4 Discussion

4.1 Comparison with $\zeta$ Pup and $\lambda$ Cep

At this stage it is worth comparing the variability of BD  $+60^{\circ }$ 2522 with that of the two most prominent members of the Oef class: $\zeta$ Pup and $\lambda$ Cep.

Optical and UV observations of $\zeta$ Pup revealed appreciable variability on different time scales. Moffat & Michaud (1981) and Howarth et al. (1995) detected a modulation of the stellar wind of $\zeta$ Pup with a period of 5.0-5.2 days thought to be the stellar rotation period. Moffat & Michaud (1981) accordingly suggested that the inner regions of the stellar wind are forced into corotation by a magnetic field and $\zeta$ Pup could thus be a decentered oblique magnetic rotator.

In addition to the rotational modulation, the spectrum of $\zeta$ Pup displays also variations on two shorter time scales. The discrete absorption components (DACs) in the UV line profiles appear with a recurrence time of about 19 hrs (Howarth et al. 1995). A perhaps related time scale of 16.7 hrs was reported by Berghöfer et al. (1996) from an analysis of the variations of the H$\alpha$ line and the ROSAT-PSPC count rate in the 0.9-2.0 keV energy range. On the other hand, photospheric absorption lines exhibit moving bumps on time scales of $\sim$8.5 hrs. These features are usually interpreted as due to non-radial pulsations (e.g. Baade 1988; Reid & Howarth 1996).

Finally, the existence of small scale clumpy structures in the wind of $\zeta$ Pup was suggested by Eversberg et al. (1998). These authors obtained a set of high quality high resolution spectra of the He II$\lambda$ 4686 emission line that show stochastic variable substructures that they interpret as a manifestation of turbulent clumps propagating outward with the wind.

Henrichs (1991) reported covariability between the equivalent width of the He II$\lambda$ 4686 line and the blue steep edge of the C  IV resonance lines in the spectrum of $\lambda$ Cep. He found a time scale of about two days for the variations of these lines, whereas the photospheric He I$\lambda$ 4713 line displayed variations, likely due to non-radial pulsations, with a period of about 6.5 hrs. Variations in the H$\alpha$ line on time scales of 4.8 days and 1.2 days were found by Kaper et al. (1997), whereas de Jong et al. (1999) confirmed the existence of NRPs with periods of 6.6 and 12.3 hrs. The latter authors suggested that beating among multimode NRPs could lead to cyclical surface amplitude enhancements that may eventually generate wind perturbations.

From their analysis of several observing campaigns with the IUE, Kaper et al. (1999) noted that the recurrence time of DACs in the UV spectrum of $\lambda$ Cep changed with time. From the October 1989 data, they found a time scale around 2.2-2.5 days, while the February 1991 and October 1991 data yielded time scales of 4.3 and 1.4 days respectively. This situation is somewhat reminiscent of the results of our Fourier analysis of the He II$\lambda$ 4686 line of BD  $+60^{\circ }$ 2522. Kaper et al. suggest that the wind of $\lambda$ Cep is modulated by rotation and the different time scales might correspond to different integer fractions of the rotational period.

In summary, it appears that NRPs are a common feature among Oef stars and that, for lines formed in the stellar wind, profile modulation on several, sometimes variable, time scales is not unusual either.

4.2 The role of stellar rotation

Our analysis of BD  $+60^{\circ }$ 2522 reveals profile variability of the double-peaked He II$\lambda$ 4686 line on time scales of a few days. Both the time scale and shape of the variability pattern change as a function of time. Therefore, it seems unlikely that the phenomenon is governed by a (single) stable clock such as the rotation of the star. Nevertheless, it is interesting to briefly consider the constraints on the rotational period of BD  $+60^{\circ }$ 2522.

Conti & Ebbets (1977) quoted a projected rotational velocity of 240 km s^-1. More recently, Penny (1996) and Howarth et al. (1997) used IUE spectra to infer $v~\sin{i}$ of 214 and 178 km s^-1 respectively. Though these values are not exceptionally large, we note nevertheless that they place the star in the extended high velocity tail of the distribution of observed projected rotational velocities as presented by Penny (1996). This conclusion holds true regardless which of the above values we actually consider. Assuming a radius of 15 $R_{\odot}$ (Howarth & Prinja 1989), we derive an upper limit on $P_{\rm rot}$ in the range 3.17-4.27 days depending on the actual value of $v~\sin{i}$. We note that the morphology of the He II$\lambda$ 4686 line in the spectrum of BD  $+60^{\circ }$ 2522 closely ressembles the synthetic H$\alpha$ profiles simulated by Petrenz & Puls (1996) for large values of i. This suggests that the true rotational period could be pretty close to the upper limit derived hereabove.

