Low T/∣W∣ dynamical instabilities in differentially rotating stars: Diagnosis with canonical angular momentum

Abstract

We study the nature of non‐axisymmetric dynamical instabilities in differentially rotating stars with both linear eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We especially investigate the following three types of instability; the one‐armed spiral instability, the low T/|W| bar instability, and the high T/|W| bar instability, where T is the rotational kinetic energy and W is the gravitational potential energy. The nature of the dynamical instabilities is clarified by using a canonical angular momentum as a diagnostic. We find that the one‐armed spiral and the low T/|W| bar instabilities occur around the corotation radius, and they grow through the inflow of canonical angular momentum around the corotation radius. The result is a clear contrast to that of a classical dynamical bar instability in high T/|W|. We also discuss the feature of gravitational waves generated from these three types of instability.