Kelvin-Helmholtz instabilities and their application to B-type variables

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Abstract
A Kelvin–Holmholtz instability, formed from the differential rotation in the narrow region between the core and envelope, is proposed as a promising mechanism responsible for the excitation of pulsations in B-type variables (53 Per variables and β Cep stars), in which the unstable inertia wave resulting from this instability resonates with an eigenmode of the non-radial oscillation of the whole star. The degeneracy of the two frequencies is found to be expected at any evolutionary stage of a star. The equations for a Kelvin–Helmholtz instability have been formulated for the stellar case, and in the cylindrical configuration limit, the necessary condition for instability and characteristics of the instability have been discussed. It is shown that prograde modes with large |m| for a given l are excited in almost all cases; which seems to agree with observations. The back reaction of the excited modes on the differential rotation is discussed in these stars, and it is pointed out that the differential rotation can be significantly affected by this effect in a short time.

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