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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, an analytical expression is derived for the optimal signal-to-noise ratio S/N for detecting the GR from a rapidly rotating 1.4M⊙ neutron star.
Abstract: The instability in the r-modes of rotating neutron stars can (in principle) emit substantial amounts of gravitational radiation (GR) which might be detectable by LIGO and similar detectors. Estimates are given here of the detectability of this GR based on the non-linear simulations of the r-mode instability by Lindblom, Tohline and Vallisneri. The burst of GR produced by the instability in the rapidly rotating 1.4M⊙ neutron star in this simulation is fairly monochromatic with frequency near 960 Hz and duration about 100 s. A simple analytical expression is derived here for the optimal signal-to-noise ratio S/N for detecting the GR from this type of source. For an object located at a distance of 20 Mpc we estimate the optimal S/N to be in the range 1.2–12.0 depending on the LIGO II configuration.

29 citations


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

  • ...(4) The discrete Fourier transform of the gravitational wave signal from our rescaling of the simulation of Lindblom et al (2001a) is shown in figure 4....

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  • ...We direct those readers who might be interested in the wider range of subjects covered in the talk to the recent review by Lindblom (2001), and the recent papers by Lindblom et al (2001b) and by Lindblom and Owen (2002)....

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  • ...Fortunately, tests have shown (Lindblom et al 2001b) that the maximum amplitude which the r-mode achieves (and hence the maximum value of J22) is relatively insensitive to the strength of the GRR force....

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  • ...These lead to large surface waves which break and shock (Lindblom et al 2001a, 2001b)....

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  • ...2. r-mode evolution model We base our estimates of the GR produced by the non-linear evolution of an unstable r-mode on the numerical simulations by Lindblom et al (2001a, 2001b)....

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Journal ArticleDOI
Marc Favata1
TL;DR: In this article, 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

28 citations

Journal ArticleDOI
TL;DR: In this article, the authors revisited the possibility and detectability of a stochastic gravitational wave (GW) background produced by a cosmological population of newborn neutron stars (NSs) with r-mode instabilities.
Abstract: We revisit the possibility and detectability of a stochastic gravitational wave (GW) background produced by a cosmological population of newborn neutron stars (NSs) with r-mode instabilities. The NS formation rate is derived from both observational and simulated cosmic star formation rates (CSFRs). We show that the resultant GW background is insensitive to the choice of CSFR models, but depends strongly on the evolving behavior of CSFR at low redshifts. Nonlinear effects such as differential rotation, suggested to be an unavoidable feature which greatly influences the saturation amplitude of the r-mode, are considered to account for GW emission from individual sources. Our results show that the dimensionless energy density Ω GW could have a peak amplitude of ≃(1-3.5) x 10 -8 in the frequency range (200-1000) Hz, if the smallest amount of differential rotation corresponding to a saturation amplitude of order unity is assumed. However, such a high-mode amplitude is unrealistic as it is known that the maximum value is much smaller and at most 10 -2 . A realistic estimate of Ω GW should be at least four orders of magnitude lower (~10 -12 ), which leads to a pessimistic outlook for the detection of the r-mode background. We consider different pairs of terrestrial interferometers (IFOs) and compare two approaches to combine multiple IFOs in order to evaluate the detectability of this GW background. Constraints on the total emitted GW energy associated with this mechanism to produce a detectable stochastic background (a signal-to-noise ratio of 2.56 with 3 year cross-correlation) are ~10 -3 M ⊙ c 2 for two co-located advanced LIGO detectors, and 2 x 10- 5 M ⊙ c 2 for two Einstein telescopes. These constraints may also be applicable to alternative GW emission mechanisms related to oscillations or instabilities in NSs depending on the frequency band where most GWs are emitted.

28 citations


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

  • ...On the other hand, differential rotation, first suggested by Rezzolla et al. (2000, 2001a, 2001b), is an unavoidable feature of nonlinear r-modes (Stergioulas & Font 2001; Lindblom et al. 2001; Sá 2004)....

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Journal ArticleDOI
TL;DR: In this paper, the authors proposed an alternative explanation to the rapid cooling of neutron star in Cas A. They suggested that the star is experiencing the recovery period following the r-mode heating process, assuming the star was differentially rotating.
Abstract: We proposed alternative explanation to the rapid cooling of neutron star in Cas A. It is suggested that the star is experiencing the recovery period following the r-mode heating process,assuming the star is differentially rotating. Like the neutron-superfluidity-triggering model, our model predicts the rapid cooling will continue for several decades. However, the behavior of the two models has slight differences, and they might be distinguished by observations in the near future.

28 citations

Journal ArticleDOI
TL;DR: In this article, the evolution of a nonaxisymmetric bar-mode perturbation of rapidly rotating stars due to a secular instability induced by gravitational wave emission is studied in post-Newtonian simulations taking into account gravitational radiation reaction.
Abstract: The evolution of a nonaxisymmetric bar-mode perturbation of rapidly rotating stars due to a secular instability induced by gravitational wave emission is studied in post-Newtonian simulations taking into account gravitational radiation reaction. A polytropic equation of state with the polytropic index n=1 is adopted. The ratio of the rotational kinetic energy to the gravitational potential energy T/|W| is chosen in the range between 0.2 and 0.26. Numerical simulations were performed until the perturbation grows to the nonlinear regime, and illustrate that the outcome after the secular instability sets in is an ellipsoidal star of a moderately large ellipticity > or approx. 0.7. A rapidly rotating protoneutron star may form such an ellipsoid, which is a candidate for strong emitter of gravitational waves for ground-based laser interferometric detectors. A possibility that effects of magnetic fields neglected in this work may modify the growth of the secular instability is also mentioned.

27 citations