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Astron. Astrophys. 362, 1020-1040 (2000)

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7. Discussion

Ground-based photometric campaigns (Stagg et al. 1988), Hvar (Pavlovski et al. 1997) and AAVSO (Percy et al. 1996) surveys, and space data provided by the Hipparcos mission and analyzed in Hubert & Floquet (1998) have given us information on the occurrence of temporary fadings in EW Lac on time-scales of a few days, with [FORMULA]V = [FORMULA]Hp = 0.15 mag (Fig. 17a). The shortest time span detected between two fadings from those data is about 60 days. We argue that fadings are related to episodic outflows in this Be star seen nearly equator-on. Results derived from the 1993 multi-site campaign have provided evidence of other signs of episodic outflows, such as broad additional "pseudo-photospheric" absorption slowly expanding, discrete and narrow blue-shifted absorptions, and temporary enhancement of polarized flux. The correlation between EW He I and polarization is unmistakable, but on the other hand, there is little or no direct correlation between polarization and H[FORMULA]. Our investigation of Fe II [FORMULA] 6456 and 6516, H[FORMULA] and He I 6678 seems to show that there is no clear link between the "pseudo-photosphere" and CS layers, even if the latter are fed by transfer of material ejected from the star.

[FIGURE] Fig. 17a-c. Hipparcos photometry for EW Lac. a: over the whole Hipparcos run; b: two continuous series of Hipparcos observations HJD 2448168 and HJD 2448371 put together. These series are shifted in time and also in magnitude ([FORMULA]Hp = -0.006 for the observations at HJD 2448371) to put their variations in coincidence; c: continuous series of Hipparcos observations at HJD 2448695. Note the difference in amplitude variation between b and c

Rivinius et al. (1998a and b) have recently shown that outbursts in µ Cen are governed by the zero phase difference and the maximum amplitude sum of two given nrp modes of same [FORMULA] and m. In the case of EW Lac, such a conclusion is premature. Indeed, only two sets of data (August-September 1989 and August-September 1993) limited to the He I 6678 line are available. As shown, this line is particularly sensitive to stellar and circumstellar activity, and our investigation of nrp remains very limited since the stability and the phase coherence of main frequencies could not be sought with good accuracy. Nevertheless it is interesting to note the presence of the same frequencies, within the accuracy limits, in several previous photometric and spectroscopic analyses and in both sets of data of our study (see Table 7). Investigation of short-term variability in several continuous series of Hipparcos data from end-1989 to mid-1993, also supports this conclusion. It has shown evidence of the 0.60 d period (1.67 c/d frequency), with a total amplitude 0.055 mag, near epochs of fadings. Another series in 1992, apparently not disturbed by fadings, has shown a longer period 0.68 d (frequency 1.4 c/d), with a lower total amplitude (0.02 mag) (Figs. 17b and c).


[TABLE]

Table 7. Common frequencies detected in EW Lac from different studies


The amplitude maxima in short-term variability of He I radial velocity over the run in 1993 is observed around HJD 2449231.6-2449232.1 and HJD 2449237.6-2449238.0, which corresponds quite well to the beat of the 1.39 and 1.55 c/d frequencies (cf Fig. 5b and Table 5).

The following discussion will focus on some particularities and interpretation of signals associated with frequencies detected in 1993, and on some physical parameters which can be derived from detected orbiting clouds and from evolution of the behaviour of the He I line profile.

7.1. nrp and rotational modulation

According to Sect. 2, frequencies 1.39, 1.55 and 1.22 c/d are distinct from the rotational frequency ([FORMULA] c/d). Results given in Sect. 5 (Table 6) enable us to assert the presence, in 1989 and 1993, of two groups of frequencies of stellar origin: 1.55-3.20 and 1.39-2.76 c/d. The 1.55 c/d frequency is also the dominant frequency, in the limit of accuracy, detected in 1989 over the He I 6678 line profile. In terms of nrp this could be associated with a low degree sectoral or tesseral mode. Its power distribution concentrated in the wings indicates for dominating horizontal velocities and favours a g-mode. This frequency is also detected over the H[FORMULA] emission line. As emission is formed in geometrically extended CS layers going up to several stellar radii, we argue that this frequency concerns the subjacent photosphere and not the extended CS layers which mainly contribute to the H[FORMULA] emission strength (see Sect. 5.2). Note that Peters (1998) also suspected a similar frequency (P = 0.60: d) in the equivalent width of C IV UV resonance lines from continuous 24-hour monitoring with IUE during the last day of the optical multi-site campaign. So, this frequency is present in the wind and in the photosphere.

