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Astron. Astrophys. 333, 125-140 (1998)

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7. Star-to-disk mass transfer

In order to make the complex picture of the circumstellar variability reported in Sects.  3- 6more legible, we insert here a short, purely descriptive picture of the kinematics of an outburst. We derive from it qualitative, observable phenomena and compare them with the actual variations. Smith et al. (1991) and Hanuschik et al. (1993) developed rather similar conjectures, which partly have old historical roots, and also go through some numerical exercises. We largely refrain here purposely from the latter in order not to overload the paper. In addition to the ephemeral mass loss, there may also be a continuous wind (see Lamers & Pauldrach 1991 and Bjorkman & Cassinelli 1993 for winds of Be stars in general and Peters 1979 for UV observations of µ Cen) which, too, is omitted from this description. This high-velocity mass loss is often assumed to be more pronounced at higher stellar latitudes.

The initial growth mainly of the wings of the emission lines probably indicates the presence of rapidly rotating or other high-velocity gas close to the star, since the wings are present also for higher Balmer lines with comparable strength as in the lower ones. One would not expect significant contribution from Thomson scattering for the higher Balmer lines. So this hints to an ejection of matter from the star. This has been observed in other stars, too (Guinan & Hayes, 1984; Hayes & Guinan, 1984; Baade, 1986). By analogy to other Be stars, one would expect an accompanying increase in linear polarization that is also due to this matter close to the star but which would additionally show that the gas is concentrated towards a plane (Hayes & Guinan, 1984; Guinan & Hayes, 1984; Baade, 1986). Since in the stars observed only the amount of polarization increased but the polarization angle remained constant, that plane would be the plane of the circumstellar disk (Hayes, 1980; Hayes & Guinan, 1984; Clarke, 1990).

The physical process that leads to the temporarily strongly enhanced ejection of matter is still unknown. However, there is persuasive evidence that in µ Cen a strong causal link exists to the photospheric variability (Rivinius et al. 1998b; Paper IV, in preparation).

If, therefore, the origin of the outbursts is in the central star, also the steep decrease in line emission strength during the precursor phase should originate from the star. The drop in emission strength would thus not be caused by a sudden, temporary loss of circumstellar matter but rather be due to a quickly reduced rate of recombinations in that matter. For the central star to trigger this reduction, one possibility would be a partial loss of the stellar ionizing far-ultraviolet flux. The same was also surmised by Oudmaijer & Drew (1997), although mainly on the basis of a very short time scale of the recovery of the line emission. Another possibility is that some locally highly increased matter density (ejecta, see below) affects the recombination conditions by shielding of the stellar radiation.

Whether the gas ejection takes place all along the equator or is concentrated at particular stellar longitudes and whether an outburst consists of only one continuous (or instantaneous) outflow or several separate ejections, can at best be speculated about. The variability of the high-velocity absorptions (Sect.  6) could be an indication of a spatially and/or temporally inhomogeneous outflow (as might be the discrete absorption components of UV resonance lines - Grady et al. 1987a). But they could also result from instabilities in the outflow (cf. e.g., Peters 1988).

A stronger hint at spatial inhomogeneities is provided by the sudden onset of the [FORMULA] variability and the subsequent slow decline of its amplitude. It might be attributed to a cloud of gas orbiting the star. It would be most compact right after the ejection by the star. But as its azimuthal distribution (and orbit?) is circularized and/or more matter is ejected, the amplitude of the [FORMULA] variability would decrease. For a non-critically rotating star, the Keplerian orbital period of such a cloud of gas might even be shorter than the stellar rotation period. This is not impossible for plausible stellar parameters of µ Cen but requires that this gas be quite close to the stellar surface. If magnetic fields play a role in confining the cloud of gas, the 0.6-day quasi-period (Sect.  5.2) could also be due to the rotation of the central star. However, the [FORMULA] 5% outburst-to-outburst variation of the [FORMULA] time scales (Sect.  5and Fig. 9) would rather favour the orbital-motion interpretation.

On the other hand, the apparent relative constancy of the 0.6-day cycle length over 8 consecutive nights (Sect.  5.2) would be more readily reconcilable with the magnetic model. But the weight of this argument is reduced because during the same time the nightly mean separation between the two H [FORMULA] emission peaks fluctuated by [FORMULA] 3% but did not systematically decrease. Accordingly, the radius of the H [FORMULA] -emitting zone would have remained constant (but matter could still have drifted through it).

