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3 Line-profile variability at optical wavelengths

To obtain a detailed picture of lpv in P Cygni's optical spectrum we studied the simultaneous behaviour of about 60 lines (permitted and forbidden) of different ions (such as NaI, CaII, HI, MgII, HeI, FeIII, NII, SiIII, SiIV, OII and SIII) over a period of 8 months in 1990.

\includegraphics[width=8.8cm]{Figures/fig1.eps}\end{figure} Figure 1: Examples of clear line-splitting observed in the 1990 spectrum of P Cygni. The profiles have been offset vertically by an amount that provides better visibility. The horizontal axes are scaled in heliocentric radial velocity (HRV)

3.1 DAC-induced variability

Photographic spectral observations carried out by different investigators at different epochs suggest that Balmer and HeI lines appear to be the best indicator of DACs in P Cygni's optical spectrum (see Table 1 in Israelian & de Groot 1999). This fact does not necessarily mean, however, that ALL lines of the two ions shows DACs at ALL observational epoch. Based on our own experience we can state that line-splitting can be confidently and frequently detected in Balmer lines with principal quantum number $9\leq n \leq 15$ and in HeI lines from the 21S level ( $\lambda \leq 3964$ Å). As an additional indicator of DACs, one may also use the K-line of CaII, MgII $\lambda $4481.14 and HeI lines of:

the triplet series 23P - n3D with $\lambda \leq 3819$ Å;

the triplet series 23P - n3S with $\lambda \leq 4713$ Å;

the singlet series 21P - n1D with $\lambda \leq 4387$ Å.

With the above outlined in mind we examined the photographic spectra of our sample for the appearance of DACs and found that some of the listed lines indeed exhibited, at least occasionally, line-splitting. Line-splitting was also suspected in FeIII lines. Examples of lines with a distinct double structure in absorption are shown in Fig. 1. To find additional evidence for the existence of DACs in the 1990 spectra of P Cygni we studied the so-called "quotient'' spectra derived by dividing individual photographic spectra by the spectrum obtained on the first night of the time series (JD 2448017), which was assumed - because of the lack of line-splitting and the relatively small width and strength of the absorption troughs - to represent a minimum-absorption template. This wavelengthby-wavelength renormalization effectively removes the underlying profile, thus emphasising small changes in line depth: parts of a profile that have excess absorption (or weakened emission) with respect to the corresponding "undisturbed profile" appear in the quotient spectrum as localized dips, while parts characterized by weakened absorption (or enhanced emission) relative to the "undisturbed profile" appear as localized peaks. The quotient spectra of the lines showing DACs revealed the existence of excess absorption, whose position in the troughs varied with time. The spectra also show that the emission lobes of the lines did not exhibit variations connected with those in absorption. The quotient spectra in the domain of HI $\lambda $3835.38 and HeI $\lambda $3964.73 are displayed in Fig. 2. The appearance of a sharp "emission'' bump, redward of the absorption enhancements is largely an artifact of the renormalization procedure.

\includegraphics[width=8.8cm,height=7.5cm]{Figures/fig3.eps}\end{figure} Figure 2: Quotient spectra in the domain of HI $\lambda $3835 and HeI $\lambda $3965. For better visibility successive spectra have been offset vertically and the HI $\lambda $3835 spectrum on JD 2448109 is represented with a dashed line. Horizontal axes are scaled in heliocentric radial velocity (HRV)

The quotient spectra of the lines showing DACs were measured for the position of the dips (i.e. heliocentric radial velocity, HRV), for the full width at half the maximum intensity (FWHM) and for the strength (i.e. equivalent width, EW). The velocity of each feature was measured by bisecting the lower half part of its profile. The precision of the measurements is better than 3 km s-1. The other two parameters, i.e. FWHM and EW, were estimated by means of least-squares Gaussian fits to the observed profiles. The accuracy of the individual determinations is limited by uncertainties in both the fitting procedure and the definition of the level of the continuum (typically of the order of 1 to 2 percent of the continuum flux). The estimated error is about a few hundredths of an Å in EW and 10 to 15 km s-1in FWHM. The measurements showed that:

(i) within each spectrum there exists an essentially one-to-one correspondence (in velocity and width) between the enhancements: the rms deviations in the velocity and the FWHM of the components amounted to less than 5 and 8 km s-1, respectively;

(ii) during the studied period the velocity of the enhancements increased from about 150 to about 190 km s-1;

(iii) the width of the enhancements seems to remain constant (within the error) around a mean value of 69 $\pm$ 10 km s-1;

(iv) the strength (i.e. the EW) of the enhancements varied by up to 50% with no hint of any systematics.

