7 Conclusions and discussion

Thirteen of our sample stars are now classified as confirmed SPBs and at least nine are multi-periodic. In each step of our frequency analyses, the 1% FAP-level and 3.7 S/N-level were used to judge upon the reality of different occurring frequencies. Both criteria are equivalent for multi-site data of p-mode pulsators (Alvarez et al. 1998). However, for our data of g-mode pulsators, the 3.7 S/N-level is systematically higher than the 1% FAP-level. Indeed, the mean ratio between the 1% FAP-level and the S/N-level for the variations in our single-site ground-based velocity and Geneva data respectively amounts to 2.8 and 2.9, while we find a ratio of 2.2 for the variations in the continuous space-based HIPPARCOS data. We are currently investigating the sensitivity of both significance levels to time-gaps, the length of the time-base and the amount of data for typical data-sets of g-mode pulsators. The results of our study will also be relevant for frequency searches in $\gamma$ Doradus stars (Cuypers & De Cat, in preparation).

In Sect. 6, we investigated for the first time the statistical properties of the SPB pulsations. Our results are not according to theoretical expectations and form a challenge for the latter. However, the frequencies used in Sect. 6 are the observed intrinsic frequencies while the intrinsic frequencies in the corotating frame are considered in theoretical models. It remains to be seen if this difference resolves the discrepancies between theoretical models and observations.

For some of our objects, we find indications for frequency multiplets. The firm confirmation of such multiplets is crucial as it is currently unclear how internal rotation behaves in such massive stars while rotational mixing has considerable influence on their internal structure and evolution (e.g., Maeder & Meynet 2000). The study of multiplets in pulsating stars offers the possibility to constrain the internal rotation provided that we have accurate mode identifications. The latter are the topic of the next paper of this series (Paper III). First preliminary mode identifications for all the intrinsic frequencies reported in this paper with existing methods pointed towards inconsistencies between photometric and spectroscopic identifications for quite a number of cases (De Cat 2001). We judged that these methods have too limited power to identify g-modes. We are currently improving both types of identification methods in order to obtain more reliable and consistent results for our sample SPBs in the near future.

Figure 20: Comparison of the phases of variations for the observed pulsation frequencies: Geneva B versus <v> (top), HIPPARCOS $H_{\rm p}$ versus <v> (middle), and HIPPARCOS $H_{\rm p}$ versus Geneva B (bottom). The phases for HD 24587 are marked by open triangles while the other targets are indicated by full circles. The error bars denote the standard errors of the phases. The full line denotes in the top and middle panel a phase lag $\Delta \phi$ = 0.25, and in the bottom panel $\Delta \phi$ = 0.

Acknowledgements

We are grateful to the Observatoire de Genève and to the European Southern Observatory for the generous awarding of telescope time to make this long-term project possible. Prof. W. Dziembowski and Prof. D. Kurtz are gratefully acknowledged for the constructive remarks and ideas which helped us to improve our research. We are also indebted to the referee, Dr. E. Chapellier, whose comments helped to improve the paper.