1 Introduction

About 1/6-1/3 of all Galactic B-type stars with luminosity class III-V once showed H$\alpha$ in emission and have therefore been classified as Be stars (Zorec & Briot 1997; Jaschek & Jaschek 1981). The hydrogen, He I and singly ionized metallic emission lines originate in a circumstellar gaseous quasi-Keplerian disk. The formation of the rotating disk is associated with episodic mass-loss events (e.g. Rivinius et al. 1998), however the Be star mass-loss mechanism is not yet known. Low resolution (Dachs et al. 1986) as well as high resolution spectroscopy of individual emission lines (Hanuschik et al. 1996) has provided valuable information on the structure, kinematics and evolution of Be star circumstellar disks in the Galaxy (e.g. Telting 2000 for a review).

A considerable fraction of all Galactic field Be stars exhibit a long term variable so-called V/R asymmetry (V/R means the ratio of the violet to the red continuum-subtracted peak intensity in a double peak line profile) in their emission lines with a mean cycle of 6.8 years (Copeland & Heard 1963) while the remaining fraction show symmetric emission lines. Hanuschik (1988) extended the terminology of long V/R-variables and called them Class2 line profiles to account for asymmetric and long-term variable single-peak profiles which share the same physical phenomenon seen at low inclination (see Hanuschik et al. 1995), while symmetric line profiles without V/R variability are called Class1. The cyclic behavior of Class2 emission lines was for a long time a matter of debate (for a discussion see Ballereau & Chauville 1989) but is now interpreted as due to one-armed global oscillations in a nearly Keplerian circumstellar disk (Okazaki 1991, 1997; Papaloizou et al. 1992; Savonije & Heemskerk 1993). The model predictions were confirmed by observations (Hanuschik et al. 1995; Telting et al. 1994; Hummel & Hanuschik 1997; Mennickent et al. 1997).

These waves are confined to the inner region of the circumstellar disk and the confinement radius is predicted to amount to $\simeq$10-15 stellar radii (Savonije 1999; Okazaki 1997, 2000) in agreement with results based on line profile modeling (Hummel 2000a).

In the hybrid model for global disk oscillations (hereafter GDOs) for viscous decretion disks (Okazaki 1997, hereafter O97) two different mechanisms are proposed to confine a GDO. For the late-type Be stars a quadrupole of the potential induced by the rotationally flattened star provides a deviation from the purely Keplerian flow to establish the necessary confinement constraint as proposed by Papaloizou et al. (1992). Since early-type Be stars (MK B0-B4) do not rotate as close to the critical break-up velocity as late type Be stars (MK = B5-B9) (Fukuda 1982) the quadrupole of the potential as due to rotational flattening is no longer efficient for MK=B0-B4. For early-type Be stars the optically thin line force of the stellar radiation is proposed to perform the wave confinement to establish GDOs (O97).

In this study we present an observational test for the hybrid scenario. The efficiency of the optically thin line force depends on the metallicity of the central star. The terminal velocity in winds of O stars in the SMC is usually about 1000 kms^-1 lower with respect to their Galactic counterparts (Garmany et al. 1985; Haser et al. 1998). Kudritzki et al. (1987) interpreted the lower terminal velocity as due to a lower line force and a four times lower wind momentum assuming $Z_{{\rm SMC}}$ = 0.1 $Z_{\odot}$, ($Z_{\odot}$ = 0.02, Cox 2000). We selected the young open cluster NGC 330 in the SMC, since it is one of the best studied SMC clusters and shows a large number fraction of Be/(B+Be) stars (Feast 1972; Grebel et al. 1992; Keller et al. 2000). Furthermore the metallicity of this cluster is supposed to be even lower than in the field around NGC 330, hence enhancing the metallicity effect to be studied (Grebel & Richtler 1992). Hill (1999) found Z=0.004 for NGC 330 and Z=0.006 for the field around NGC 330, meaning $Z_{{\rm NGC~330}}$ = 0.2-0.3 $Z_{\odot}$.

The relation between the optically thin line force F and the metallicity Z is not well known. For B supergiants and O-type stars F scales something between linear and square root with the metallicity (Pauldrach & Puls, priv. comm.):

$$F \sim Z^{\frac{1}{2} \ldots 1}$$ (1)

meaning that the optically thin line force can be estimated to be 0.2-0.45 (for the field) and 0.1-0.3 (for the cluster) of the Galactic value for solar abundance.

As a consequence the confinement constraint for GDOs around early-type Be stars in the SMC is predicted to be considerably reduced with respect to Galactic Be stars. The prediction of the hybrid model would be a larger confinement radius and a larger oscillation period, or even a complete lack of GDOs in early-type Be stars.

The hybrid scenario can therefore easily be tested by a comparison between the number fraction of Be stars with long-term V/R-variability (Class2 Be stars, N II) to the total number of all Be stars

$$N_{V/R} = \frac{{\rm N{\sc ii}} } {{\rm N{\sc i+ii}} }$$ (2)

where N I+II is the total number of all Be stars showing either long-term V/R-ratio variations (=Class2) or not (=Class1). We thereby assume that N_V/R is dependent on the general requirements for GDOs, like the confinement, and on the unknown excitation mechanism, since GDOs are not self-exciting. We furthermore assume the unknown excitation mechanism for GDOs to be equal for all Be stars and that the observed N_V/R measures how far the physical requirements for GDOs are met.

Figure 1: Central part (2.3 $.\mkern -4mu^\prime$$\times$ 2.3 $.\mkern -4mu^\prime$) of the preparation image (6.8 $.\mkern -4mu^\prime$$\times$ 6.8 $.\mkern -4mu^\prime$) obtained with FORS1 at Antu (former UT1) and position of photometrically identified Be stars. North is top and East is left. Prefixes: A, B from Roberts (1974), K from Keller et al. (1999) and G from Grebel (1995)