7 Discussion

We now examine what our observations imply about the Be mechanism. In the literature, binarity, pulsation and rotation have been suggested as the mechanism for the establishment and maintainence of the circumstellar material seen in Be stars.

Harmanec and K$\rm\breve{r}$i$\rm\breve{z}$ (1976) have suggested that Be stars comprise a population of interacting binaries. In this model, elaborated upon by Pols et al. (1991), emission arises from material in accretion onto the secondary component. The difficulty that remains with this model is that the expected number of close interacting binaries is too few to account for the observed population of Be stars (VanBever & Vanbeveren 1997). Our observations, particularly the high Be star ratio in NGC 330, do not favour the interacting binary hypothesis as the population of stars required to be in mass exchanging binary systems near the MS turnoff (Abt 1987) is too high.

  

Figure 17: Same as Fig. 16 but for stars near the core of NGC 346

  

Figure 18: The finding chart for the Be stars around NGC 1818. The full field is 10$\hbox{$^\prime$}\times$10$\hbox{$^\prime$}$ whilst the inner rectangle in which the search for stars with H$\alpha$ emission was performed is $7\hbox{$.\mkern-4mu^\prime$}6\times9\hbox{$.\mkern-4mu^\prime$}2$. North is to the right and east is at the top

The non-radial pulsator model for Be activity (Vogt & Penrod 1983; Baade 1987) has gained support from the recent work of Dziembowski et al. (1993). In their models, Dziembowski et al. have shown that an instability domain exists on the main-sequence that almost fills the gap between $\delta\,$Sct and $\beta\,$Cep variables. These slowly pulsating B-type stars span a range of mass from 3 to 6 $M_\odot$. The Be star $\mu\,$Cen has been intensively studied by Rivinius et al. (1998). From their analysis of photospheric radial velocity variations they have discerned six discrete periods between 0.27-0.51 days. Rivinius et al. suggest that when the majority of these modes are in constructive interference, expulsion of material and a line emission outburst occurs.

There are problems with associating the Magellanic Cloud Be stars observed here with the pulsation instability mechanism described above.

  

Figure 19: Same as Fig. 18 but for stars near the core of NGC 1818

  

Figure 20: The finding chart for the Be stars around NGC 1948. The full field is 10$\hbox{$^\prime$}\times$10$\hbox{$^\prime$}$ whilst the inner rectangle in which the search for stars with H$\alpha$ emission was performed is $7\hbox{$.\mkern-4mu^\prime$}6\times9\hbox{$.\mkern-4mu^\prime$}2$. North is to the right and east is at the top

Firstly, in conditions of reduced metallicity such as those within the Magellanic Clouds, the extent of the pulsation instability domain is reduced (Dziembowski et al. 1993) and $\beta\,$Cep instability is seemingly extinguished (Balona 1992). Most importantly, the Be stars observed here are by no means confined to a range $M_\odot$. Indeed our observations show that the largest proportion of Be stars occurs at $\sim 14-15~M_\odot$.

The most widely accepted explanation for the Be phenomenon is that it is a result of the rapid rotation of the B star. This explanation was originally put forward by Struve (1931). In its modern incarnation, due to Bjorkman & Cassinelli (1993), the stellar wind from a rapidly rotating star is concentrated and confined to a disk around the equatorial plane of the star. The model of Bjorkman and Cassinelli predicts a maximum likelihood for disk formation near spectral type B2 (where the stellar angular velocity required for disk formation is 55% that of the critical breakup velocity).

  

Figure 21: The finding chart for the Be stars around NGC 2004. The field size is 10$\hbox{$^\prime$}\times$10$\hbox{$^\prime$}$. North is to the right and east is at the top

  

Figure 22: Same as Fig. 21 but for stars near the core of NGC 2004

Observations of Galactic Be stars find that the highest Be star fraction does indeed occur at early spectral types (B1 according to Zorec & Briot 1997). Within our sample spectral types are available for only five of our flagged Be candidates. We will present further spectral types in a forthcoming paper.