The "classical'' picture we have of DAC behavior is that broad absorption components appear at low velocity (one and the same for lines of different ions) and evolve towards higher velocity while narrowing. Thus we see that the behavior of the observed absorption enhancements only partially resembles the behavior of "classical'' DACs. The fact that both the width and the strength of the enhancements do not show variations typical for bluewardmigrating DACs, i.e. do not decrease with increasing velocity, indicates, either that the components do not belong to one and the same DAC episode, or that another variable phenomenon, different from the DAC-induced variability, exists and modifies the characteristics of the line profiles.

Unfortunately, our data sample has large gaps between data points and is not extensive enough to allow any specification in terms of different DAC episodes to be made. By chance, our photographic observations partly overlap the UV observations studied by Israelian et al. (1996). Combining the velocity measurements obtained for DACs in the optical (present study) with measurements derived for DACs in the UV we found that the two datasets agreed quite well in a sense that they defined a smooth curve of gradually increasing velocity (Fig. 3). This result suggests that the studied features are likely to belong to one and the same DAC episode. The observed duration of the episode is about 200 days. A linear interpolation of the data presented in Fig. 3 gives a mean acceleration of 0.37 and 0.10 cm s-2 for DACs with velocities between 150 and -190 km s-1 and between -190 and -200 km s-1, respectively. Notice that the phase of slower acceleration appears to consist of two subphases: one of almost zero DAC acceleration (between JD 2448120 and JD 2448230) followed by another with futher DAC acceleration (after JD 2448230). The separation does not seem to be an artifact of bad data sampling since similar effect has been observed during previous DAC episodes (Markova 1986b, Fig. 1 components Nos. 2 and 6; Fig. 3). The possibility that DACs may not accelerate continuously during their life-time is really unexpected and need futher investigation. It may well be, however, that the observed effect has no physical cause but reflects some kind of observational difficulty, e.g. unresolved blends between consecutive DACs.

\includegraphics[width=8.8cm,height=5cm]{Figures/fig4.eps}\end{figure} Figure 3: Velocity curve for absorption enhancements in the wind of P Cygni in 1990. Velocities are measured with respect to the Sun. Filled circles denote measurements in the optical (i.e. our data) while open circles - measurements in the UV (Israelian et al. 1996). Error bars are also drawn

3.2 "Swaying'' variability

Most lines in P Cygni's optical spectrum do not show clear line-splitting but exhibit significant variations in their profiles (Markova 1993; Stahl et al. 1994). In order to specify the properties of this variability we examined the temporal behavior of all lines in our sample simultaneously and looked for possible relationships between different kinds of lpv. (Note that because of the short-wavelength cut-off of the CCD observations the behaviour of some lines, e.g. the higher members of the Balmer and HeI series, remains beyond the scope of this analysis.) Figure 4 (left panels) shows representative profiles of lines of different ions. Profiles are normalized to the continuum. The wavelengths of each of the transitions and the Julian Date of observation are indicated. It is immediately apparent from this figure that different lines show qualitatively similar lpv, expressed mainly by changes in line absorption over a wide range of velocities. Variations in the width and the blue-edge velocity of the troughs are also apparent. In Fig. 4 (right panels) the distribution of the variability (by means of rms deviations, $\sigma_\lambda$) across the line profiles is shown as a function of velocity. The quantity $\sigma_\lambda$ was calculated using the expression

\begin{displaymath}\sigma_\lambda^2 =
\frac{[f_i(\lambda)- F (\lambda)]^2}{(N-1)f (\lambda)} %
\end{displaymath} (1)

where $f_i(\lambda)$ is the normalized intensity in the $i^{{\rm th}}$ of N spectra, and $F(\lambda)$ is the mean spectrum. In our case N=46. This formulation, first used by Prinja et al. (1996), provides a good approximation to the Temporal Variance Spectrum (TVS) described by Fullerton et al. (1996), under the additional assumption that the noise is dominated by photon noise and is nearly the same for each spectrum in the time series. The results obtained show that:

\includegraphics[width=8.8cm,height=12cm,clip]{Figures/fig7.eps}\end{figure} Figure 4: Sets of observational profiles of optical lines of various ions from the 1990 data (left panels). The panels on the right show the rms deviations for the entire data set as a function of velocity in each of the lines shown on the left

(i) the variability is dominated by changes in the troughs, which extend from zero velocity (in lines of higher excitation such as SiIV) to about -250 to -300 km s-1 (in the strongest HI and HeI lines). Because we did not detect any DACs with velocity lower than 140 km s-1 (Sect. 3.1), we suggested that another form of lpv, in addition to the DAC-induced variability, exists and affects the deeper layers of P Cygni's wind;

(ii) for lines with P Cygni-type profiles the variations also extend throughout the emission region with two well-defined peaks of maximum activity situated, respectively, at about +100 to +130 km s-1, and at about -20 to +20 km s-1.

