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Astron. Astrophys. 348, 831-842 (1999)

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7. Implications for disk formation

The transfer of matter to the disk with higher specific angular momentum than the one of matter co-rotating at the stellar equator remains unexplained by all of the above conjectures. In the case of outbursts à la µ Cen (Rivinius 1999, Baade 1998, 1999), it must form part of the still unknown outburst mechanism. Osaki (1999) has made a first qualitative suggestion based on the breaking of waves in the non-linear regime of nonradial pulsation. But µ Cen may not be representative of all Be stars, and even in µ Cen not all mass accumulated in the disk may be due to outbursts only. Therefore, other physical processes need to be considered that can build up disks around single stars in a more continuous fashion.

One of the few models that have attempted this to date is the wind-compressed disk (WCD) model by Bjorkman & Cassinelli (1993). It is based on the presumably line-driven, high-velocity wind which for long has been detected in UV resonance lines of Be stars viewed at a smaller inclination angle than shell stars (e.g., Prinja 1989). In the presence of rapid rotation, wind stream lines are deflected towards and concentrated about the equatorial plane. From there, part of the matter flows inwards back to the star but much of it leaves the star, so that a quasi-stationary disk-like concentration of circumstellar matter develops. However, as was pointed out before by Owocki (1997, private communication; 1998; see also Owocki et al. 1996for a more complete assessment of the WCD model), this does not solve the angular momentum problem posed by Kepler-like rotating disks. The severity of the problem is only further emphasized by the explanation of CQE's by Hanuschik's model.

The sharpness, contrast, and degree of centering within shell lines of the CQE's should also put limits on any outflow in the disk. In a numerical simulation of the WCD model, Owocki et al. (1994) obtain an outflow velocity profile in the plane of the disk, which becomes positive (i.e., outward directed) about 1 photospheric radius above the star and accelerates roughly linearly to 400 km/s at a distance of 5 stellar radii. By contrast, the IR excess observed in numerous Be stars by the IRAS satellite has been used to infer an expansion velocity at the level of 10 km/s or less (Lamers & Waters 1987). A break in the energy distribution towards the mm domain suggests a truncation of the disk or a re-acceleration of the disk matter only at very large radii (Waters et al. 1991).

The ubiquity of V/R variations and inferred oscillations of Be star disks probably require that the observations cover at least one V/R cycle before the degree of centering of CQE's within the shell profiles can be properly quantified. But the sharpness and contrast of the CQE's suggest already that any acceleration within the radial range of formation of the lines concerned should not be by more than [FORMULA]20 km/s when CQE's are present. Otherwise, the visibility of CQE's would be much reduced by the outflow velocity gradient in the line of sight similar to the effects of turbulence or other line broadening mechanisms.

With a typical pole-to-equator outflow velocity contrast of [FORMULA]1000 km/s vs. [FORMULA]100 km/s, the bistability model of Lamers & Pauldrach (1991) might in this respect face a similar problem as the WCD model. This model is based on a rather sharp boundary in effective temperature near 19 300 K, above and below which winds are, in the Lyman continuum, optically thin and thick, respectively. In the presence of rapid rotation, the two domains could occur in one and the same star but in a region above and below, respectively, a critical stellar latitude.

However, as Lamers & Pauldrach emphasize, this model is not by itself able to produce a disk, because the equatorial velocities of Be stars are too small. Therefore, there are no detailed numerical simulations that could be used to judge whether disk outflow velocities as low as required by CQE's and suggested by the far-IR excess are possible. If the extra mechanism necessary to (a) make the bistability model applicable to Be stars and (b) provide the angular momentum transfer were co-rotating magnetic fields or nonradial pulsation-driven outbursts, the angular momentum problem could possibly be solved at the same time. But a high disk outflow velocity would still require attention. A rotating magnetic wind model has been proposed by Poe & Friend (1986).

In all chains of observations attributed to and models developed for the formation of disks one or more links are missing to make them fully self-sufficient and -consistent. But the one missing between (a) the unknown mechanism that leads to outbursts as the result of some temporary increase of the nonradial pulsation amplitude and (b) the ad hoc mechanism assumed by Kroll and Hanuschik (1997) presently appears to be one of the smallest ones. Moreover, at the moment, this chain is one of the very few ones that would produce a Keplerian disk in a relatively uncontrived way.

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© European Southern Observatory (ESO) 1999

Online publication: August 13, 199