Finally, (part of) the ejected matter merges with the disk which in this picture would be more or less detached from the star. This is in accordance with the observed decrease in separation between the peaks of emission lines. In the absence of a new outburst, this would correspond to the phase of relative quiescence. Since the emission peak separation of Si ii [FORMULA] 6347 during this phase was lower in 1996 than in 1995, Keplerian rotation as well as angular momentum conservation would imply a higher radius of the line forming region in 1996. Although we could not define a relative quiescence phase in 1997, the peak separation was about the same as observed in the 1996 quiescent phase. However, now even Fe ii emission was present more persistently, with a peak height of about 4-5 % above the continuum.

If the region of formation of the latter lines is purely rotationally supported, the rate of change of their peak separation, 1-1.5 [FORMULA] d-1 (Fig. 6), implies an expansion velocity of less than 5 [FORMULA] for basically all sets of reasonable parameters (e.g.  [FORMULA] [Brown & Verschueren 1997], [FORMULA]), using

[EQUATION]

for Keplerian orbits, following Huang (1972) but modified for the case of a non-critically rotating star. The cumulative growth between two larger outbursts separated by an observed typical time of about 50 days would then amount to [FORMULA] km. The radius of the region from where the emission peaks arise would accordingly increase from the initial 1.7 [FORMULA] (for [FORMULA]) by 1.5-2 [FORMULA] to 3-4 [FORMULA].

Note that this alone does not permit to distinguish between the two extreme possibilities of all ejected matter falling back to the star or merging with the disk. However, Fig. 2 indicates that the projected equatorial velocity observed in the Fe ii lines at the very beginning of the outbursts can be as high as 220 km s-1, which is about 170 % of [FORMULA]. For inclination angles, i, between 30 and 45 degrees, the upper limit of the actual velocity of the Fe ii ions is between 440 and 340 km s-1, respectively. This range is sufficiently close to the stellar break-up velocity noted above that gas at the high end of the velocity distribution may conceivably have enough angular momentum to stay in orbit.

As another approach, since Be stars are known to be the most rapidly rotating B-type stars, one can use the ratios [FORMULA] / [FORMULA] provided by Brown & Verschueren (1997) for a number of stars. In their sample are 16 (emission line and non-emission line) stars with spectral type between B1 and B3 and luminosity class between V and III (i.e., bracketing µ Cen) with this ratio exceeding 0.5. If one star with [FORMULA] is excluded, the mean ratio becomes 0.62 [FORMULA] 0.08 which should be a statistical lower limit for µ Cen. Since the velocity of the Fe ii ions exceeds the stellar rotational velocity also in the equatorial plane by 70 %, one would also on this basis conclude that at least part of the ejected matter may reach the disk.

If, alternatively, one adopts the case of conservation of angular momentum,

[EQUATION]

the absolute numbers change, of course, but not their order of magnitude.

This simple picture of the kinematics of an outburst does not seem to be dominated by the presence or not of a dynamically stable disk. One might conclude this on the basis of the very similar (but poorly sampled) strong [FORMULA] variability observed by Baade et al. (1988) during the 1987 February outburst of µ Cen when there was close to no persistent H [FORMULA] emission. Observations by Baade (1991) in early April, 1986, when the [FORMULA] emission disappeared within less than 10 days, permit a similar conjecture.

Our description of an outburst leaves open the in some sense opposite question of the effect of the outbursts on the disk. In particular, it does not state to what extent outbursts contribute to the replenishment of the disk which under the influence of stellar radiation pressure and internal instabilities would otherwise dissipate. It would certainly be premature at this moment to attribute all variations of emission lines of Be stars to outbursts of the type described here because also the high-velocity component of the mass loss from Be stars, i.e. their wind, undergoes drastic variations which do not seem to be closely correlated with H [FORMULA] outbursts (Grady et al., 1987b; Sonneborn et al., 1988).

The sudden drop in line emission from the disk which precedes any other early symptom of an outburst is presently the strongest indication that the outburst does not leave the disk unaffected. The simple model considered here would suggest (see above) that this effect is not the loss of mass from the disk but a loss of ionizing radiation reaching the disk. Apart from a (not otherwise postulated) real temporary reduction in stellar UV flux, the model could also accommodate the notion of shielding of the disk by the ejected cloud(s) of gas.

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© European Southern Observatory (ESO) 1998

Online publication: April 15, 1998
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