R-mode oscillations of rapidly rotating Newtonian stars - A new numerical scheme and its application to the spin evolution of neutron stars

Abstract

We have developed a new numerical scheme to solve r-mode oscillations of {\it 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 $Y_l^m$. These results have been applied to investigate 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.

LaTeX 12 pages with 19 figures, to be published in PRD

References in corpus (2)

• Viscous Boundary Layer Damping of R-Modes in Neutron Stars
• Inertial modes of slowly rotating isentropic stars

Cited by in corpus (9)

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• Explaining observations of rapidly rotating neutron stars in LMXBs
• R-modes of neutron stars with a solid crust
• R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars
• Time evolution of the linear perturbations of a rotating Newtonian polytrope
• Linear Stability Analysis of Differentially Rotating Polytropes -- New results for the m = 2 f-mode dynamical instability --
• Nonlinear Couplings Between r-modes of Rotating Neutron Stars
• Spin evolution of neutron stars in wind-fed high mass X-ray binaries
• Importance of Perturbed Gravitational Potentials in Differentially Rotating Newtonian Stars