| Abstract
| - Context. The recent variability survey of the NGC 3766 cluster revealed a considerable number of periodic variable stars in a region of the Hertzsprung-Russell diagram where no pulsations were expected. This region lies between the instability strips of the δ Scuti and slowly pulsating B (SPB) stars. Moreover, the periods of the new phenomenon, P ~ 0.1−0.7 d, do not allow us to associate it a priori to either of these two types of pulsations. Aims. Stars in the NGC 3766 cluster are known to be fast rotators with rotational velocities typically larger than half of their critical velocity. Rotation can affect both the geometrical properties and period domain of pulsations. It also alters the apparent luminosity of a star through gravity darkening, an effect seldom taken into account in theoretical studies of the rotation-pulsation interaction. We explore whether these effects are able to deliver a consistent interpretation for the observed properties of the new variables in NGC 3766: that is, explaining their presence outside the instability strips of known pulsators and the domain of their variability periods. Methods. We carry out an instability analysis of SPB models within the framework of the traditional approximation of rotation. We then study the visibility of excited modes according to the angle of view and rotation. We also check how gravity darkening affects the effective temperature and luminosity of stellar models for different angles of view and rotational velocities. We adopt the simple approach of von Zeipel to express gravity darkening. Results. At the red (cold) border of the instability strip, prograde sectoral modes, which are equatorially trapped waves, are preferentially excited and their visibilities are maximum when seen equator-on. From a linear computation, the amplitudes of the prograde sectoral modes are at best ~40% of their non-rotating counterparts. This ratio qualitatively reproduces the properties of the variability amplitudes observed between the SPBs and new variables in NGC 3766. Furthermore, low-mass SPB models seen equator-on can appear in the gap between non-rotating SPB and δ Scuti stars as a result of gravity darkening. In that case, the periods of most visible modes are shifted to the 0.2-0.5 d range owing to the effects of the Coriolis force. We therefore suggest that the new variable stars observed in NGC 3766 are actually fast rotating SPB pulsators.
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