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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.
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 attem
Dynamical instabilities in protoneutron stars may produce gravitational waves whose observation could shed light on the physics of core-collapse supernovae. When born with sufficient differential rotation, these stars are susceptible to a shear insta
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
We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three-dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the uns
Viscosity driven bar mode secular instabilities of rapidly rotating neutron stars are studied using LORENE/Nrotstar code. These instabilities set a more rigorous limit to the rotation frequency of neutron star than the Kepler frequency/mass shedding