The effect of non-adiabaticity on avoided crossings of non-radial stellar oscillations

Abstract

Avoided crossing among modes of non-radial stellar oscillation is analyzed using a perturbation technique, taking non-adiabaticity into account. To simplify the notation a Hilbert space formulation of the equations of non-adiabatic oscillation is set up; as a by-product this indicates the possibility of generalizing to non-radial oscillations the Woltjer method of stability calculation from adiabatic eigenfunctions. It is found that for sufficiently strong non-adiabaticity the avoided crossing is changed into a crossing of the real parts of the eigenfrequencies, corresponding to a decoupling of the two modes of oscillation. At smaller non-adiabaticity an otherwise stable mode may be excited by avoided crossing with an unstable mode. Some possible consequences for stellar evolution are briefly discussed.