Evolution Equations for Slowly Rotating Stars

Stavridis, Adamantios; Kokkotas, Kostas D.

doi:10.1142/s021827180500592x

Cited by 16 publications

(12 citation statements)

References 26 publications

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“…The explicit form of the linear angular operators L ±j i are given in Appendix B. As in the case of uniformly rotating stars [24,25], Eqs. (4)(5)(6)(7)(8) form an infinitely coupled system of equations.…”

Section: The Perturbative Frameworkmentioning

confidence: 99%

Nonaxisymmetric oscillations of differentially rotating relativistic stars

2008

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Non-axisymmetric oscillations of differentially rotating stars are studied using both slow rotation and Cowling approximation. The equilibrium stellar models are relativistic polytropes where differential rotation is described by the relativistic j-constant rotation law. The oscillation spectrum is studied versus three main parameters: the stellar compactness M/R, the degree of differential rotation A and the number of maximun couplings ℓmax. It is shown that the rotational splitting of the non-axisymmetric modes is strongly enhached by increasing the compactness of the star and the degree of differential rotation. Finally, we investigate the relation between the fundamental quadrupole mode and the corotation band of differentially rotating stars.

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Section: The Perturbative Frameworkmentioning

confidence: 99%

Nonaxisymmetric oscillations of differentially rotating relativistic stars

2008

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“…(21) are integrated numerically (from the center outward), for a given central pressure p c (see Table II), using a standard fourth-order Runge-Kutta integration scheme with adaptive step size.…”

Section: Appendix B: Numerical Details Code Tests and Mode Frequenciesmentioning

confidence: 99%

“…Although most of the work in perturbation theory has been done (and is still done) using a frequency-domain approach (in order to accurately compute mode frequencies), time-domain simulations are also needed to compute full waveforms [11][12][13][14][15][16][17][18][19][20][21][22][23]. In particular, Allen et al [12], via a multipolar expansion, derived the equations for the evenparity perturbations of spherically symmetric relativistic stars and produced explicit waveforms.…”

Section: Introductionmentioning

confidence: 99%

Gravitational waves from pulsations of neutron stars described by realistic equations of state

Bernuzzi

Nagar

2008

Phys. Rev. D

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In this work we discuss the time evolution of nonspherical perturbations of a nonrotating neutron star described by a realistic equation of state (EOS). We analyze 10 different EOS for a large sample of neutron star models. Various kinds of generic initial data are evolved and the gravitational signals are computed. We focus on the dynamical excitation of fluid and spacetime modes and extract the corresponding frequencies. We employ a constrained numerical algorithm based on standard finitedifferencing schemes which permits stable and long-term evolutions. Our code provides accurate waveforms and allows one to capture, via Fourier analysis, the frequencies of the fluid modes with an accuracy comparable to that of frequency-domain calculations. The results we present here are useful for providing comparisons with simulations of nonlinear oscillations of (rotating) neutron star models as well as test beds for 3D nonlinear codes.

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“…we use the so called Cowling approximation since we want to focus on the behavior of the stellar fluid. The slow rotation approximation has been extensively used in the study of stellar perturbations both in Newtonian and in general relativistic approach [34,35,36,37]. Here we study the spectrum of axisymmetric perturbations in order to test the accuracy of our approximation technique against published results by nonlinear numerical codes [32,33].…”

Section: Introductionmentioning

confidence: 99%

Nonradial oscillations of slowly and differentially rotating compact stars

2007

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The equations describing nonradial adiabatic oscillations of differentially rotating relativistic stars are derived in relativistic slow rotation approximation. The differentially rotating configuration is described by a perturbative version of the relativistic j-constant rotation law. Focusing on the oscillation properties of the stellar fluid, the adiabatic nonradial perturbations are studied in the Cowling approximation with a system of five partial differential equations. In these equations, differential rotation introduces new coupling terms between the perturbative quantites with respect to the uniformly rotating stars. In particular, we investigate the axisymmetric and barotropic oscillations and compare their spectral properties with those obtained in nonlinear hydrodynamical studies. The perturbative description of the differentially rotating background and the oscillation spectrum agree within a few percent with those of the nonlinear studies.PACS numbers: 04.40. Dg, 95.30.Sf, 97.10.Sj

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Evolution Equations for Slowly Rotating Stars

Cited by 16 publications

References 26 publications

Nonaxisymmetric oscillations of differentially rotating relativistic stars

Nonaxisymmetric oscillations of differentially rotating relativistic stars

Gravitational waves from pulsations of neutron stars described by realistic equations of state

Nonradial oscillations of slowly and differentially rotating compact stars

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