7 - The oscillations of rapidly rotating stars

Summary

We review the effects of rotation on the oscillation spectrum of rapidly rotating stars. We particularly stress the novelties introduced by rotation: for instance, the disappearance of modes in the low frequency band due to the ill-posed natured of the underlying mathematical problem. This is mainly an effect of the Coriolis acceleration. The centrifugal effect changes the shape of the star in the first place. The possible consequences of this deformation on the oscillation spectrum are briefly analyzed. We also describe other possibly important effects of the centrifugal acceleration which come about on the time scale of star evolution.

A short introduction to rapidly rotating stars

All stars are affected by rotation but some of them, the rapid rotators, are more affected than the others! Astronomers usually qualify as rapid rotators all the stars with v sin i ≥ 50 kms⁻¹, i.e. those with an equatorial velocity larger than 50kms⁻¹. Such a value should be compared to the Keplerian limiting velocity which is

V_kep ∼ 440kms⁻¹ (M/M⊙)^0.1

for stars on the main sequence (we used the mass-radius relation given by Hansen and Kawaler 1994). Thus, for these stars the limiting velocity is weakly mass-dependent and rapid rotators appear as stars whose centrifugal acceleration exceeds 10% of the surface gravity; since this ratio measures the impact of rotation on the star structure, rapid rotators are those stars whose shape is significantly distorted by rotation.