On a role of corotation radius in the low $T/W$ dynamical instability of differentially rotating stars

Abstract

We investigate the nature of so-called low $T/W$ dynamical instability in a differentially rotating star by focusing on the role played by the corotation radius of the unstable oscillation modes. An one dimensional model of linear perturbation, which neglects dependence of variables on the coordinate along the rotational axis of the star, is solved to obtain stable and unstable eigenmodes. A linear eigenmode having a corotation radius, at which azimuthal pattern speed of the mode coincides with the stellar angular velocity, is categorized to either a complex (growing or damping) mode or a purely real mode belonging to a continuous spectrum of frequency. We compute canonical angular momentum and its flux to study eigenmodes with corotation radius. In a dynamically unstable mode, sound wave transports its angular momentum in such a way that the absolute value of the angular momentum is increased on both sides of the corotation radius. We further evaluate growth of amplitude of reflected sound wave incident to a corotation point and find that the over-reflection of the wave and the trapping of it between the corotation radius and the surface of the star may qualitatively explain dependences of eigenfrequencies on the stellar differential rotation. The results suggest that the low $T/W$ instability may be caused by over-reflection of sound waves trapped mainly between the surface of the star and a corotation radius.

14 pages, 14 figures. To appear in MNRAS

References in corpus (5)

• Accurate simulations of the dynamical bar-mode instability in full General Relativity
• Unexpected Dynamical Instabilities In Differentially Rotating Neutron Stars
• Super-Reflection in Fluid Discs: Corotation Amplifier, Corotation Resonance, Rossby Waves, and Overstable Modes
• The intimate relation between the low T/W instability and the co-rotation point
• Unstable normal modes of low T/W dynamical instabilities in differentially rotating stars

Cited by in corpus (7)

• Insights into non-axisymmetric instabilities in three-dimensional rotating supernova models with neutrino and gravitational-wave signatures
• Mapping the stability of stellar rotating spheres via linear response theory
• Revisiting the maximum mass of differentially rotating neutron stars in general relativity: Übermassive stars with realistic equations of state
• Effect of stellar rotation on the development of post-shock instabilities during core-collapse supernovae
• Impact of rotation on the evolution of convective vortices in collapsing stars
• The Kinematic Richness of Star Clusters - II. Stability of Spherical Anisotropic Models with Rotation
• Impact of ultralight bosonic dark matter on the dynamical bar-mode instability of rotating neutron stars