R modes of slowly pulsating B stars

Abstract

We examine pulsational stability of low $m$ $r$ modes in SPB stars by calculating fully nonadiabatic oscillations of uniformly rotating stars, where $m$ is an integer representing the azimuthal wave number around the rotation axis. $R$ modes are rotationally induced, non-axisymmetric, oscillation modes, whose oscillation frequency strongly depends on the rotation frequency $\Omega$ of the star. They are conveniently classified by using two integer indices $m$ and $l^\prime\ge |m|$ that define the asymptotic oscillation frequency $2m\Omega/[l^\prime(l^\prime+1)]$ in the limit of $\Omega\to 0$. We find low $m$, high radial order, odd $r$ modes with $l^\prime=m$ in SPB stars are excited by the same iron opacity bump mechanism that excites low frequency $g$ modes of the variables, when the rotation frequency $\Omega$ is sufficiently high. No even $r$ modes with low $m$ are found to be pulsationally unstable. Since the surface pattern of the temperature perturbation of odd modes is antisymmetric about the equator of the star, observed photometric amplitudes caused by the unstable odd $r$ modes with $l^\prime=m$ are strongly dependent on the inclination angle between the axis of rotation and the line of sight. Applying the wave-meanflow interaction formalism to nonadiabatic $r$ modes in rapidly rotating SPB models, we find that because of the $r\phi$ component of the Reynolds stress and the radial transport of the eddy fluctuation of density in the rotating star, the surface rotation is accelerated by the forcing due to the low $l^\prime=m$ unstable $r$ modes.Comment: submitted to m