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Journal ArticleDOI

Nonlinear evolution of the r-modes in neutron stars.

12 Feb 2001-Physical Review Letters (The American Physical Society)-Vol. 86, Iss: 7, pp 1152-1155
TL;DR: The evolution of a neutron-star r-mode driven unstable by gravitational radiation is studied here using numerical solutions of the full nonlinear fluid equations to study the nonlinear evolution of the mode.
Abstract: The evolution of a neutron-star $r$-mode driven unstable by gravitational radiation is studied here using numerical solutions of the full nonlinear fluid equations. The dimensionless amplitude of the mode grows to order unity before strong shocks develop which quickly damp the mode. In this simulation the star loses about $40%$ of its initial angular momentum and $50%$ of its rotational kinetic energy before the mode is damped. The nonlinear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and poles of the star.

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Journal ArticleDOI
TL;DR: In this paper, it was shown that the gravitational radiation-reaction force that drives the r-mode instability removes this gauge dependence, and the exponentially growing differential rotation of the unstable second-order rmode is unique.
Abstract: At second order in perturbation theory, the r-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation reaction, the differential rotation is constant in time and has been computed by Sa. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the r-mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable second-order r-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state.

3 citations

01 Apr 2002
TL;DR: In this paper, it was shown that if a nonrotating neutron star possesses a current quadrupole moment, interactions with a gravitomagnetic tidal field can lead to a compressive force on the star.
Abstract: Numerical simulations of binary neutron stars by Wilson, Mathews, and Marronetti indicated that neutron stars that are stable in isolation can be made to collapse to black holes when placed in a binary. This claim was surprising as it ran counter to the Newtonian expectation that a neutron star in a binary should be more stable, not less. After correcting an error found by Flanagan, Wilson and Mathews found that the compression of the neutron stars was significantly reduced but not eliminated. This has motivated us to ask the following general question: Under what circumstances can general-relativistic tidal interactions cause an otherwise stable neutron star to be compressed? We have found that if a nonrotating neutron star possesses a current-quadrupole moment, interactions with a gravitomagnetic tidal field can lead to a compressive force on the star. If this current quadrupole is induced by the gravitomagnetic tidal field, it is related to the tidal field by an equation-of-state-dependent constant called the gravitomagnetic Love number. This is analogous to the Newtonian Love number that relates the strength of a Newtonian tidal field to the induced mass quadrupole moment of a star. The compressive force is almost never larger than the Newtonian tidalmore » interaction that stabilizes the neutron star against collapse. In the case in which a current quadrupole is already present in the star (perhaps as an artifact of a numerical simulation), the compressive force can exceed the stabilizing one, leading to a net increase in the central density of the star. This increase is small (< or approx. 1%) but could, in principle, cause gravitational collapse in a star that is close to its maximum mass. This paper also reviews the history of the Wilson-Mathews-Marronetti controversy and, in an appendix, extends the discussion of tidally induced changes in the central density to rotating stars.« less

3 citations

Journal ArticleDOI
01 May 2007
TL;DR: In this article, the authors present the main properties of a perturbative framework for describing, in the time domain, the nonlinear coupling between the radial and nonradial perturbations of spherically symmetric and perfect fluid compact stars.
Abstract: Nonlinear stellar oscillations can be studied by using a multiparameter perturbative approach, which is appropriate for investigating the low and mild nonlinear dynamical regimes. We present the main properties of our perturbative framework for describing, in the time domain, the nonlinear coupling between the radial and nonradial perturbations of spherically symmetric and perfect fluid compact stars. This particular coupling can be described by gauge invariant quantities that obeys a system of partial differential equations with source terms, which are made up of product of first order radial and nonradial perturbations. We report the results of numerical simulations for both the axial and polar coupling perturbations, that exhibit in the stellar dynamics and in the associated gravitational wave signal some interesting nonlinear effects, such as combination harmonics and resonances. In particular, we concentrate on the axial case, where the linear axial perturbations describe a harmonic component of a differentially rotating neutron star. The gravitational wave signal of this stellar configuration mirrors at second perturbative order the spectral features of the linear radial normal modes. In addition, a signal amplification appears when one of the radial frequencies is close to the axial w-mode frequencies of the star.

3 citations


Cites background from "Nonlinear evolution of the r-modes ..."

  • ... enable us to simulate non-linear evolutions of various physical systems such as core collapse [33, 34], non-linearoscillations of differentially rotating stars [104], non-linear saturation ofr-modes [15, 71, 72, 105], non-linear radial pulsations [102], etc. In perturbation theory, the second perturbative order has been developed for studying Schwarzschild black holes [46, 41]. In particular, the authors treated ...

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  • ...s can be better addressed in numerical relativity by evolving the full set of non-linear Einstein equations [35, 105, 103]. Furthermore, recent works on the core collapse [33, 34], r-mode instability [94, 68, 71], accretion from a companion [40], or supernova fall back material [113], show that a neutron star manifests a degree of differential rotation. These studies have clarified the effects of rotation on t...

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Journal ArticleDOI
19 Oct 2022-Universe
TL;DR: In this paper , the relativistic r-modes of slowly rotating nonbarotropic neutron stars are described by nonanalytic functions of stellar angular velocity, which makes the perturbation techniques, used so far in the r-mode theoretical studies, inapplicable.
Abstract: We show that the r-modes of slowly rotating nonbarotropic neutron stars are described by nonanalytic functions of stellar angular velocity, which makes the perturbation techniques, used so far in the r-mode theoretical studies, inapplicable. In contrast to those studies and in accordance with numerical calculations beyond the slow rotation approximation, the obtained r-mode spectrum is discrete, which resolves the continuous spectrum problem, lasting since 1997. Our findings imply that the relativistic r-modes in slowly rotating neutron stars dramatically differ from their Newtonian cousins, which may have important implications for the detectability of r-mode signatures in observations, in particular for the r-mode excitation efficiency during the neutron star inspirals.

3 citations

Journal ArticleDOI
TL;DR: In this paper , the effects of three-mode couplings on amplitude evolutions were investigated in early type main sequence stars. And they showed that the non-linear excitation and amplitude saturation of g-modes, rmodes and overstable convective (OsC) modes are not necessarily effective to achieve amplitude saturation.
Abstract: We discuss non-linear excitation and amplitude saturation of g-modes, r-modes and overstable convective (OsC) modes in early type main sequence stars, taking account of the effects of three-mode couplings on amplitude evolutions. OsC modes are rotationally stabilized convective modes in the convective core and they resonantly excite low frequency g-modes to obtain large amplitudes in the envelope when the rotation rate of the core is larger than critical rates. We use, for a network of three-mode couplings, amplitude equations governing the time evolution of the mode amplitudes where each of three-mode couplings is assumed to occur between two stable modes and one unstable mode. Assuming that the unstable modes in the couplings are OsC modes in the core and the stable modes are g- and r-modes in the envelope, we integrate the amplitude equations to see how the g- and r-modes are non-linearly excited by the OsC modes and whether or not the amplitude evolutions tend toward a state of finite amplitudes. We find that the non-linear three-mode couplings do excite low frequency g- and r-modes but they are not necessarily effective to achieve amplitude saturation since the three-mode couplings between the OsC modes with large growth rates and g- and r-modes with small damping rates tend to destabilize amplitude evolutions.

2 citations