8 Discussion

8.1 f$_\mathsfsl{1}$: NRPs versus rotation models

The frequency f₁ is strong and clearly detected in many line quantities and LPVs. It cannot be due to a one-day window alias. Although the multi-site campaign does not completely remove possible effects of a one-day alias, the RLC method does and its resolution allows to separate P₁ = 0.97 d from 1 d (see Sect. 5.1). Moreover the sinusoidal shape of line quantities folded with P₁ (Figs. 7 and 9) and the travelling pattern on the greyscale plot (Fig. 16) remove any doubt about the reality of this periodicity. It can be attributed to a NRP mode with l = 2 or 3, |m| = 2 (see Sects. 6.2 and 6.3).

A rotation model with 2 starspots placed exactly opposite each other at the equator will reproduce variations similar to a l = 2, |m|=2 NRP mode, whereas at high latitude it will reproduce variations similar to a l = 3, |m|=2 NRP mode. Although this configuration could happen by chance, these kinds of variations have been seen in many Be stars and it is statistically rather unlikely that all these stars have 2 opposite spots exactly at the right latitude. A magnetic dipole with the magnetic axis perpendicular to the axis of rotation could explain two opposite spots at the equator. Nevertheless, no magnetic dipole configuration could explain the other positions of spots, and up to now only one Be star is known to host a magnetic field ($\beta$ Cep, Henrichs et al. 2000a).

On the other hand, the patterns are also seen travelling back (Fig. 16). This can be explained by NRPs or with starspots, but in the latter case only spots at high latitude will produce a backward moving pattern as strong as the forward moving pattern, as observed here. The pattern created with such spots would then be observed over a smaller velocity range than $\pm$$v\sin i$, which is obviously not the case.

Therefore, it is more probable that NRPs are involved in $\omega$ Ori. If NRPs are indeed present, the outburst which occurs in $\omega$ Ori could be the result of a beating effect of NRP modes as Rivinius et al. (1998c) showed for the star $\mu$ Cen.

By comparing the photospheric lines and the lines with additional outer emission components, one can investigate the link between the photosphere and the inner circumstellar layers close to the central star.

From the velocity range determined with the variance (Sect. 5) for the He I and other species lines, we know that the extremes of the wings of the strong He I lines are formed out of the photosphere. These parts of the He I lines also pulsate with the frequency f₁ (e.g. Fig. 16), as can be seen on a zoom of greyscale spectra, not corrected from the mean spectrum, of the He I 6678 blue wing (Fig. 22). The results are similar for the red wing.

Kambe et al. (1993b) observed the same phenomenon in the Be star $\lambda$ Eri and suggested that it is due to lpv seen in a rotationally accelerated equatorial region. However in $\lambda$ Eri the velocity measured for the outer regions of the lines corresponds to the break-up velocity, which is not the case in $\omega$ Ori. Moreover, the velocity phase in the outer regions of the lines is different from the one in their core (e.g. He I 6678 in Fig. 15).

Therefore, we cannot exclude that some of the ejected material pulsates with the same frequency as the star but with a different velocity phase, probably due to the difference in density between the photosphere and the envelope, and we conclude that a part of the ejected material could still be linked to the star.

Figure 22: Greyscale spectra of the blue wing of the He I 6678 line. The black line indicates the velocity region determined from the variance of the purely photospheric lines, whereas the white line indicates the region determined for the He I lines with a circumstellar component.

8.2 f$_\mathsfsl{2}$: orbiting material

The frequency f₂ is mostly detected in red He I lines affected by emission, but this segregation could be due to the faintness of the other studied lines. Nevertheless, as it is especially powerful in the emission wings of the red He I lines during the first half of the campaign (Fig. 19), this frequency is thought to be due to a cloud of orbiting material. The variations in V/R during the first week of observations with a period P₂ = 2.17 d (Fig. 21) are very similar to the ones observed by several authors in Be stars (e.g. Baade 1982; Smith 1989).

