Gravitational Radiation Reaction Driven Secular Instability of f-Mode Oscillations in Differentially Rotating Newtonian Stars

摘要

We have carried out the linear stability analysis of equilibrium sequences of differentially rotating Newtonian polytropic stars. In particular, we have found critical points along the equilibrium sequences for the gravitational radiation reaction driven secular instability of f-mode oscillations with azimuthal wavenumbers m = 2, 3, and 4. We show that the critical values of T/|W| where the instability sets in strongly depend on the degree of differential rotation of the models. Here, T and W are the rotational kinetic energy and the gravitational energy of the star, respectively. We also find that as the degree of differential rotation is increased, the dependence of the critical value of T/|W| on the equations of state becomes weaker.