TY - JOUR

T1 - Relativistic R-modes in slowly rotating neutron stars

T2 - Numerical analysis in the cowling approximation

AU - Yoshida, Shijun

AU - Lee, Umin

PY - 2002/3/10

Y1 - 2002/3/10

N2 - We investigate the properties of relativistic r-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis-like force on the stellar oscillations but ignore the effects of the centrifugal-like force. For three neutron star models, we calculate the fundamental r-modes with l′ = m = 2 and 3. We find that the oscillation frequency σ̄ of the fundamental r-mode is given in a good approximation by σ̄ K 0Ω, where σ̄ is defined in the corotating frame at spatial infinity and Ω is the angular frequency of rotation of the star. The proportional coefficient K0 is only weakly dependent on Ω, but it strongly depends on the relativistic parameter GM/c2R, where M and R are the mass and the radius of the star. All the fundamental r-modes with l′ = m computed in this study are discrete modes with distinct regular eigen-functions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation. These relativistic r-modes are obtained by including the effects of rotation higher than the first order of Ω so that the buoyant force plays a role, the situation of which is quite similar to that for Newtonian r-modes.

AB - We investigate the properties of relativistic r-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis-like force on the stellar oscillations but ignore the effects of the centrifugal-like force. For three neutron star models, we calculate the fundamental r-modes with l′ = m = 2 and 3. We find that the oscillation frequency σ̄ of the fundamental r-mode is given in a good approximation by σ̄ K 0Ω, where σ̄ is defined in the corotating frame at spatial infinity and Ω is the angular frequency of rotation of the star. The proportional coefficient K0 is only weakly dependent on Ω, but it strongly depends on the relativistic parameter GM/c2R, where M and R are the mass and the radius of the star. All the fundamental r-modes with l′ = m computed in this study are discrete modes with distinct regular eigen-functions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation. These relativistic r-modes are obtained by including the effects of rotation higher than the first order of Ω so that the buoyant force plays a role, the situation of which is quite similar to that for Newtonian r-modes.

KW - Instabilities

KW - Stars: neutron

KW - Stars: oscillations

KW - Stars: rotation

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U2 - 10.1086/338663

DO - 10.1086/338663

M3 - Article

AN - SCOPUS:0011650537

SN - 0004-637X

VL - 567

SP - 1112

EP - 1120

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 2 I

ER -