To quantify the observed variability we measured, using a fitting procedure with Gaussians, the absorption troughs and the emission lobes of the lines for the magnitude and position (i.e. heliocentric radial velocity, HRV) of the maximum absorption depth or emission excess and for equivalent width. The measurements are partly illustrated in Figs. 5 to 10. In particular, Fig. 5 emphasizes the similarity in the velocity variability of lines of different ions and optical depth. Note that, in contrast to the DAC-induced variability which is characterized by a gradual increase in velocity, this sort of variability consists of fluctuations above and below a mean velocity level specific for each line. The amplitude of the fluctuations ranges from about 10 to about 30 km s-1 with a tendency to increase with decreasing Total Excitation Energy (TEE = excitation potential + ionization potential). No clear evidence for a time-lag in the variation of lines of different ions was found. It is worth noting that the mean velocity around which the position of the absorption core of the SiIV $\lambda $4116 line varies amounts to -20 $\pm$ 8 km s-1 in the star's rest frame, i.e. it is practically equal to the isothermal sound speed (-19 km s-1). This result indicates that the "swaying'' variability affects the deepest layers of the supersonic wind down to its base. On the other hand, as far as the strongest lines of HI and HeI also exhibit variations in velocity similar to that in high-excitation lines (upper panel in Fig. 5), we suggest that upper wind layers - at least up to about 14 R*, where the H$\alpha$ line forms (Vakili et al. 1997) - also respond to the perturbation(s) that causes the "swaying'' variability of the inner wind.

\includegraphics[width=8.8cm,height=10cm]{Figures/fig8.eps}\end{figure} Figure 5: Variations in the velocity of the absorption cores of lines of various ions. Vertical axes are scaled in heliocentric radial velocity (HRV). All velocities are negative

Apart from modulations in the velocity of the absorption cores, we have also observed changes in the magnitude of the maximum absorption flux, $F_{{\rm max}}{\rm (abs)} = 1 - {\rm Min}
(F_\lambda/F_{\rm c})$, and emission excess, $F_{{\rm max}}{\rm (em)}$ = Max $(F_\lambda/F_{\rm c})$, of the lines, as well as variations in emission and absorption strength, EW. Variations in the position of the emission peaks were also found. The measurements show that the variability in question consists of fluctuations around a mean level. Different lines seem to behave in a similar way. Modulations in absorption resp. emission EW are usually correlated with changes in $F_{{\rm max}}$(abs) resp. $F_{{\rm max}}$(em). The variability (in flux and strength) of the emission lobes is similar to but not identical to the variability of the troughs. Although the established line-flux (strength) modulations are usually small - for example, in the case of NII $\lambda $4630 the rms deviations in emission and absorption EW amount to 0.06 and 0.05 Å  respectively, while the rms deviation in the $F_{{\rm max}}$(abs) and $F_{{\rm max}}$(em) is only 2% of $F_{\rm c}$ - they must be genuine since their amplitudes are larger than the accuracy of the individual determinations. In particular, the modulations cannot be artifacts of inconsistent continuum placement. Otherwise one would observe a distinct anticorrelation between variations in emission and in absorption. The pattern of variations in the NII $\lambda $4630 line is illustrated in Fig. 6.

\includegraphics[width=8.8cm,height=9.5cm]{Figures/fig9a.eps}\end{figure} Figure 6: Variability of measured properties of the absorption trough (circles joined by a solid line) and the emission lobe (circles joined by a dashed line) of the NII $\lambda $4630 line. $F_{{\rm max}}$(abs) = 1 - Min( $F_\lambda /F_{\rm c}$) and $F_{{\rm max}}$(em) = Max( $F_\lambda /F_{\rm c}$). For further explanation see the text

The present data are obviously insufficient to perform a detailed time-series analysis and to find out whether the established "swaying'' variability is periodic or not. On the other hand, they clearly indicate that the phenomenon is recurrent. During the period studied we observed two cycles in the velocity modulations (the second one is incomplete) with a peak-to-peak time-scale of about 100 days, and almost three cycles in the line-flux (strength) modulations, with peak values separated by about 60 days. The estimates obtained, although rather uncertain, imply that the time-scale for modulations in velocity of the absorption cores might differ from the time-scale associated with modulations in emission and absorption-line strength (flux).