A lower limit on $P_{\rm rot}$ can be obtained from the critical rotational velocity. Adopting $\log L/L_{\odot} = 5.6$, $T_{\rm eff} = 37~500$ K and $M = 44~M_{\odot}$ (Howarth & Prinja 1989) and using the relation from Lamers & Leitherer (1993) to evaluate the ratio of the stellar luminosity to the Eddington luminosity, we derive a critical rotational period of 1.17 days.

The modulation of the line profile could occur with a period representing an integer fraction of the rotational period $P_{\rm rot}/n$ if there were n corotating structures in the stellar wind. The changes in the time scale of the variations might then reflect a change in the number of structures n creating the modulation. However, the above constraints on $P_{\rm rot}$ leave little room for any combination of integer numbers that might suit the various observed time scales.

These results do not imply that rotation does not contribute at all to the observed variability of the He II$\lambda$ 4686 line, but they indicate that rotation cannot be the sole cause of the phenomenon at all epochs. For instance, we note that the frequency that turns up most often in our Fourier analysis ( $\nu = 0.34$ d^-1) yields a "period'' of 2.94 days that is rather close to the upper limit on $P_{\rm rot}$ and this frequency might well be related to the rotational frequency.

4.3 Towards a possible interpretation

Let us now consider some possible scenarios that could explain the observed variability of the He II$\lambda$ 4686 emission line in the spectrum of BD  $+60^{\circ }$ 2522. First, we note that a binary scenario is rather unlikely because we find no significant RV variations. Also, such a scenario would not provide an explanation for the changing periodicity. A single non-radial pulsation seems equally unlikely. In fact, the time scales observed in the variations of the He II$\lambda$ 4686 line are much too long compared to the time scales of the variations of the absorption lines.

It seems therefore most likely that the phenomenon is associated with some transient large scale structure in the stellar wind. The lack of a single time scale in the modulation of the He II$\lambda$ 4686 line suggests that the phenomenon might not be related to corotating structures. Such corotating structures are predicted for instance by the so-called corotating interaction region model (Cranmer & Owocki 1996; Owocki 1999) and are believed to generate the cyclical modulation of the P-Cygni absorptions in UV resonance lines observed for a number of OB stars (e.g. Fullerton et al. 1997).

Let us emphasize that the double-peaked morphology of the He II$\lambda$ 4686 line clearly suggests that the stellar wind must be rotating at an appreciable velocity out to at least the radius of the formation region of this line. For instance, the wind could be forced to corotate with the star through the effect of a moderate stellar magnetic field. This situation could lead to some confinement of the stellar wind in latitude (see e.g. Babel & Montmerle 1997) and there is some observational evidence for an equatorial compression of the stellar wind of Oef stars. In fact, such a compression of the wind of $\zeta$ Pup was put forward by Harries & Howarth (1996) based on their spectro-polarimetric observations of the H$\alpha$ line in the spectrum of this star.

A variation of the global mass loss rate would change the extent of the corotating confined wind and could therefore induce some changes in the time scale of the variability. However, in case of a change of the overall mass loss rate, we would also expect to see epoch dependent changes in the emission strengths. The mean profiles displayed in Fig. 5 and the lack of a clear long term trend in the EWs listed in Table 3 do not support this idea.

It is worth pointing out that the pattern of the emission line profile variability in September 2000 is very much reminiscent of the model calculations of recurrent line profile variations presented by Lépine (2002). In these simulations, Lépine assumes a large number of discrete locally optically thick wind inhomogeneities moving around a common rotation axis. This model is designed to simulate the line profile variations arising from a perturbation at the surface of a rotating Wolf-Rayet star core that triggers waves that propagate outwards in the wind and create several overdense rotating "spiral arms''. The main difference between the Lépine model and our observations of the He II$\lambda$ 4686 line in the spectrum of BD  $+60^{\circ }$ 2522 is the lack of a single stable period in the observed modulation.

A possible explanation of the modulation of the He II$\lambda$ 4686 line in the spectrum of BD  $+60^{\circ }$ 2522 might be a density perturbation propagating across (rather than just rotating with) the confined part of the wind. We could imagine this as some sort of analogue of the large scale oscillations of Be-like disks. This density perturbation could be triggered by an episodic enhancement of the local mass loss at the tip of a large amplitude NRP wave. A slightly similar mechanism, "NRP wave breaking'', was proposed by Osaki (1999) to explain the episodic mass loss in Be stars. Such a large amplitude NRP wave could arise e.g. from beating among various NRP modes. While this scenario could easily account for the lack of a single stable period (through the effect of the propagation velocity of the perturbation and the interplay of various clocks: pulsations, rotation...), it seems more difficult to explain the changing pattern of the TVS. For instance, if a density wave moves around the star, why would it not affect the absorption and the emission components in a similar manner? One possibility could be that the density perturbation affects the absorption column only as long as it remains close to the stellar surface whilst the impact on the emission lines would be larger when the perturbation has moved outwards, but this is admittedly still rather speculative.