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We study the pulsational properties of rapidly rotating main-sequence B-typestars using linear non-adiabatic analysis of non-radial low-frequency modestaking into account the effect of rotation. We compare the properties ofprograde sectoral $g$ and retrograde $r$ modes excited by the $\kappa$mechanism at the Fe opacity peak with the newly discovered period-luminosityrelation that is obeyed by a group of fast-rotating B-type stars in the youngopen cluster NGC 3766. The observed relation consists of two sequences in theperiod versus magnitude diagram, at periods shorter than 0.5 days. We find thatthis property is consistent with similar period-luminosity relations predictedfor excited sectoral prograde $g$-modes of azimuthal orders $m=-1$ and $m=-2$in fast-rotating stars along an isochrone. We further show that some of therapidly rotating stars that have photometric variability with periods longerthan a day may be caused by $r$-mode pulsation predicted to be excited in thesestars. One fast-rotating star, in particular, shows both short and long periodsthat can be explained by the simultaneous excitation of $g$- and $r$-modepulsations in models of fast-rotating stars.

Period-luminosity relations of fast-rotating B-type stars in the young open cluster NGC3766