The 1.39 c/d frequency is essentially detected in the wings of He I 6678 (see Fig. 11) as opposed to frequencies 1.55, 3.20 c/d and also 2.76 c/d; its power distribution peaks at [FORMULA] [FORMULA]. However it is stronger in the blue wing and is probably disturbed by the blue absorption component (b) located near -200 km s-1. Its corresponding period 0.72 d has often been reported as the photometric period (Stagg et al. 1988). If the 1.55 and 1.39 c/d frequencies are related to nrp effects on the stellar surface, a strong coupling between them is suggested by the RV centroid behaviour (cf. Fig. 5).

As mentioned above, the 2.76 c/d frequency could first be understood as the first harmonic of 1.39 c/d, except that its behaviour across the line profile is somewhat different (see Fig. 11). Indeed, its power distribution is strongly enhanced at the R emission wing, and its phase velocity breaks off near +150 km s-1. If asymmetry in power distribution is not induced by non-adiabatic temperature effects, it could be indicative of "a wave leakage through the surface and presumably into the wind", according to Townsend (1997a, b). Influence of photospheric variability on the close CS matter has already been detected in another Be star, µ Cen, as reported by Rivinius et al. (1998a, b). This frequency is also present in UV photospheric lines (Peters & Gies 2000), and could be attributed to an independent nrp mode (see Table 6, case B).

Other frequencies, 0.92 and 1.22 c/d, are mainly detected in the blue wing of He I 6678 and cannot be associated with nrp. The 1.22 c/d frequency could be the result of a beat between 2.76 and 1.55 c/d. A 1.25 c/d frequency is weakly present in 1989 data and appears among frequencies derived by Pavlovski et al. (1997) and by Percy (private communication) from the August/September 1993 photometric campaign. Both frequencies 0.92 and 1.22 c/d are inferred in short-term variations of main quantities and lpv of He I 6678; they are probably linked with outflows modulated by rotation or with a coupling between frequencies presumably associated with nrp and rotation.

It is quite evident that this nrp investigation is only exploratory, as no comparison between computed and observed line profiles could be made. In fact, the He I 6678 profiles obtained in 1993 are so affected by pseudo-photosphere contribution that they are inappropriate for a comparison with modelled photospheric profiles. The stronger argument for nrp put forth in this paper is the evidence of common frequencies in both sets of analyzed data and the fact that some of them are also present in previous spectroscopic and photometric studies (Table 7).

7.2. CS activity versus stellar activity

As it is not easy to find direct links between stellar and circumstellar variability in this complex shell star, we have tried to underscore the results that could shed some light on this point. To begin with, the concept of an extended photosphere/pseudo-photosphere was introduced in the past by several authors. Harmanec (1983) introduced the concept of a pseudo-photosphere by taking into account the inner parts of the envelope which are flattened towards the stellar equator and optically thick in the continuum to explain the observed photometric correlations by an aspect angle. Hirata (1995) assumed the presence of an "extended atmosphere" optically thick even in the optical continuum, in order to explain a drastic change in brightness prior to envelope enhancement (H[FORMULA] emission) in late active Be stars (Pleione, 88 Her and [FORMULA] Dra). Similarly, Koubský et al. (1997) argued that the formation of a new Be phase in the late Be type star 4 Her started with the creation of a slightly cooler pseudo-photosphere at the equatorial region which grows into an optically thin extended envelope. EW Lac is a new example of a Be star showing a pseudo-photosphere. However the time scale, as well as the lines sensitive to the effect of the building of a pseudo-photosphere, are probably different in early Be type stars. The common behaviour of the additional broad variable "pseudo-photospheric" component (a) described in Sect. 4.2 and of the V and R outer emission components of He I have to be emphasized. Both are relevant to the same ejected layer: component (a) strength weakens over the 8.6 day run; simultaneously the peak separation of V and R components decreases from 800 to 720 km s-1 as R moves from +380 to + 320 km s-1. Qualitatively this can be explained by a ring first rotating closely to the stellar surface at Keplerian velocity, then detaching from the star and slowly expanding over some days during which opacity decreases.

