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

## TL;DR

This study models pulsations in fast-rotating B-type stars to explain observed period-luminosity relations in NGC 3766, revealing the role of g- and r-mode pulsations in their variability.

## Contribution

It demonstrates that the observed period-luminosity sequences in NGC 3766 can be explained by excited prograde g-modes and r-modes in fast-rotating B-type stars, advancing understanding of stellar pulsations.

## Key findings

- Period-luminosity relations match models of excited prograde g-modes.
- Some stars' variability is explained by r-mode pulsations.
- Stars can exhibit both g- and r-mode pulsations simultaneously.

## Abstract

We study the pulsational properties of rapidly rotating main-sequence B-type stars using linear non-adiabatic analysis of non-radial low-frequency modes taking into account the effect of rotation. We compare the properties of prograde sectoral $g$ and retrograde $r$ modes excited by the $\kappa$ mechanism at the Fe opacity peak with the newly discovered period-luminosity relation that is obeyed by a group of fast-rotating B-type stars in the young open cluster NGC 3766. The observed relation consists of two sequences in the period versus magnitude diagram, at periods shorter than 0.5 days. We find that this property is consistent with similar period-luminosity relations predicted for 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 the rapidly rotating stars that have photometric variability with periods longer than a day may be caused by $r$-mode pulsation predicted to be excited in these stars. One fast-rotating star, in particular, shows both short and long periods that can be explained by the simultaneous excitation of $g$- and $r$-mode pulsations in models of fast-rotating stars.