Determining the stiffness of the equation of state using low T/W dynamical instabilities in differentially rotating stars

Abstract

We investigate the nature of low T/W dynamical instabilities in various ranges of the stiffness of the equation of state in differentially rotating stars. Here T is the rotational kinetic energy, while W the gravitational binding energy. We analyze these instabilities in both a linear perturbation analysis and a three-dimensional hydrodynamical simulation. An unstable normal mode of a differentially rotating star is detected by solving an eigenvalue problem along the equatorial plane of the star. The physical mechanism of low T/W dynamical instabilities is also qualitatively confirmed by a scattering of sound waves between corotation and the surface caused by the corotation barrier. Therefore, we can draw a picture of existing pulsation modes unstabilized due to an amplified reflection of sound waves from the corotation barrier. The feature in the eigenfrequency and eigenfunction of the unstable mode in the linear analysis roughly agrees with that in the three-dimensional hydrodynamical simulation in Newtonian gravity. Moreover, the nature of the eigenfunction that oscillates between corotation and the surface for an unstable star requires reinterpretation of pulsation modes in differentially rotating stars. Finally, we propose a manner by which to constrain the stiffness of the equation of state by the direct detection of mode decomposed gravitational waveforms.

21 pages with 16 figures, revtex4-1.cls. Accepted for publication in the Physical Review D

References in corpus (11)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• 3D Collapse of Rotating Stellar Iron Cores in General Relativity including Deleptonization and a Nuclear Equation of State
• Unexpected Dynamical Instabilities In Differentially Rotating Neutron Stars
• The $m=1$ instability \& gravitational wave signal in binary neutron star mergers
• 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
• On a role of corotation radius in the low $T/W$ dynamical instability of differentially rotating stars
• Faraday resonance in dynamical bar instability of differentially rotating stars
• Unstable normal modes of low T/W dynamical instabilities in differentially rotating stars
• Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

Cited by in corpus (5)

• Characteristic Time Variability of Gravitational-Wave and Neutrino Signals from Three-dimensional Simulations of Non-Rotating and Rapidly Rotating Stellar Core-Collapse
• A New Gravitational Wave Signature of Low-$T/|W|$ Instability in Rapidly Rotating Stellar Core Collapse
• 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
• Revealing Phase Transition in Dense Matter with Gravitational Wave Spectroscopy of Binary Neutron Star Mergers