Nonlinear evolution of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>r</mml:mi></mml:math>-modes: The role of differential rotation

Sá, Paulo M.; Tomé, Brigitte

doi:10.1103/physrevd.71.044007

Cited by 34 publications

(66 citation statements)

References 23 publications

(81 reference statements)

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“…arbitrary stationary differential rotation, stratified on the cylinders). However, an important point of these papers, namely that "differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r-modes in the nonlinear theory" (see abstract in Sá & Tomé 2005) is not true: we present a parameter set for analytical second order solution obtained by Sá (2004); Sá & Tomé (2005) with vanishing secular drift (below we refer to it as to "non-drifting solution"). 1 We argue that existence of second order solution with vanishing drift is not coincidental feature, specific for r-modes only, but rather is a general property of oscillation modes.…”

Section: Most Of the Papers Discussing R-modes In Nss Eithermentioning

confidence: 99%

“…In Sec. 2 we discuss nonmagnetized (B = 0) NSs, following the approach suggested by Sá (2004); Sá & Tomé (2005). As they have shown, the second order r-mode solution is not unique, but determined up to any differential rotation, which can exist in nonoscillating star (i.e.…”

Section: Most Of the Papers Discussing R-modes In Nss Eithermentioning

confidence: 99%

“…3 we reconsider the effect of magnetic field on r-modes in second order in amplitude by accurate treatment of magnetic stresses within ideal magnetohydrodynamics (MHD). Rezzolla et al (2000Rezzolla et al ( , 2001a ar-1 Sá (2004) and Sá & Tomé (2005) base their conclusion on the oscillation averaged second order perturbations of Eulerian velocity. Indeed, these perturbations are nonvanishing for all possible second order solutions.…”

Section: Most Of the Papers Discussing R-modes In Nss Eithermentioning

confidence: 99%

“…5 We use normalization of the mode amplitude from Owen et al (1998), which is usually applied for r-mode instability analysis. Sá (2004); Sá & Tomé (2005) apply slightly different normalization, namely their amplitude…”

Section: R-modes In Nonmagnetized Nsmentioning

confidence: 99%

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Differential rotation and r-modes in magnetized neutron stars

Chugunov

2015

Monthly Notices of the Royal Astronomical Society

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] draw attention to the second order secular drift associated with r-modes and claimed that it should lead to magnetic field enhancement and suppression of r-mode instability in magnetized neutron stars. We critically revise these results. We present a particular second order r-mode solution with vanishing secular drift, thus refuting a widely believed statement that secular drift is an unavoidable feature of r-modes. This non-drifting solution is not affected by magnetic field B, if B ≪ B crit ≈ 10 17 (ν/600 Hz) G (ν is a spin frequency) and does not lead to secular evolution of magnetic field. For general second order r-mode solution the drift does not necessarily vanish, but the solution can be presented as a superposition of two solutions: one describes evolution of differential rotation in nonoscillating star (which describes secular drift; for nonmagnetized star it is arbitrary stationary rotation stratified on cylinders; for magnetized star differential rotation evolves on the Alfvén timescale and may lead to magnetic energy enhancement), and another one is non-drifting r-mode solution mentioned above. This representation allows us to conclude that enhancement of magnetic field energy is limited by initial energy of differential rotation, which is much less (for a factor ∝ α 2 , where α is mode amplitude) than the total energy of r-mode. Hence, magnetic field enhancement by drift cannot suppress r-mode instability. Results can be generalized for any oscillation mode in any medium, if this mode has non-drifting solution for B = 0.

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Section: Most Of the Papers Discussing R-modes In Nss Eithermentioning

confidence: 99%

Section: Most Of the Papers Discussing R-modes In Nss Eithermentioning

confidence: 99%

Section: Most Of the Papers Discussing R-modes In Nss Eithermentioning

confidence: 99%

Section: R-modes In Nonmagnetized Nsmentioning

confidence: 99%

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Differential rotation and r-modes in magnetized neutron stars

Chugunov

2015

Monthly Notices of the Royal Astronomical Society

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“…[27], this differential rotation plays a relevant role in the nonlinear evolution of the r-mode instability. Indeed, in a newly born, hot, non-magnetized, rapidly rotating neutron star, r-modes saturates a few hundred seconds after the mode instability sets in; the saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity [27]. Now, the question that remains unsolved is whether GR reaction also induces differential rotation, making an extra contribution.…”

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confidence: 99%

r-mode instability: Analytical solution with gravitational radiation reaction

Dias

Sá

2005

Phys. Rev. D

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Analytical r-mode solutions are investigated within the linearized theory in the case of a slowly rotating, Newtonian, barotropic, non-magnetized, perfect-fluid star in which the gravitational radiation (GR) reaction force is present. For the GR reaction term we use the 3.5 post-Newtonian order expansion of the GR force, in order to include the contribution of the current quadrupole moment. We find the explicit expression for the r-mode velocity perturbations and we conclude that they are sinusoidal with the same frequency as the well-known GR force-free linear r-mode solution, and that the GR force drives the r-modes unstable with a growth timescale that agrees with the expression first found by Lindblom, Owen and Morsink. We also show that the amplitude of these velocity perturbations is corrected, relatively to the GR force-free case, by a term of order Ω 6 , where Ω is the angular velocity of the star.

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Gravitational Wave Astronomy

Kokkotas

2008

Reviews in Modern Astronomy

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As several large scale interferometers are beginning to take data at sensitivities where astrophysical sources are predicted, the direct detection of gravitational waves may well be imminent. This would open the gravitational-wave window to our Universe, and should lead to a much improved understanding of the most violent processes imaginable; the formation of black holes and neutron stars following core collapse supernovae and the merger of compact objects at the end of binary inspiral.Comment: 22 pages, 2 figure

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Nonlinear evolution ofr-modes: The role of differential rotation

Cited by 34 publications

References 23 publications

Differential rotation and r-modes in magnetized neutron stars

Differential rotation and r-modes in magnetized neutron stars

r-mode instability: Analytical solution with gravitational radiation reaction

Gravitational Wave Astronomy

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