Differential rotation of nonlinear<i>r</i>-modes

Sá, Paulo M.

doi:10.1103/physrevd.69.084001

Cited by 37 publications

(91 citation statements)

References 24 publications

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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%

“…secular increase of the Lagrangian displacement, is not determined by the second order Eulerian velocity only, but has correction associated with Stokes drift induced by the first order motion of the fluid elements (see Longuet-Higgins 1953;Rezzolla et al 2001a or Eqs. (28) and (12) in Sá 2004 andSá &Tomé 2005, respectively). This correction allows to have second order solution with vanishing secular drift, but nonvanishing oscillation averaged Eulerian velocity (see Sec.…”

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%

“…Second order (in oscillation amplitude) r-mode solution was obtained by Sá (2004). This solution is applicable if oscillation amplitude α ≫ (Ω/ΩK) 2 (here ΩK ≈ GM/R 3 is the mass shedding frequency).…”

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: 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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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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Gravitational waves from r-modes

Sá

Tomé

2007

Isolated Neutron Stars: From the Surface to the Interior

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Differential rotation of nonlinearr-modes

Cited by 37 publications

References 24 publications

Differential rotation and r-modes in magnetized neutron stars

Differential rotation and r-modes in magnetized neutron stars

Gravitational Wave Astronomy

Gravitational waves from r-modes

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