2 The binary models and the role of duplicity for the Be phenomenon

Kríz & Harmanec (1975) and Harmanec & Kríz(1976) formulated a general hypothesis of the binary nature of Be stars, explaining the Be star envelope as an accretion disk created from gas flowing to the Be star via a Roche-lobe overflow from its unrecognized binary companion. They pointed out that with increasing orbital period one observes either a typical Algol interacting binary or a Be binary or a symbiotic star. Since a given B star occupies less and less space when placed in a binary system with longer and longer orbital period, the space available for the formation of an extended accretion disk also gets larger with increasing orbital period. In systems with shorter orbital periods, the Roche-lobe filling and less massive secondaries are usually much less luminous than their B-type primaries. Only for very long orbital periods do the absolute dimensions of the Roche lobe around the secondary become so large that even a very cool secondary has an optical luminosity comparable to, or even larger than the B star and one observes a symbiotic binary. Kríz & Harmanec (1975) were also able to explain rapid rotation of Be stars as a consequence of tangential accretion from the disk which brings some extra angular momentum. Furthermore, they explained at least some of the observed types of variations of Be stars, for instance the phase-locked V/R, RV, line-width and luminosity changes or long-term E/C and V/R variations and offered some ideas as to how rapid changes could be related to co-rotating structures in the accretion disks, caused by resonances.

While their hypothesis certainly represents a serious attempt to address the Be phenomenon in its complexity and very probably explains the nature of some of the actually observed Be binaries (for example AX Mon, RX Cas, SX Cas, KX And, V360 Lac, $\beta$ Lyr etc. - see Harmanec 2001 for a catalogue of known emission-line binaries), it is now well proven that it cannot be accepted as a universal explanation for the origin of Be envelopes. Already Plavec (1976) pointed out that if all Be stars were binaries with Roche-lobe filling secondaries, one should observe more eclipsing binaries among them than what is actually observed. While Harmanec (1987) slightly weakened this objection, there is a stronger one: detailed studies of several known Be binaries ($\varphi~$Per = HD 10516: Poeckert 1981, Gies et al. 1998; V839 Her = 4 Her: Koubský et al. 1997, for instance) clearly demonstrated that the secondaries in those binaries are not Roche-lobe filling objects but very small stars. The same is also true of binaries composed of a Be star and a compact, X-ray companion. Harmanec (1985) came up with the provocative suggestion that even in massive X-ray binaries the mass is flowing from the X-ray star towards the Be primary and presented some observational facts to support such a view. Recalling an earlier suggestion by Kríz (1982), he also argued that the contraction of the originally mass-losing star had to lead to its rotational instability near the equator, leading to another phase of mass transfer from this star to its (now more massive) counterpart. He called it a case PB of mass transfer and mentioned $\varphi$ Per as a system being possibly in such a mass transfer stage. It is obvious, however, that unless somebody can show how to excite X-ray emission from compact stars without allowing them to accrete mass from their optical companions, Harmanec's (1985) idea is not tenable.

Obviously unaware of Kríz's (1982) and Harmanec's (1985) studies, Pols et al. (1991) also investigated the possibility of formation of Be stars as products of case B mass exchange in binaries. Their approach was different, however. They accepted the idea of Kríz & Harmanec (1975) that some Be stars are case B mass-exchanging binaries but argued that the majority of Be stars are remnants of case B mass exchange in intermediate-mass close binaries after the termination of mass transfer. In other words, they postulated that the Be phenomenon occurs due to some still unknown physical mechanism which is only operational in rapidly rotating stars. The role of the mass exchange in their hypothesis is to rejuvenate and spin-up the original secondaries in binaries. They argued that Be stars in mass-exchanging binaries represent only a small fraction of all Be stars. Estimating the lifetimes of different evolutionary stages, they concluded that more than 80% of post mass-transfer Be stars should have a helium-star companion and that there should be 10 times more Be stars with a white-dwarf companion than those with a neutron-star secondary (observable as an X-ray source). They predicted that many new helium-star and white-dwarf companions should be detectable in the XUV spectral region.

The role of duplicity was critically examined by Baade (1992). Using high-S/N IR spectra near 880 nm, he carried out a search for late-type companions of 35 southern Be stars with a completely negative result. He also expressed some doubts about the existence of many binaries with hot compact companions and his conclusion was that the cause of the Be phenomenon cannot be related to their duplicity.

For the following reasons we believe, however, that the role of duplicity was not still investigated well enough and that Baade's view cannot be accepted as the final word:

1.

Perhaps most importantly, the number of known binaries among emission-line stars has been growing steadily - see, e.g., Gies (2000) or Harmanec (2001). As pointed out by Harmanec (2001), duplicity of Be stars can actually serve two different roles: (i) to explain the formation of Be envelopes via some kind of binary interaction, and (ii) to explain some of the variability patterns of Be stars.

2.

Studies by Slettebak (1987) or Harmanec (2000) demonstrated that Be stars are observed among stars of clearly different evolutionary ages. This may indicate that the cause of the Be phenomenon has to be sought in some external mechanism, not primarily in a physical mechanism related to the stars themselves.

3.

Such a view can be also supported by another similar argument. B stars span a huge range of stellar masses and it is well known from the theory of stellar evolution that the time scales of all processes depend strongly on the stellar mass. However, as pointed by Horn et al. (1982) the time scale of the formation of a new Be envelope was found to be very similar for three Be stars of spectral classes B0, B6 and B8. This again seems to indicate an external mechanism for the formation of such envelopes.

It is obvious that a new generation of powerful optical interferometers will soon be able to resolve many close binaries, so far detectable only by spectroscopy. This should allow new stringent tests for various binary scenarios of the Be phenomenon.