It is known (Hanuschik et al. 1993; R1) that the V/R variations are stronger right before and during an outburst and best seen in the strong red He I lines. Therefore it is expected that a cloud of material has been ejected shortly before or at the beginning of the MuSiCoS 98 campaign and we see it orbiting around the star (see V/R in Fig. 13) and going towards the already existing envelope (see peak separation in Fig. 12). After a few revolutions around the star, the cloud is not detected anymore.

Two schematic scenarios are proposed here to explain the V/R variations at the beginning of the observing campaign and the large fluctuation observed between HJD 2451144.5 and 2451148. These scenarios need to be investigated further in the context of a global theoretical model.

Scenario A: a first compact cloud of material is ejected just prior to or at the beginning of the MuSiCoS campaign and is a precursor of a subsequent bigger ejection. After a few stellar rotational cycles, at HJD 2451147, this new material is ejected in an axisymmetrical way making the total emission stronger (Fig. 11). It dilutes the cloud, therefore the amplitude of the V/R variations decreases (Fig. 13). The slow decrease of total emission observed after the outburst suggests that part of the ejected material falls back onto the star.

Scenario B: a compact cloud of material is ejected right before or at the beginning of the MuSiCoS campaign, and this is the only ejection. After a few rotational cycles, at HJD 2451147, the cloud reaches the already existing envelope and is circularized and diluted in the envelope, causing a decrease of the V/R variations (see Fig. 13). The emissivity of recombination lines is proportional to the density squared. Therefore the total emission of the cloud merged with the disk is higher than the summed emission of the cloud alone plus the disk alone (Fig. 11). This last statement is true only if the mass of the cloud is not negligible compared to the emitting mass of the disk. For $\omega$ Ori the mass of the cloud is not negligible, as we detect the V/R variations it produces during the first part of the campaign. The slow decrease of total emission observed after the outburst suggests that when the dense cloud has been completely diluted in the disk, its contribution is not significant anymore, and/or the volume of the disk expanded because of the merging.

If the cloud of material seen before HJD 2451148 corotates with the star, f₂ = 0.46 c d^-1 would be the rotational frequency of $\omega$ Ori. However, we showed that $f_{\rm rot}$ is around 0.73 c d^-1 which implies that the cloud rotates slower than the star itself. If the cloud is in Keplerian orbit, using $R = 6.8 ~R_{\odot}$ and $M = 8.0 ~M_{\odot}$ determined in Sect. 2, it is situated at a radius of 2.07 R_*. The variation in the peak separation of H$\alpha$ between HJD 2451147 and 48 indicates (Hanuschik et al. 1993) that, during the outburst, material was pushed out from a Keplerian orbit with radius $\sim$2.05 R_* up to $\sim$2.30 R_*. This gives good confidence that the cloud was indeed pushed further away from the star at this period.

Taking extremes values for R and M (see Table 1), the lowest possible inner radius of the disk is not larger than the equatorial radius of the star. Therefore we cannot exclude that the disk is attached to the star. However, the extremes values of Rand M are unlikely for such a star; the mean values of R and M are much more realistic and lead to a detached disk.

We stress the difficulty of finding a clear common definition of an outburst and its beginning. The word "outburst'' has been used in the literature to describe a sudden enhancement of light or emission in lines. But it is also usually linked to an ejection of material, considered as the cause of the sudden light or emission increase.

In the case studied in this paper, an increase of emission occurred between HJD 2451147 and 2451148 and this is what we call here an outburst. It can be due to an ejection occuring at HJD 2451147 (scenario B) or to the merging of a cloud from a previous ejection with the disk (scenario A).

The time of beginning of the outburst depends on the line considered. For $\mu$ Cen (R1) observed that H$\delta$ is the best line for determining the beginning of an outburst. This line was not observed as a good indicator for $\omega$ Ori, but following their paper, the beginning of the outburst in H$\delta$ would be at HJD 2451148, as weak emission seems to affect this line between HJD 2451148 and 52.