Non-radial oscillations of rotating stars and their relevance to the short-period oscillations of cataclysmic variables

Abstract

We consider the usual hypothesis that the short-period coherent oscillations seen in cataclysmic variables are attributable to g modes in a slowly rotating white dwarf. We show that this hypothesis in untenable for three main reasons: (i) the observed periods are too short for reasonable white dwarf models, (ii) the observed variability of the oscillations is too rapid and (iii) the expected rotation of the white dwarf, due to accretion, invalidates the slow rotation assumption on which standard g-mode theory is based. We investigate the low-frequency spectrum of a rotating pulsating star, taking the effects of rotation fully into account. In this case there are two sets of low-frequency modes, the g modes, and modes similar to Rossby waves in the Earth's atmosphere and oceans, which we designate r modes. Typical periods for such modes are 1/m times the rotation period of the white dwarfs outer layers (m is the azimuthal wavenumber). We conclude that non-radial oscillations of rotating white dwarfs can account for the properties of the oscillations seen in dwarf novae. Application of these results to other systems is also discussed.