Nonlinear coupling network to simulate the development of the r-mode instability in neutron stars. I. Construction

Brink, Jeandrew; Teukolsky, Saul A.; Wasserman, Ira

doi:10.1103/physrevd.70.124017

Cited by 52 publications

(88 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For less relativistic models with a central energy density 1/10 that of BU1, this changes to σ max = Ω(1.93 − 1.03m), close to what Lindblom & Ipser [11] predicted and Brink et al [16] found for Newtonian stars where σ max ≈ Ω(2 − m).…”

Section: ]supporting

confidence: 51%

“…Later Brink et al [16] computed a large set of such modes in the same framework and confirmed modes up to 30th order to have frequencies confined within this range. Ruoff et al [17] studied the inertial mode spectrum for relativistic barotropic (as well as non-barotropic) stars in the slow-rotation approximation by including coupling of modes up to a maximum harmonic index ℓ max .…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Eigenmode frequency distribution of rapidly rotating neutron stars

Boutloukos

Nollert

2007

Phys. Rev. D

View full text Add to dashboard Cite

We use perturbation theory and the relativistic Cowling approximation to numerically compute characteristic oscillation modes of rapidly rotating relativistic stars which consist of a perfect fluid obeying a polytropic equation of state. We present a code that allows the computation of modes of arbitrary order. We focus here on the overall distribution of frequencies. As expected, we find an infinite pressure mode spectrum extending to infinite frequency. In addition we obtain an infinite number of inertial mode solutions confined to a finite, well-defined frequency range which depends on the compactness and the rotation frequency of the star. For non-axisymmetric modes we observe how this range is shifted with respect to the axisymmetric ones, moving towards negative frequencies and thus making all m > 2 modes unstable. We discuss whether our results indicate that the star's spectrum must have a continuous part, as opposed to simply containing an infinite number of discrete modes.

show abstract

Section: ]supporting

confidence: 51%

Section: Introductionmentioning

confidence: 98%

Eigenmode frequency distribution of rapidly rotating neutron stars

Boutloukos

Nollert

2007

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…This approximation was proposed by Cutler and Lindblom [48] and adopted by Kokkotas and Stergiouluas [49] for the r-mode and by Brink et al [21,22,23,24] for inertial modes. Table I compares the bulk viscosity timescales for several different inertial modes of n = 1 polytrope computed by Lockitch and Friedman [30] with those computed for an incompressible model.…”

Section: Discussionmentioning

confidence: 99%

“…The rotational phase τ is defined by dτ = Ω dt. In terms of the amplitude variables of Schenk et al [19] and Brink et al [21,22,23] C j = Ω(t)c j (t), which are normalized to unit energy, i.e., mode amplitudes of c j = 1 correspond to a mode energy E j = ǫ = M R 2 Ω 2 equal to the rotational energy of the star 2 . The equations of motion in Schenk et al assume constant Ω.…”

Section: Setup a Three-mode Evolution Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Spinning down newborn neutron stars: Nonlinear development of ther-mode instability

2009

Self Cite

View full text Add to dashboard Cite

We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near resonant inertial modes that couple to it. We find that the spectrum of evolutions is more diverse than previously thought. We start our evolutions with a star of temperature ∼ 10 10 K and a spin frequency close to the Kepler break-up frequency. We assume that hyperon bulk viscosity dominates at high temperatures (T ∼ 10 9 − 10 10 K) and boundary layer viscosity dominates at lower temperatures (∼ a few × 10 8 K). To explore possible nonlinear behavior, we vary properties of the star such as the hyperon superfluid transition temperature, the strength of the boundary layer viscosity, and the fraction of the star that cools via direct URCA reactions. The evolution of the star is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects become important when the r-mode amplitude grows above its first parametric instability threshold. The balance between neutrino cooling and viscous heating plays an important role in the evolution. Depending on the initial r-mode amplitude, and on the strength of the viscosity and of the cooling this balance can occur at different temperatures. If thermal equilibrium occurs on the r-mode stability curve, where gravitational driving equals viscous damping, the evolution may be adequately described by a one-mode model. Otherwise, nonlinear effects are important and lead to various more complicated scenarios. Once thermal balance occurs, the star spinsdown oscillating between thermal equilibrium states until the instability is no longer active. The average evolution of the mode amplitudes can be approximated by quasi-stationary states that are determined algebraically. For lower viscosity we observe runaway behavior in which the r-mode amplitude passes several parametric instability thresholds. In this case more modes need to be included to model the evolution accurately. In the most optimistic case, we find that gravitational radiation from the r-mode instability in a very young, fast spinning neutron star within about 1 Mpc of Earth may be detectable by advanced LIGO for years, and perhaps decades, after formation. Details regarding the amplitude and duration of the emission depend on the internal dissipation of the modes of the star, which would be probed by such detections.

show abstract

Gravitational Wave Astronomy

Kokkotas

2008

Reviews in Modern Astronomy

View full text Add to dashboard Cite

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

show abstract

Nonlinear coupling network to simulate the development of the r-mode instability in neutron stars. I. Construction

Cited by 52 publications

References 21 publications

Eigenmode frequency distribution of rapidly rotating neutron stars

Eigenmode frequency distribution of rapidly rotating neutron stars

Spinning down newborn neutron stars: Nonlinear development of ther-mode instability

Gravitational Wave Astronomy

Contact Info

Product

Resources

About