Self-Consistent Simulations of the Bar-mode Instability in Rotating Quasi-Stable Neutron Stars

Rotating neutron stars (NSs) in low-mass X-ray binaries and newly formed proto-NSs serve as ideal laboratories for investigating the dynamical stability and internal physics of dense matter under extreme conditions. In this study we use GRoovy, a new, dynamical-spacetime general relativistic hydrodynamics code, to self-consistently model the dynamical bar-mode instability. Using singular curvilinear coordinates, in which fluid flows largely follow coordinate lines, GRoovy minimizes angular momentum loss due to numerical diffusion, enabling accurate, long-term simulations of quasi-stable NS configurations with realistic finite-temperature equations of state (EoSs) and neutrino radiation via a leakage scheme. We systematically analyze the growth rates and lifetimes of bar-mode instabilities across various EoSs, revealing how heating and neutrino cooling influence the evolution and stability of the system. Additionally, we extract gravitational wave signatures from our simulations, and demonstrate that these kHz-frequency signals possess the potential to place stringent constraints on the NS EoS. Our results not only enhance the fidelity of NS dynamical models but also provide critical insights for future gravitational wave observations aimed at probing the fundamental properties of dense nuclear matter.