AMR simulations of the low T/|W|T/|W| bar-mode instability of neutron stars

It has been recently argued through numerical work that rotating stars with a high degree of differential rotation are dynamically unstable against bar-mode deformation, even for values of the ratio of rotational kinetic energy to gravitational potential energy as low as O(0.01)O(0.01). This may have implications for gravitational wave astronomy in high-frequency sources such as core collapse supernovae. In this paper we present high-resolution simulations, performed with an adaptive mesh refinement hydrodynamics code, of such low T/|W|T/|W| bar-mode instability. The complex morphological features involved in the nonlinear dynamics of the instability are revealed in our simulations, which show that the excitation of Kelvin–Helmholtz-like fluid modes outside the corotation radius of the star leads to the saturation of the bar-mode deformation. While the overall trends reported in an earlier investigation are confirmed by our work, we also find that numerical resolution plays an important role during the long-term, nonlinear behavior of the instability, which has implications on the dynamics of rotating stars and on the attainable amplitudes of the associated gravitational wave signals.