Unstable normal modes of low T/W dynamical instabilities in differentially rotating stars

Abstract

We investigate the nature of low T/W dynamical instabilities in differentially rotating stars by means of linear perturbation. Here, T and W represent rotational kinetic energy and the gravitational binding energy of the star. This is the first attempt to investigate low T/W dynamical instabilities as a complete set of the eigenvalue problem. Our equilibrium configuration has "constant" specific angular momentum distribution, which potentially contains a singular solution in the perturbed enthalpy at corotation radius in linear perturbation. We find the unstable normal modes of differentially rotating stars by solving the eigenvalue problem along the equatorial plane of the star, imposing the regularity condition on the center and the vanished enthalpy at the oscillating equatorial surface. We find that the existing pulsation modes become unstable due to the existence of the corotation radius inside the star. The feature of the unstable mode eigenfrequency and its eigenfunction in the linear analysis roughly agrees with that in three-dimensional hydrodynamical simulations in Newtonian gravity. Therefore, our normal mode analysis in the equatorial motion proves valid to find the unstable equilibrium stars efficiently. Moreover, the nature of the eigenfunction that oscillates between corotation and the surface radius for unstable stars requires reinterpretation of the pulsation modes in differentially rotating stars.

arXiv comment7 pages with 4 figures, revtex4-1.cls. Accepted for publication in the Physical Review D

References in corpus (22)

• Dynamical instability of differentially rotating stars
• Dynamical Rotational Instability at Low $T/W$
• Relativistic Simulations of Eccentric Binary Neutron Star Mergers: One-arm Spiral Instability and Effects of Neutron Star Spin
• Acoustic oscillations in rapidly rotating polytropic stars I. Effects of the centrifugal distortion
• Dynamical bar-mode instability of differentially rotating stars: Effects of equations of state and velocity profiles
• Gravitational Wave Signatures from Low-mode Spiral Instabilities in Rapidly Rotating Supernova Cores
• The nature of low T/|W| dynamical instabilities in differentially rotating stars
• One-arm Spiral Instability in Hypermassive Neutron Stars Formed by Dynamical-Capture Binary Neutron Star Mergers
• One-Armed Spiral Instability in Differentially Rotating Stars
• Unexpected Dynamical Instabilities In Differentially Rotating Neutron Stars
• Formation and Coalescence of Cosmological Supermassive Black Hole Binaries in Supermassive Star Collapse
• Pulsation modes in rapidly rotating stellar models based on the Self-Consistent Field method
• Low T/|W| dynamical instability in differentially rotating stars: Diagnosis with canonical angular momentum
• Pulsations of rapidly rotating stars: I. The ACOR numerical code
• The Transient Gravitational-Wave Sky
• Super-Reflection in Fluid Discs: Corotation Amplifier, Corotation Resonance, Rossby Waves, and Overstable Modes
• Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars
• Non-axisymmetric instability and fragmentation of general relativistic quasi-toroidal stars
• Linear Stability Analysis of Differentially Rotating Polytropes -- New results for the m = 2 f-mode dynamical instability --
• Black hole formation through fragmentation of toroidal polytropes
• The intimate relation between the low T/W instability and the co-rotation point
• Faraday resonance in dynamical bar instability of differentially rotating stars

Cited by in corpus (11)

• Rotating Stars in Relativity
• On the dynamical stability of quasi-toroidal differentially rotating neutron stars
• Revisiting the maximum mass of differentially rotating neutron stars in general relativity: Übermassive stars with realistic equations of state
• Merger-inspired rotation laws and the low-T/W instability in neutron stars
• On a role of corotation radius in the low $T/W$ dynamical instability of differentially rotating stars
• Decihertz gravitational waves from double white dwarf merger remnants
• Revealing Phase Transition in Dense Matter with Gravitational Wave Spectroscopy of Binary Neutron Star Mergers
• The Kinematic Richness of Star Clusters - II. Stability of Spherical Anisotropic Models with Rotation
• Determining the stiffness of the equation of state using low T/W dynamical instabilities in differentially rotating stars
• The equilibrium of over-pressurised polytropes
• Exploring the Potential for Detecting Rotational Instabilities in Binary Neutron Star Merger Remnants with Gravitational Wave Detectors