TY - JOUR

T1 - R-mode oscillations of rapidly rotating Newtonian stars

T2 - A new numerical scheme and its application to the spin evolution of neutron stars

AU - Karino, Shigeyuki

AU - Yoshida, Shin'ichirou

AU - Yoshida, Shijun

AU - Eriguchi, Yoshiharu

PY - 2000/10/15

Y1 - 2000/10/15

N2 - We have developed a new numerical scheme to solve r-mode oscillations of rapidly rotating polytropic stars in Newtonian gravity. In this scheme, Euler perturbations of the density, three components of the velocity are treated as four unknown quantities together with the oscillation frequency. For the basic equations of oscillations, the compatibility equations are used instead of the linearized equations of motion. By using this scheme, we have solved the classical r-mode oscillations of rotational equilibrium sequences of polytropes with the polytropic indices N=0.5, 1.0, and 1.5 for m=2, 3, and 4 modes. Here m is the rank of the spherical harmonics Ylm. These results have been applied to investigate the evolution of uniformly rotating hot young neutron stars by considering the effect of gravitational radiation and viscosity. We have found that the maximum angular velocities of neutron stars are around 10-20% of the Keplerian angular velocity irrespective of the softness of matter. This confirms the results obtained from the analysis of r-modes with the slow rotation approximation employed by many authors.

AB - We have developed a new numerical scheme to solve r-mode oscillations of rapidly rotating polytropic stars in Newtonian gravity. In this scheme, Euler perturbations of the density, three components of the velocity are treated as four unknown quantities together with the oscillation frequency. For the basic equations of oscillations, the compatibility equations are used instead of the linearized equations of motion. By using this scheme, we have solved the classical r-mode oscillations of rotational equilibrium sequences of polytropes with the polytropic indices N=0.5, 1.0, and 1.5 for m=2, 3, and 4 modes. Here m is the rank of the spherical harmonics Ylm. These results have been applied to investigate the evolution of uniformly rotating hot young neutron stars by considering the effect of gravitational radiation and viscosity. We have found that the maximum angular velocities of neutron stars are around 10-20% of the Keplerian angular velocity irrespective of the softness of matter. This confirms the results obtained from the analysis of r-modes with the slow rotation approximation employed by many authors.

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U2 - 10.1103/PhysRevD.62.084012

DO - 10.1103/PhysRevD.62.084012

M3 - Article

AN - SCOPUS:16644394516

VL - 62

SP - 1

EP - 11

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 8

M1 - 084012

ER -