F_{{\rm max}}$(em), of selected high-excitation lines is compared with changes in the stellar brightness. The photometric data presented are taken from Markova et al. (2000b). It is apparent from this figure that:

(i) the modulations in the $F_{{\rm max}}$(abs) and $F_{{\rm max}}$(em) tend to be anti-correlated with the variations in the brightness;

(ii) the modulations in the velocity of the absorption cores appear to be correlated with changes in the brightness with a probable phase lag.

Notice that most of the time the fluctuations in $F_{{\rm max}}$(em) have been accompanied by similar fluctuations in $F_{{\rm max}}$(abs), a fact that completely rules out the suspicion one may have, when looking at the apparent anticorrelation between variations in the NII $\lambda$4630 luminosity and in the V-band, that the line-flux variability is only a reflection of the changing continuum. It is also worth noting that Markova et al. (2000b) have established variations in the stellar temperature that correlate with changes in the V-band, so that when the brightness increases the temperature decreases.

The above allows us to suggest that the "swaying'' variability of P Cygni's wind is probably triggered by photospheric processes. This assumption seems to be supported also by two additional results. First, the finding that the time-scale of the "swaying'' variability equals at least 21 $t_{{\rm flow}}$ (during the studied period) together with the fact that the modulations last for more than 82 $t_{{\rm flow}}$, indicate that these modulations are not transient features of the wind, but persist for many flow times and seem to be caused by photospheric processes. And, second, the radialvelocity measurements convincingly showed that the modulations affected the deepest layers of the supersonic wind down to its base. Evidence for a possible relationship between variations in the wind and in the stellar parameters was reported by different investigators. For example, de Groot (1990) noted that an increase in the star's brightness seemed to be accompanied by a decline in the strength of H$\alpha$ emission and by an increase in B-V. A probable correlation between variations in the velocity of the absorption cores and changes in the brightness was suggested by Kolka (1991). All this suggests that the "swaying'' variability of P Cygni's wind is more likely coupled to the photosphere.

If the modulations of P Cygni's wind are indeed triggered by photospheric processes what could these be? On the one hand, the position of P Cygni on the HR-diagram falls within the predicted instability strip for strange-mode oscillations (Kiriakidis et al. 1993) thus suggesting that non-radial pulsations (NRP) of strange-mode oscillations could be a possible cause for the ST photometric variability of the star. On the other hand, Lamers et al. (1998) have recently argued that the microvariability of LBVs appears to be very similar to the variability of normal B-supergiants and slowly-pulsating B-stars - both due to NRPs of gravitational-mode oscillations. The authors showed further that the microvariability of LBVs can also be explained by means of NRPs of g-modes of low l. Thus we suggest that a possible cause for the ST photometric variability (i.e. for microvariability) of P Cygni are NRPs of either s-mode or g-mode oscillations. Small variations in stellar parameters could lead to variations in the properties of the wind due to the postulated sensitivity of P Cygni's wind (Pauldrach & Puls 1990).

Summarizing, we conclude that the "swaying'' variability of P Cygni's optical wind is most likely triggered by either s-mode or g-mode NRPs in the photosphere.

4.3 Are the modulations and DACs linked to each other?

There are at least two pieces of evidence suggesting that the modulations and the DACs are probably not linked to each other. In particular, it seems unlikely that the modulations of the troughs are caused by the DACs themselves. First, the time-scales of the two phenomena are too different to suggest they might be physically coupled and, second, there are lines (e.g. the resonance lines of NaI and CaII) that show DACs but do not show modulations in velocity or strength of their troughs.

On the other hand, Markova (1993) found that on two different occasions in 1981 the increase in the velocity of the absorption cores of high-excitation optical lines (i.e. the rising branch of a modulation in velocity) seemed to precede the appearance of DACs in low-excitation lines. Unfortunately, due to the very limited number of available photographic spectra, we were not able to look for such a relationship in 1990. According to Israelian et al. (1996), however, a new DAC event should appear around JD 2448147. From a casual inspection of the data presented in Fig. 6 it seems that this event corresponds to a maximum in the velocity curve of the "swaying'' variability, thus supporting the result reported by Markova (1993). These results imply that a possible relationship between the modulations in the velocity of the absorption cores of the lines and the DACs cannot be excluded. If this is true then some additional factor would be needed to explain why structures of sufficient strength to produce observable DACs do not occur during every cycle of the modulations.