It is possible to think that this ring is formed by repeated discrete outflows of matter that are progressively pushed, since some facts could support this hypothesis. V emission peak minima do not always have the same intensity, and sometimes emission in the blue edge disappears completely (V=1); these pronounced minima occurred more conspicuously at the beginning of the run at intervals of about 1.1 d, corresponding to the frequency 0.92 c/d, and near HJD 2449236 at intervals of about 0.77-0.80 d in agreement with frequency 1.22 c/d. These two frequencies are the most dominant in 1993 data but with unequally distributed power, stronger in the blue wing of He I 6678. Epochs with V=1 could correspond to a dimming of the blue lobe due to an ejected ring associated with the broad component (a), as discrete outflows occur. It is rather interesting to note that the frequency 1.22 c/d, is compatible with the most probable one (1.28 c/d) derived by Percy (private communication) from the 1993 photometric campaign. Is this photometric period due to rotational modulation of some discrete outflows?

7.3. Characteristics of an orbiting circumstellar cloud

Smith & Polidan (1993) showed that a He I 6678 absorption line is formed in rings with column densities at least as high as [FORMULA] [FORMULA] He I atoms in the [FORMULA] level. This is consistent with an optical depth in the center of the line [FORMULA] [FORMULA] [FORMULA] for [FORMULA] [FORMULA] K. We note that our interpretation of the He I 6678 line characteristics demands optical depths [FORMULA] [FORMULA] (see Sect. 7.4). To derive some physical characteristics of the cloud, which produces the non-periodic sharp absorption in the He I 6678 line, we can think of it as a gaseous spherical blob with radius [FORMULA] that crosses over the stellar disc. The residual intensity [FORMULA] of the absorption feature that it produces is then given by:

[EQUATION]

where [FORMULA] and [FORMULA] [FORMULA] for excitation temperatures [FORMULA] K at the distances [FORMULA] derived in Sect. 5.1.4 from kinematic arguments. The relation between [FORMULA] and the extent [FORMULA] comes from Moujtahid et al. (2000). We note that these temperatures are typical for environments which produce "shell" spectra. Hence, assuming a marginal value [FORMULA] from (Eq. 2) and the measured value [FORMULA], we obtain: [FORMULA]. If the cloud is assumed to have a uniform density and a mean temperature calculated from those derived above, the column density [FORMULA] corresponding to [FORMULA] is consistent with [FORMULA] [FORMULA] cm-3. This implies that the mass of the absorbing cloud is of the order [FORMULA].

7.4. Interpretation of the normalized He I 6678 line profile

Among the outstanding characteristics observed in the He I 6678 line of EW Lac normalized to the mean 1989 profile (Fig. 4) is the presence of weak emissions at nearly [FORMULA] km s-1 for which maximum intensities and positions vary only slightly, while the blue absorption "plateau" varies from a residual intensity 0.975 to about 0.998. Such behaviour is reminiscent of absorption lines produced by gaseous rings surrounding the star. It can be explained by preserving the source function factor [FORMULA] = source function of the line; [FORMULA] = projected surface of the ring) as the ring opacity decreases (Cidale & Ringuelet 1989). The high velocities at which the emission line shoulders appear in EW Lac imply that rings are rotating and perhaps expanding somewhat.

Another explanation for the He I 6678 line profile can be tried with a line source function perturbed by a variable chromosphere-corona like temperature structure of the stellar atmosphere. The observed intensity behaviour of the emission shoulders and the central "plateau" would demand, however, variable physical conditions in only those atmospheric layers which concern the central parts of the line profile, but these changes should keep the source function enhancement in the wings almost constant. Besides that, in this scenario the shoulder emissions are also signatures of the same variable stellar activity. In this paper we then explore the explanation for the line profiles shown in Fig. 4 based on circumstellar rings. Let us assume a central star surrounded by an inner cylindrical emitting ring at a distance [FORMULA] from the stellar surface (ring 1). The ring is assumed to have Keplerian rotational velocity [FORMULA], velocity [FORMULA] in the radial direction, total height [FORMULA] and radial opacity [FORMULA] at the center of the He I 6678 line. The emission produced by the ring was calculated assuming the presence of an underlying absorption photospheric component. The latter was obtained from a Gaussian profile with the same equivalent width as the 1989 mean profile, which was broadened by the adopted [FORMULA] values. As no resulting "star + ring1" profile divided by the underlying stellar rotationally broadened profile was asymmetric enough to account for the narrower central component, we assumed the presence of a second ring (ring 2) situated at [FORMULA] and characterized by the set of parameters [FORMULA], [FORMULA], [FORMULA] and [FORMULA]. We assumed that both rings are symmetric with respect to the equatorial plane that contains the line of sight.

