Gravitational-Wave Driven Instability of Rotating Relativistic Stars

Friedman, John L.; Lockitch, Keith H.

doi:10.1143/ptps.136.121

Cited by 30 publications

(41 citation statements)

References 40 publications

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“…(17), (19), (31) and (32), which are adequate approximation to this order. This equation is of course reduced to the leading order equation (23), when the second-order rotational effects and the coupling to the polar modes are neglected.…”

Section: Including Second-order Correctionsmentioning

confidence: 87%

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Approximate equation relevant to axial oscillations on slowly rotating relativistic stars

Kojima

Hosonuma

2000

Phys. Rev. D

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Axial oscillations relevant to the r-mode instability are studied with slow rotation formalism in general relativity. The approximate equation governing the oscillations is derived with second-order rotational corrections. The equation contains an effective 'viscosity-like' term, which originates from coupling to the polar g-mode displacements. The term plays a crucial role on the resonance point, where the disturbance on the rotating stars satisfies a certain condition at the lowest order equation. The effect is significant for newly born hot neutron stars, which are expected to be subject to the gravitational radiation driven instability of the r-mode.

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Section: Including Second-order Correctionsmentioning

confidence: 87%

“…The first term in D 0 contains fourth derivative of Φ L with respect to r, since U L can be expressed by the second derivative of Φ L as shown in Eq. (19). The highest derivative term of Φ L with respect to r is therefore given by…”

Section: Including Second-order Correctionsmentioning

confidence: 99%

Approximate equation relevant to axial oscillations on slowly rotating relativistic stars

Kojima

Hosonuma

2000

Phys. Rev. D

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“…One possibility is the radiation of gravitational waves from the rapidly rotating pulsars. In particular, neutron stars may suffer a number of instabilities which come in different flavors but they have a general feature in common; they can be directly associated with unstable modes of oscillation [46,4,18,19,58,49,6,5,34,7,10,8,65,11,29,2,50,22,36,53,25,35]. The r-modes are oscillations of rotating stars whose restoring force is the Coriolis force.…”

Section: Introductionmentioning

confidence: 99%

R-mode constraints from neutron star equation of state

Papazoglou

Moustakidis

2016

Astrophys Space Sci

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The gravitational radiation has been proposed a long time before, as an explanation for the observed relatively low spin frequencies of young neutron stars and of accreting neutron stars in low-mass X-ray binaries as well. In the present work we studied the effects of the neutron star equation of state on the r-mode instability window of rotating neutron stars. Firstly, we employed a set of analytical solution of the Tolman-Oppemheimer-Volkoff equations with special emphasis on the Tolman VII solution. In particular, we tried to clarify the effects of the bulk neutron star properties (mass, radius, density distribution, crust size and elasticity) on the r-mode instability window. We found that the critical angular velocity Ω c depends mainly on the neutron star radius. The effects of the gravitational mass and the mass distribution are almost negligible. Secondly, we studied the effect of the elasticity of the crust, via to the slippage factor S and also the effect of the nuclear equation of state, via the slope parameter L, on the instability window. We found that the crust effects are more pronounced, compared to those originated from the equation of state. Moreover, we proposed simple analytical expressions which relate the macroscopic quantity Ω c to the radius, the parameter L and the factor S. We also investigated the possibility to measure the radius of a neutron star and the factor S with the help of accurate measures of Ω c and the neutron star temperature. Finally, we studied the effects of the mutual friction on the instability window and discussed the results in comparison with previous similar studies.

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“…[3,4]; for r-mode oscillations see [5,6,7]). At the early stage of those investigations, the r-mode oscillations were found to become significantly unstable for some range of the core temperature [8,9,10].…”

Section: Introductionmentioning

confidence: 99%

R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars

2001

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For the analysis of the r-mode oscillation of hot young neutron stars, it is necessary to consider the effect of differential rotation, because viscosity is not strong enough for differentially rotating young neutron stars to be lead to uniformly rotating configurations on a very short time scale after their birth. In this paper, we have developed a numerical scheme to solve r-mode oscillations of differentially rotating polytropic inviscid stars. This is the extended version of the method which was applied to compute r-mode oscillations of uniformly rotating Newtonian polytropic stars. By using this new method, we have succeeded in obtaining eigenvalues and eigenfunctions of r-mode oscillations of differentially rotating polytropic stars.Our numerical results show that as the degree of differential rotation is increased, it becomes more difficult to solve r-mode oscillations for slightly deformed configurations from sphere compared to solving r-mode oscillations of considerably deformed stars. One reason for it seems that for slightly deformed stars corotation points appear near the surface region if the degree of differential rotation is strong enough. This is similar to the situation that the perturbational approach of r-mode oscillations for slowly rotating stars in general relativity results in a singular eigenvalue problem.

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Gravitational-Wave Driven Instability of Rotating Relativistic Stars

Cited by 30 publications

References 40 publications

Approximate equation relevant to axial oscillations on slowly rotating relativistic stars

Approximate equation relevant to axial oscillations on slowly rotating relativistic stars

R-mode constraints from neutron star equation of state

R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars

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