Nonlinear coupling network to simulate the development of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>r</mml:mi></mml:math>mode instability in neutron stars. II. Dynamics

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

doi:10.1103/physrevd.71.064029

Cited by 42 publications

(67 citation statements)

References 23 publications

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“…We focus on T c 5 × 10 9 K for which nonlinear effects are important. For low T c 3 × 10 9 K, Wagoner [1] showed that the evolution reaches a steady state at amplitudes below the lowest parametric instability threshold found by Brink et al [28]. It is important to note that all our evolutions start on the part of the r-mode stability curve that decreases with temperature and that the bulk viscosity does not play a role in any of our bound evolutions.…”

Section: Introductionmentioning

confidence: 52%

“…In this picture, the star evolves near the r-mode stability curve until an equilibrium between accretion spin-up and gravitational radiation spin-down is achieved. The value of the r-mode amplitude remains below the lowest instability threshold found by Brink et al [26,27,28] for modes with n < 30, and hence in this regime nonlinear effects may not play a role.…”

Section: Introductionmentioning

confidence: 76%

“…They assumed a small r-mode amplitude and treated the oscillations of the modes with weakly nonlinear perturbation theory via three-mode couplings. This assumption was tested by Arras et al [19] and Brink et al [26,27,28]. Arras et al proposed that a turbulent cascade would develop in the strong driving regime.…”

Section: Introductionmentioning

confidence: 99%

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Spin evolution of accreting neutron stars: Nonlinear development of ther-mode instability

2007

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The nonlinear saturation of the r-mode instability and its effects on the spin evolution of Low Mass X-ray Binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three mode amplitudes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasi-stationary states that change slowly as the temperature and spin of the star evolve. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. The evolution of the neutron star angular velocity and temperature follow easily calculated trajectories along these sequences of quasi-stationary states. The outcome depends on whether or not the star will reach thermal equilibrium, where the viscous heating by the three modes is equal to the neutrino cooling (H = C curve). If, when the r-mode becomes unstable, the star spins at a frequency below the maximum of the H = C curve, then it will reach a state of thermal equilibrium. It can then either (1) undergo a cyclic evolution with a small cycle size with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long timescale of ≈ 10 6 years. If the star does not reach a state of thermal equilibrium, then a faster thermal runaway (timescale of ≈ 100 years) occurs and the r-mode amplitude increases above the second parametric instability threshold. Following this evolution requires more inertial modes to be included. The sources of damping considered are shear viscosity, hyperon bulk viscosity and viscosity within the core-crust boundary layer. We vary proprieties of the star such as the hyperon superfluid transition temperature Tc, the fraction of the star that is above the threshold for direct URCA reactions, and slippage factor, and map the different scenarios we obtain to ranges of these parameters. We focus on ∼ 1 and we find that in this case the r-mode instability would be active for about 1 in 1000 LMXBs and that only the gravitational waves from LMXBs in the local group of galaxies could be detected by advanced LIGO interferometers.

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Section: Introductionmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 76%

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Spin evolution of accreting neutron stars: Nonlinear development of ther-mode instability

2007

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“…In order to model this scenario accurately one would have to include an oscillator network that takes into account not only direct couplings to the r-mode, but also couplings among inertial modes similar to the work of Brink et al [21,22,23].…”

Section: Density Of Resonances and The Effective Three Mode Coupling mentioning

confidence: 99%

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

2009

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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.

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“…Arras et al (2003) propose that energy cascades from parent mode to descendant modes in a way similar to the Kolmogorov turbulent energy cascade. However, Brink et al (2005) conclude that a small fraction of 3-mode couplings dominate the energy cascade and that the energy spectrum differs from Kolmogorov. 13 See Figure 4 in .…”

Section: Outburstsmentioning

confidence: 87%

DAVs: Red Edge and Outbursts

Luan

Goldreich

2018

ApJ

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As established by photometric surveys, white dwarfs with hydrogen atmospheres and surface gravity, log(g)≈8.0 pulsate as they cool across the temperature range of 12,500 KT eff 10,800 K. Known as DAVs or ZZ Ceti stars, their oscillations are attributed to gravity modes excited by convective driving. Overstability requires convective driving to exceed radiative damping. Previous works have demonstrated that ωmax(τ c −1 , L ℓ,b ) is a necessary and sufficient condition for overstability. Here τ c and L ℓ,b are the effective thermal timescale and Lamb frequency at the base of the surface convection zone. Below the observational red edge, L ℓ,b ?τ c −1 , so overstable modes all have ωτ c ?1. Consequently, their photometric amplitudes are reduced by that large factor rendering them difficult to detect. Although proposed previously, the condition ωL ℓ,b has not been clearly interpreted. We show that modes with ω<L ℓ,b suffer enhanced radiative damping that exceeds convective driving rendering them damped. A quasi-adiabatic analysis is adequate to account for this enhancement. Although this approximation is only marginally valid at the red edge, it becomes increasingly accurate toward both higher and lower T eff . Recently, Kepler discovered a number of cool DAVs that exhibit sporadic flux outbursts. Typical outbursts last several hours, are separated by days, and release ∼10 33 -10 34 erg. We attribute outbursts to limit cycles arising from sufficiently resonant 3-mode couplings between overstable parent modes and pairs of radiatively damped daughter modes. Limit cycles account for the durations and energies of outbursts and their prevalence near the red edge of the DAV instability strip.

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Nonlinear coupling network to simulate the development of thermode instability in neutron stars. II. Dynamics

Cited by 42 publications

References 23 publications

Spin evolution of accreting neutron stars: Nonlinear development of ther-mode instability

Spin evolution of accreting neutron stars: Nonlinear development of ther-mode instability

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

DAVs: Red Edge and Outbursts

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