For typical electron densities in circumstellar envelopes of Be stars [FORMULA] cm-3 and at a temperature [FORMULA], the ratio of source terms in the source function of the He I 6678 line is [FORMULA] [FORMULA], where [FORMULA] = collisional source term and [FORMULA] = radiative term, and the ratio of sink terms is [FORMULA] [FORMULA], where [FORMULA] = collisional sink term and [FORMULA] = radiative term. Hence, the source function of the line can be safely considered a collisionally dominated type. To a good degree of approximation the line source function can then be written (Mihalas 1978):

[EQUATION]

For simplicity we adopted a Gaussian intrinsic line profile [FORMULA]. The displacement[FORMULA] is produced by the total velocity along the line of sight [FORMULA] [µ = cos(radial direction, line of sight)] and the signs are chosen according to the observed half of the ring and correspondence to its front or rear part.

For a non-negligible value of the source function and for a suitable opacity and [FORMULA], each ring produces a symmetric line profile with shoulder emissions and central absorption with a slight emission-like reversal. The "plateau" observed in the blue line velocity interval [FORMULA] km s-1 is obtained by introducing [FORMULA], so that a P-Cyg like asymmetry is reproduced. However, the velocity in the radial direction needs to be [FORMULA], or else the blue emission component disappears. This condition, together with the high displacement of the emission shoulders, implies that the Keplerian velocity of the inner ring needs to be [FORMULA] km s-1. At a given value of the source function of the inner ring, increasing values of [FORMULA] produce increasing shoulder emissions but also a deeper central absorption "plateau". On the other hand, for a given opacity, increasing values of the source function increase the shoulder emission and reduce the "plateau" absorption.

At the low opacity "phases" the only way to obtain enough emission in the shoulders is by increasing the value of H. By trial and error we then obtained the ring parameters that roughly account for the global features observed in the He I 6678 line shown in Fig. 4. Though the measured value of [FORMULA] in EW Lac is [FORMULA] km s-1, we calculated two sets of line profiles, one set for the measured [FORMULA] (case a) and the other for [FORMULA] km s-1 (case b). In each case we distinguish two "phases": "phase 1", which corresponds to a higher value of [FORMULA], and "phase 2" for a lower value of this opacity. The calculated line profiles which seem to resemble those observed closely are shown in Fig. 18. The corresponding model parameters are given in Table 8. Depending on the case, some observed features are better represented than others. At any rate, the crude necessarily model does not allow us to expect to account for all aspects observed. Some of them may be produced by radiation transfer effects due to density, temperature and velocity gradients in the rings, which were not taken into account in the present simulation.

[FIGURE] Fig. 18a and b. Model He I 6678 line profiles normalized to the photospheric component. Case a uses [FORMULA] km s-1 and case b [FORMULA] km s-1. Phase (1) is for higher [FORMULA] values and phase (2) for the lower ones (see Fig. 4)


[TABLE]

Table 8. Model parameters of circumstellar rings


However, from the results obtained we can draw some general conclusions. If the rings are due to ejected matter from the central star, the supposed Keplerian velocities cannot be caused simply by the angular momentum transfer from the stellar surface. This is, however, a general problem encountered in all models of circumstellar discs with Keplerian rotation. Within the uncertainties involved in the choice of ring parameters, the source function of each ring seems to be fairly constant: [FORMULA] and [FORMULA] as one passes from one opacity phase to the other. As the inner ring expands ([FORMULA]), it seems to undergo acceleration, reduction of its radial opacity and increase of its height. The external ring is predominantly an absorption front ([FORMULA]) situated at about the same distance whatever the opacity phase [[FORMULA]]. Its velocity in the radial direction [FORMULA] implies a shrink phenomenon, and its opacity increases when the opacity of the inner ring decreases.

As a matter of fact, it should be pointed out that components (a) and (b) (see Sect. 4.2) are seemingly produced in ring 1, and components (c) and (d) result from the absorbing effect of both rings.

We note that the expansion velocities needed to account for the shapes of line profiles do give only order of magnitudes and should not be considered as precise estimates. They do seem to be supersonic. The rings may then be the result of wind-circumstellar envelope interaction phenomena with shock fronts (Zorec et al. 2000), which need a more thorough description that cannot be done with the simple model used in the present calculation. Case b (Table 8) gives values more consistent with the time-scale of the components (a), (b) and V and R (see Sect. 4.2). However, these values are only indicative; the comparison remains limited as no reliable radial velocity value can be obtained without a good model for the pseudo-photosphere, which extends more or less in a radial direction and whose [FORMULA] is a function of the radius.

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Online publication: October 30, 2000
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