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.

arXiv comment14 pages, 14 figures. To appear in MNRAS

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• Rotating Stars in Relativity
• 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
• On the dynamical stability of quasi-toroidal differentially rotating neutron stars
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• Merger-inspired rotation laws and the low-T/W instability in neutron stars
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• Decihertz gravitational waves from double white dwarf merger remnants
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• Determining the stiffness of the equation of state using low T/W dynamical instabilities in differentially rotating stars
• Impact of ultralight bosonic dark matter on the dynamical bar-mode instability of rotating neutron stars