6 Discussion and future prospects

Gas-dynamical simulations of flow structure in binary Be stars has proven the existence of another possible mechanism for the formation of a Be-type envelope in binary Be stars: outflow of matter from the vicinity of "asynchronous'' inner Lagrangian point $L_1^{\rm rot}$ of a rapidly rotating B star. Note that for the values of macroscopic parameters, typical for Be binaries, the energy of the gas is insufficient to reach the inner Lagrangian point L₁ of the binary, therefore there is no mass transfer between the binary components involved in the process. The outflowing gas only forms an envelope around the B star.

The main characteristics of such an envelope, according to our first numerical simulations, are:

1.

The envelope has a complex shape; is is not axially symmetric but elongated in one direction.

2.

Rapid cyclic changes of the envelope geometry between the disk-like and torus-like shape occur on a time scale almost an order of magnitude shorter than the binary orbital period.

3.

The envelope undergoes a fast retrograde apsidal motion, again on a time scale of a fraction of the orbital period, and the speed of this apsidal advance differs for the inner and outer parts of the envelope, indicating differential rotation inside the envelope.

Opponents of this interpretation can object that statistical studies showed that the Be stars are rotating well below their break-up velocities at the equator, which makes the mechanism proposed here inoperational. We do believe that the question of how close the true rotational velocities to the critical ones are needs to be carefully investigated for particular Be stars, not only on statistical grounds. Note, for instance, that Harmanec (2002) found that the observed v sin iof $\gamma$ Cas seems to agree with the expected break-up velocity for the best currently available estimates of the basic physical properties of this Be binary.

Undoubtedly, the complex variations of the envelope shape found here would strongly influence the observational appearance of Be stars in detached binaries. However - being aware of the limitations of our present gas-dynamical simulations - we are not attempting to compare our results with the observed variations for real detached Be binaries and postpone that for another study in this series, based on longer series of gas-dynamical modelling.

Here, we only offer a few thoughts on the potential of the new model:

1.

Our modelling should be complemented by calculations of emission-line profiles for the variable Be envelopes originating from the outflow discussed here. Yet, it seems that one should observe rapid changes in the intensity, width and V/R ratio of emission profiles, probably phase shifted for different lines, originating in different parts of the envelope. Even more stringent constraints may come from the analyses of forthcoming interferometric observations with VLTI focal instruments, such as a detection of phase-locked variations of the intensity maps at different wavelengths, both in the spectral lines and in continuum.

2.

We believe that the new model has the potential to explain the observed irregular emission-line episodes of Be stars. If a B star in a binary system is close to the limit of its rotational instability, even a small accidental disturbance can lead to the outflow of matter via the $L_1^{\rm rot}$ point. This can lead to a change in the total angular momentum of the system which, in turn, can either facilitate the outlow of matter or to stop it. One can assume that there should be a longer period of quiescence after a large emission episode than after a minor one.

3.

An interesting area for investigation is the case when the parameter of asynchronous rotation f is small, say 2 or so, since our analysis showed that this leads to conditions favourable for mass transfer between the binary components in systems which are still detached from the Roche lobe. Existence of such systems would substantially alter our current ideas about the process of mass transfer in binaries.

In the following papers of this series, we intend to address the above ideas via detailed modelling.

Acknowledgements

We thank the referee, Dr. Philippe Stee, for his constructive suggestions which helped us to improve and clarify some parts of the text. The use of the computerized bibliography from the NASA Astronomical Data System is also gratefully acknowledged. The study of PH was partly supported from the research plans J13/98 113200004 and AV 0Z1 003909 and from project K2043105. PH also acknowledges the support from the collaborative program KONTAKT ME402(2000) and CONACyT. D.B., A.B. and O.K. were partly supported by RFBR via grants 02-02-16088 and 00-15-96722, by FP "Astronomy", by program of RAS "Nonstationary Stars" and by INTAS via grant 00-491.