\includegraphics[width=8.8cm,height=10cm]{Figures/fig15.eps}\end{figure} Figure 7: Variations in the peak emission of lines formed at different optical depths. The pattern of variations in the strongest Balmer and HeI lines is obviously different from that in NII $\lambda $4630. In the former lines line-flux modulations are superimposed on a LT variation in $F_{{\rm max}}$(em), while in NII $\lambda $4630 only modulations in $F_{{\rm max}}$(em) have been observed. Note the apparent decrease in the amplitude of the LT variation with decreasing optical depth. For further explanation see the text

3.3 Long-term variability and red-emission-wing variability due to traveling bumps

Stahl et al. (1994) published radial-velocity and emissionpeak-intensity measurements of the strongest HI and HeI lines in P Cygni's optical spectrum. The presented data suggest the existence of a slow variation in both the velocity of the cores and the intensity of the peaks of the lines. Analyzing the data, we found in addition that:

(i) the LT variation in velocity was anti-correlated with the LT variation in emission-peak intensity in the sense that when the size of the emission peak increased the absorption core moved to longer wavelength;

(ii) the amplitude of the LT variation, both in velocity and intensity, tended to decrease with decreasing line optical depth thus indicating that, whatever the cause of the LT variability, its activity presumably decreased inwards without reaching the deepest layers of the wind. This assumption was confirmed by our measurements, which showed that neither weaker lines of HI and HeI nor lines of higher-excited ions experienced variation in velocity or emission-peak intensity similar to the LT variability.

The effect of inward-decreasing amplitude of the LT emission-peak-intensity variation is illustrated in Fig. 7, where the limiting case of a line with and without LT variability is represented, respectively, by H$\alpha$ and NII $\lambda $4630. Note that all lines presented exhibit modulations in the magnitude of their emission peaks but only in the stronger Balmer and HeI lines do these modulations coexist with the LT variation, in fact they are superimposed on the declining branch of the LT variation. Note also that the two kinds of variations do not appear to be linked. Even when they spread through one and the same region (in velocity space) they do not interact.

In addition, we would like to highlight the presence of a third peak in the distributions of the variability across P Cygni profiles (right panels of Fig. 4). This peak indicates that the high-velocity region of the red emission wings of the profiles, namely those between +90 and +230/250 km s-1, is time variable. Close inspection of several P Cygni profiles enables us to suggest that this variability seems to be due to the occurrence of low-intensity bumps whose position on the wings varies in time.

3.4 Variability of some "special'' lines

In this section we focus on the lpv of a number of "special'' lines in P Cygni's optical spectrum in 1990. These are the resonance lines of NaI, forbidden lines and lines with a pure emission profile. Properties of the lines from the last two groups have recently been studied by Markova & de Groot (1997).

The resonance lines of NaI $\lambda\lambda$5890 (D2), 5896 (D1) are situated on the red emission wing of the HeI $\lambda $5876 line. During 1990 the profiles of the lines consisted of a blueshifted absorption component in addition to the IS component. Figure 8 (upper panel) displays representative profiles of the D1 and D2 lines. The lower panel of the figure shows the rms deviations of the variations across the profiles for the entire data set. It is evident that both lines have exhibited variations in their troughs. The apparent variability of the IS components certainly has no physical reason and should be ignored since the features are very deep and narrow and, hence, extremely sensitive to small errors in the tracing of the spectra. For example, even when individual spectra in the time series are aligned to within 1 pixel or less, significant deviations occur over this interval within the IS D-lines. To quantify the variability of the stellar components, we measured the FWHM, the normalized flux - i.e. $F_{{\rm min}}$ = Min $(F_\lambda/F_{\rm c})$ - and the position - i.e. HRV - of the maximum absorption depth of the absorption trough of the D2-line; the absorption trough of the D1-line is strongly influenced by the red wing of the FeIII $\lambda $5892 pure emission line. The measurements, which are illustrated in Fig. 9, show that, starting on the first night of the time series until JD 2448109, the properties of the line did not change significantly: the rms deviation amounted to only 2.8 km s-1 in HRV, 0.03 in $F_{{\rm min}}$ and 0.053 Å  in FWHM. After JD 2448109 we observed a systematic increase in the velocity and the width of the trough, which was accompanied by an increase in $F_{{\rm min}}$, i.e. by a decrease in the maximum absorption depth. During this episode an absorption bump appeared in the trough at about -200 km s-1. This feature persisted at almost unchanged position for about a month. The variations must be real: in particular, they cannot be artifacts of inconsistent continuum placement or of changes in the strength of the emission wing of the HeI $\lambda $5876 line, since the rms deviations in the velocity and strength of the nearby IS component amounted to only 2 km s-1 and 0.008 Å  respectively. No variations similar to either the "swaying'' variability or the LT variability were observed.

