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

Motoyuki Saijo, Shin'Ichirou Yoshida

研究成果: Article査読

9 被引用数 (Scopus)


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 a 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.

ジャーナルPhysical Review D
出版ステータスPublished - 2016 10月 21

ASJC Scopus subject areas

  • 物理学および天文学(その他)


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