  

Figure 23: The finding chart for the Be stars around NGC 2100. The field size is 10$\hbox{$^\prime$}\times$10$\hbox{$^\prime$}$.North is to the right and east is at the top

  

Figure 24: Same as Fig. 23 but for stars near the core of NGC 2100

Assuming the Be phenomenon is related to the formation of an equatorial disk caused by rapid rotation, we would expect that clusters which form from gas that has a high angular momentum content would contain a high fraction of Be stars. Indeed, the evidence is suggestive that Galactic clusters whose stars present a higher than average rotational velocity have larger populations of Be stars (Mermilliod 1982).

In the Magellanic Clouds, the cluster NGC 330 has a noticeably ellipsoidal shape which may suggest that the cluster as a whole formed from material of higher angular momentum and that, as a consequence, the cluster stars have a rapid rotation rate. This would certainly be consistent with the high Be star content of NGC 330. In a future paper we will examine the rotation velocities of samples of stars within and around the clusters NGC 330 and NGC 2004 to see if the overall Be star fraction is related to average cluster star rotation velocity.

The tendency for there to be a higher Be star fraction near the main-sequence turnoff in some clusters also appears consistent with the rapid rotation hypothesis for Be star formation. The evolution of rapidly rotating stars has been examined by Endal & Sofia (1979) and Endal (1982). These models explicitly follow the radial exchange of angular momentum with evolution.

In the models of Endal and Sofia, stars commencing their main-sequence lives with relatively slow angular velocity remain slow rotators throughout the whole of the main-sequence evolutionary phase (although there is a marked increase in angular velocity of all stars during the core contraction phase associated with exhaustion of hydrogen in the core, this evolutionary phase is far too short to account for the observed proportion of Be stars). Thus slow rotators will never evolve into Be stars.

In contrast to the slow rotators, the models of Endal and Sofia show that stars commencing their lives with an angular velocity greater than 56-76% of the critical breakup velocity $\omega_{\rm c}$ spin up to the critical velocity over a moderate fraction of the main-sequence lifetime.

In a cluster where some fraction of the stars is formed with angular velocity greater than $\sim$50% of $\omega_{\rm c}$, those stars nearer the main-sequence turnoff are more likely to be Be stars since they will have been more spun up by evolution than the less luminous stars that have not evolved as far through the main-sequence phase. This process could explain the concentration of Be stars to the main-sequence tip seen in NGC 330, NGC 2004 and NGC 1818. We add the cautionary note that Endal & Sofia (1979) and Endal (1982) made a detailed study of only a single star which had a mass of 5 $M_\odot$,much less than the turnoff masses of $\sim$15 $M_\odot$ which is appropriate for the clusters observed here. For comparison with Magellanic Cloud data, models such as those of Endal and Sofia need to be made at higher masses and lower metallicities.

Other factors which might influence the Be star fraction are metallicity and age. However, neither of these factors seem to influence the Be star fractions in our data. To examine abundance dependence, we note that the two SMC clusters are probably more metal poor than the LMC clusters by a factor of about two (Russell & Bessell 1989). However, in the SMC, NGC 330 has a high Be star content while NGC 346 does not. At the higher abundance of the LMC, clusters with a range of Be star content are present, and the range is similar to the range in the SMC in spite of the abundance difference between SMC and LMC. Turning to age, we note that the clusters studied here have ages of $\sim 1~-~3~10^7$years, although these ages are uncertain by factors of 2-3 because of uncertainties in the amount of convective core overshoot which occurs in real stars. For comparison of Be star fractions with age, we take from the literature the following ages: NGC 330, 20 Myr (Chiosi et al. 1995); NGC 346, 13 Myr (Massey et al. 1989); NGC 1818, 30 Myr (Will et al. 1995); NGC 1948, 15 $\pm$ 5 Myr (Vallenari et al. 1993); NGC 2004, 20 Myr (Caloi & Cassatella 1995); NGC 2100, 15 Myr (Cassatella et al. 1996). There does not appear to be any correlation of Be star fraction with age: the cluster NGC 330 with the highest Be star fraction has an intermediate age and the oldest cluster (NGC 1818) has an intermediate Be star fraction.

This result contrasts with the results of Mermilliod (1982) who noted a trend of decreasing Be fraction with increasing age amongst young Galactic clusters.