The above indicates that the available observations are insufficient to enable us to resolve completely the problem of a possible relationship between the modulations and the DACs. The establishment of such a relationship is a very difficult task since - due to the long time-scale of the DAC phenomena - it demands a very long-term monitoring campaign with high temporal and spectral resolution. Another requirement is that the observations must cover a spectral window that is going down to about 3500 Å  since in the higher members of the Balmer and HeI series the modulations and the DACs should coexist.

4.4 A few concluding remarks

In the previous subsection we have noted that DACs in P Cygni are not obviously connected to the stellar rotation. This is what distinguishes the wind variability of this Btype hypergiant from the variability of O-star winds, for which the observations clearly indicate a close relationship between the recurrence of DACs and the rotational period (Kaper et al. 1996, 1997, 1998). In addition, O-star winds do not give evidence for continuous modulations. However, P Cygni's wind variability is similar to that of another B supergiant, HD 64760. DACs in this star appear on a timescale that is two to three times longer than the estimated rotational period (Prinja et al. 1995). A further comparison of our results with those published by Prinja et al. (1995) and Fullerton et al. (1997) for HD 64760 showed that the wind variability of these B-type luminous stars appears to be qualitatively similar in several aspects. For example, both stars exhibit line-flux modulations that extend over the troughs and the lobes of the lines and occur on time-scales that vary slowly with time: HD 64760 in UV lines, P Cygni in optical lines; both stars show DACs which recur on time-scales that are not related to the rotation: HD 64760 in UV lines, P Cygni in UV and optical lines; in both stars DACs consist of a "slower'' pattern of wind variability on which a "faster'' pattern caused by line-flux modulations is superimposed; in both stars the modulations and the episodic DACs do not interact in an obvious manner; both stars give suggestive evidence for a "photospheric connection'' either through variations in low-velocity ($v\simeq 0$) wind layers (HD 64760, Massa et al. 1995; P Cygni, present study) or through close relationships between spectral and photometric variations (P Cygni, Markova et al. 2000a).

The periodic modulations in HD 64760 have been interpreted in terms of few corotating spirals that modulate the optical depth of the wind (Fullerton et al. 1997). Since the basic physical ingredients responsible for the appearance of the spirals - photospheric variability and stellar rotation - occur very commonly among OB stars the modulations are expected to be a common signature of wind variability of many early type stars. To explain the lack of observational evidence for rotational modulation of Ostar winds Fullerton et al. (1997) supposed that due to the smaller curvature of the spirals the structures are intrinsically more difficult to detect in these stars. (Note that the winding of a kinematic spiral is largely determined by the ratio $V_{{\rm rot}}/V_{{\rm inf}}$, which is expected to be smaller for O-stars - due to their systematically higher wind terminal velocities - than for B-stars.)

In this connection it is worth emphasizing that P Cygni and HD 64760 strongly differ in their stellar and wind parameters, especially rotational velocity and wind terminal velocity: while the former is a slowly rotating star (vsini = 40 km s^-1) with a slow wind ( $V_{{\rm inf}}$ = 230 km s^-1, Markova & de Groot 1997; Stahl et al. 1991), the latter is an extremely rapid rotator (vsini = 238 km s^-1 Hoffleit & Jaschek 1982) emitting a fast stellar wind ( $V_{{\rm inf}}$ = 1500 km s^-1, Massa et al. 1995), The two stars however have almost the same values of $V_{{\rm rot}}/V_{{\rm inf}}$: 0.16 for HD 64760 and 0.17 for P Cyg. This result together with the noted qualitative similarity in their wind variability seem to support the assumption of Fullerton et al. about the essential role that the ratio $V_{{\rm rot}}/V_{{\rm inf}}$ may play in determining the properties of wind variability of early type stars.

The fact that wind variability consisting of continuous modulations and DACs was detected in P Cygni through optical observations emphasizes the importance of longterm ground-based surveys as a powerful tool for the study of wind variability of stars with at least stronger stellar winds. This finding is quite comforting and promising especially under the tangible absence of the IUE satellite services nowadays.

Acknowledgements

I wish to thank Drs. Mart de Groot and Garik Israelian for their detailed comments on this work. I am also grateful to Dr. Otmar Stahl and his collegues at the Landessternwarte, Heidelberg for making their observations of P Cygni available by publishing them in The Journal of Astronomical Data. This work was supported by NSF to MES trough grants No. F-813/1998.