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

TL;DR

This study explores low T/W dynamical instabilities in differentially rotating stars, analyzing their physical mechanisms and proposing a method to constrain the equation of state stiffness through gravitational wave detection.

Contribution

It combines linear perturbation analysis and 3D hydrodynamical simulations to understand the instabilities and suggests a new way to measure the equation of state stiffness via gravitational waveforms.

Findings

Unstable modes are identified through eigenvalue problems and simulations.

Sound wave scattering between corotation and surface explains the instability mechanism.

Eigenfunctions indicate a need to reinterpret pulsation modes 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.