Stability of g-modes in rotating B-type stars

Abstract

We have studied the stability of low degree $g$-modes in uniformly rotating B-type stars, taking into account the effects of the Coriolis force and the rotational deformation. From an analysis treating rotation frequency as a small parameter it is found that slow rotation tends to $destabilize$ high radial-order $retrograde$ $g$-modes, although the effect is very small or absent for relatively low order modes. Calculating eigenfrequencies at selected rotation rates, we find, on the other hand, that rapid rotation tends to $stabilize$ $retrograde$ $g$-modes. The stabilizing effect appears stronger for less massive B-type stars having low effective temperatures. If we change rotation rate continuously, the frequency of a $g$-mode belonging to ($l', m$) crosses frequencies of other $g$-modes belonging to ($l', m$). If the parity of the two encountering modes are the same, they interact each other and the stability (i.e., imaginary part of eigenfrequency) of each mode is modified. Using an asymptotic method we discuss the property of such mode crossings and couplings. For rapidly rotating stars mode couplings are important for the stability of low degree $g$-modes. In particular, we find that the stabilization of retrograde $g$-modes in rapidly rotating stars is due to many strong mode couplings, while %prograde sectoral% modes are exceptionally immune to the damping effects from the mode couplings.