On the r-mode spectrum of relativistic stars in the low-frequency approximation

Ruoff, Johannes; Kokkotas, Kostas D.

doi:10.1046/j.1365-8711.2001.04909.x

Cited by 39 publications

(89 citation statements)

References 23 publications

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“…1 We should note that several studies about the general relativistic r-mode have been done (e.g., Kojima 1998;Kojima & Hosonuma 2000;Lockitch et al 2001;Ruoff & Kokkotas 2001).…”

Section: Formulationmentioning

confidence: 99%

Nonradial oscillations of neutron stars with a solid crust

Yoshida¹,

Lee²

2002

A&A

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Abstract. Nonradial oscillations of relativistic neutron stars with a solid crust are computed in the relativistic Cowling approximation, in which all metric perturbations are ignored. For the modal analysis, we employ three-component relativistic neutron star models with a solid crust, a fluid core, and a fluid ocean. As a measure for the relativistic effects on the oscillation modes, we calculate the relative frequency difference defined as δσ/σ ≡ (σ GR − σ N )/σ GR , where σ GR and σ R are, respectively, the relativistic and the Newtonian oscillation frequencies. The relative difference δσ/σ takes various values for different oscillation modes of the neutron star model, and the value of δσ/σ for a given mode depends on the physical properties of the models. We find that |δσ/σ| is less than ∼0.1 for most of the oscillation modes we calculate, although there are a few exceptions such as the fundamental (nodeless) toroidal torsional modes in the crust, the surface gravity modes confined in the surface ocean, and the core gravity modes trapped in the fluid core. We also find that the modal properties, represented by the eigenfunctions, are not strongly affected by introducing general relativity. It is however shown that the mode characters of the two interfacial modes, associated with the core/crust and crust/ocean interfaces, have been interchanged between the two through an avoided crossing when we move from Newtonian dynamics to general relativistic dynamics.

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“…1 We should note that several studies about the general relativistic r-mode have been done (e.g., Kojima 1998;Kojima & Hosonuma 2000;Lockitch et al 2001;Ruoff & Kokkotas 2001).…”

Section: Formulationmentioning

confidence: 99%

Nonradial oscillations of neutron stars with a solid crust

Yoshida¹,

Lee²

2002

A&A

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“…Firstly, the continuous spectrum was found to possess a position-dependent frequency component; such behaviour has been observed in numerical time evolutions of the relativistic problem [14]. Secondly, there were fixed frequency contributions from the endpoint frequencies of the continuous spectrum.…”

Section: Singular Eigenfunctionsmentioning

confidence: 63%

“…Given this result we would seem to have two options: One option is to conclude that we must have a singular metric/velocity perturbation, and since this would be unphysical we must rule out the associated solution. If we take the implications of this to the extreme, it could imply that no relativistic r-modes can exist for certain stellar parameters [14,16]. However, this conclusion is likely too extreme.…”

Section: Singular Eigenfunctionsmentioning

confidence: 98%

Regularizing the r-mode problem for nonbarotropic relativistic stars

Lockitch

Andersson

Watts

2004

Class. Quantum Grav.

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We present results for r-modes of relativistic nonbarotropic stars. We show that the main differential equation, which is formally singular at lowest order in the slow-rotation expansion, can be regularized if one considers the initial value problem rather than the normal mode problem. However, a more physically motivated way to regularize the problem is to include higher order terms. This allows us to develop a practical approach for solving the problem and we provide results that support earlier conclusions obtained for uniform density stars. In particular, we show that there will exist a single r-mode for each permissible combination of l and m. We discuss these results and provide some caveats regarding their usefulness for estimates of gravitational-radiation reaction timescales. The close connection between the seemingly singular relativistic r-mode problem and issues arising because of the presence of corotation points in differentially rotating stars is also clarified.

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“…We insist on the fact that this viscous term does not come from relativistic calculations and just aims at regularizing the solution. In figures (23), (24), (25), (26) and (27) are plotted exactly the same quantities as in the Section V. The conclusions for this preliminary relativistic calculation are the same as in the Newtonian case: a polar counter part of the velocity appears from the beginning of the evolution and most of the time, the velocity is concentrate near the equator and the surface. (24) and (25).…”

Section: Strong Cowling Approximation In Grmentioning

confidence: 76%

Inertial modes in slowly rotating stars: An evolutionary description

Villain

Bonazzola

2002

Phys. Rev. D

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We present a new hydro code based on spectral methods using spherical coordinates. The first version of this code aims at studying time evolution of inertial modes in slowly rotating neutron stars. In this article, we introduce the anelastic approximation, developed in atmospheric physics, using the mass conservation equation to discard acoustic waves. We describe our algorithms and some tests of the linear version of the code, and also some preliminary linear results. We show, in the Newtonian framework with differentially rotating background, as in the relativistic case with the strong Cowling approximation, that the main part of the velocity quickly concentrates near the equator of the star. Thus, our time evolution approach gives results analogous to those obtained by Karino et al. [1] within a calculation of eigenvectors. Furthermore, in agreement with the work of Lockitch et al.[2], we found that the velocity seems to always get a non-vanishing polar part.

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On the r-mode spectrum of relativistic stars in the low-frequency approximation

Cited by 39 publications

References 23 publications

Nonradial oscillations of neutron stars with a solid crust

Nonradial oscillations of neutron stars with a solid crust

Regularizing the r-mode problem for nonbarotropic relativistic stars

Inertial modes in slowly rotating stars: An evolutionary description

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