\includegraphics[width=8.8cm,height=7cm,clip]{Figures/fig11.eps}\end{figure} Figure 8: (upper panel) Representative observational profiles of the D1 and D2 lines of NaI from our data set. (lower panel) The rms deviations for the entire data set as a function of wavelength across the lines

In order to ascertain whether the established systematic variability of the NaI resonance lines might be due to the DAC event described in the previous section, we compared the velocity-versus-time behavior of the D2 line with the evolution of the DACs in velocity space. The bottom panel of Fig. 9 emphasizes the good correspondence (in velocity and acceleration) between the two phenomena. Summarizing, we conclude that the behaviour of the NaI resonance lines is more likely dominated (or completely determined) by outward-propagating disturbances of enhanced density, identical to those that cause the appearance of DACs in the intermediate-excitation lines (Sect. 3.1).

\includegraphics[width=8.8cm,height=9.5cm,clip]{Figures/fig12.eps}\end{figure} Figure 9: Variability of measured properties of the absorption trough of the D2 line of NaI. Upper panel: Variations in the velocity of the stellar (dots joined by a dashed line) and IS (dots joined by a solid line) components of the line. Open circles denote the velocity of a bump that occurred in the trough. Middle panel: Variations in the magnitude of the minimum flux, $F_{{\rm min}}$ = Min( $F_\lambda /F_{\rm c}$) (dashed line) and in the FWHM (solid line) of the trough. Bottom panel: Comparison between variations in velocity of the D2 line (dots and open circles) and the evolution of the DACs in velocity space (crosses joined by a solid line). All velocities are negative and measured with respect to the Sun (HRV = heliocentric radial velocity)

Studying the lpv of forbidden lines and lines with pure emission profiles we found that the former did not show any significant variations while the latter did vary, though at a low level of significance. Figure 10 shows the rms deviations across the profiles of the NII $\lambda $5755 and FeII $\lambda $4285 forbidden lines (upper panels) as well as of the FeIII $\lambda $5834 pure emission line (lower panel). The rms deviations across the DIB at $\lambda $5780 are also shown in order to give the reader an impression about the accuracy of the used technique. Note that the two peaks evident on the upper right plot of the figure do not refer to the forbidden line itself but to the SIII $\lambda $4285 and OII $\lambda $ 4289 lines, which blend with the profile of [FeII] $\lambda $4285. Because we did not study the properties of the pure emission lines we are not able to specify whether the strengths or the velocities of the profiles vary and what is the pattern of the variations. However, referring to the result reported by Markova & de Groot (1997) that the NII and FeIII pure emission lines in P Cygni's optical spectrum seem to form in the inner wind, we suggest that these lines probably show variations similar to the "swaying'' variability.

\includegraphics[width=8.8cm,height=7cm,clip]{Figures/fig13.eps}\end{figure} Figure 10: The rms deviations for the entire data set as a function of velocity (HRV = heliocentric radial velocity) in the [NII] $\lambda $5755 and [FeII] $\lambda $4285 forbidden lines (upper panels) and in the pure emission FeIII $\lambda $5834 line. For comparison the rms deviations across the DIB $\lambda $5780 are also shown

Forbidden lines in P Cygni's optical spectrum presumably originate at large distances from the star (about 100 R*) where the wind has already reached its terminal velocity ( $V_{{\rm inf}}$ = 230 km s-1; Stahl et al. 1991; Israelian & de Groot 1992; Markova & de Groot 1997) since their profiles are unshifted (in the star's rest frame) and flat-topped. (The only exception is the [NII]$\lambda $5755 line whose profile is rounded and slightly blue-shifted, thus indicating that the line is formed in an accelerating zone where the velocity of the matter has reached 0.85 $V_{{\rm inf}}$ (Markova & de Groot 1997)). The lack of apparent variability for these lines, therefore, implies either that the wind is uniform at this distance or that it is still structured, but the conditions inside the structures do not favour transitions from the relevant metastable levels. Because structures in the wind were observed at even larger distances from the star (Barlow et al. 1994), we suggest that the last hypothesis is the more probable one.

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