Linear radial perturbations of supermassive stars

Numerical integration of the linear non-adiabatic equations for radial perturbations of physical models of supermassive stars confirm the existence of both dynamical and secular instabilities above a critical mass. The value of the latter agrees very well with that deduced from approximate stability criteria. The present analysis brings out for the first time the existence of a continuous transition between dynamical and secular modes in a sequence of models of different masses.