The recent variability survey of the NGC 3766 cluster revealed a considerable number of periodic variable stars in a region of the H-R diagram where no pulsation is expected. This region lies between the instability strips of the delta Scuti and SPB stars. Moreover the periods of the new phenomenon, P~0.1-0.7 d, do not allow to associate it a priori to either of these two types of pulsations. Stars in the NGC 3766 cluster are known as 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 stellar luminosity through gravity darkening, effect seldom taken considered in theoretical studies of the rotation-pulsation interaction. We explore if both of these effects are able to deliver a consistent interpretation for the observed properties of the new variables in NGC 3766: explaining their presence outside the known instability strips and their variability periods. We carry out an instability analysis of SPB models within the framework of the Traditional Approximation of Rotation and study the visibility of 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 rotation velocities. At the red (cold) border of the instability strip, prograde sectoral modes are preferentially excited and their visibilities are maximum when seen equator-on. Furthermore low-mass SPB models seen equator-on can appear in the gap between non-rotating SPB and delta Scuti stars due to gravity darkening. In that case, periods of these most visible modes are shifted to the 0.2-0.5 d range due to the effects of the Coriolis force. We hence suggest that the new variable stars observed in NGC 3766 are actually fast rotating SPB pulsators.
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