Bulk viscosity in superfluid neutron star cores

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Once thermal balance occurs, the star spinsdown oscillating between thermal equilibrium states until the instability is no longer active.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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“…[38] R hb (T /T c ) = a 5/4 + b 1/2 2 exp 0.5068 − 0.5068 2 + y 2 (48) where a = 1 + 0.3118y 2 , b = 1 + 0.2566y 2 and y =…”

Section: Discussionmentioning

confidence: 99%

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

2009

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“…For more complicated core compositions (e.g., for nucleon-hyperon or quark matter) non-leptonic reactions are possible (e.g., Jones 2001a; Haensel, Levenfish, & Yakovlev 2002a) that do not involve neutrinos and, being more powerful than neutrino reactions, produce dominant contribution to the bulk viscosity (e.g., Jones 2001a; Haensel, Levenfish, & Yakovlev 2002b;Lindblom & Owen 2002;Gusakov & Kantor 2008, Alford et al 2010. Thus, the ratio of the bulk viscosity energy dissipation rate to luminosity can be enhanced in comparison to the nucleonic matter.…”

Section: Stabilization By the Bulk Viscosity: Too Strong Neutrino Lummentioning

confidence: 99%

R modes and neutron star recycling scenario

Chugunov¹,

Gusakov²,

Kantor

2017

Monthly Notices of the Royal Astronomical Society

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To put new constraints on the r-mode instability window, we analyse the formation of millisecond pulsars (MSPs) within the recycling scenario, making use of three sets of observations: (a) X-ray observations of neutron stars (NSs) in low-mass X-ray binaries; (b) timing of millisecond pulsars; and (c) X-ray and UV observations of MSPs. As shown in previous works, r-mode dissipation by shear viscosity is not sufficient to explain observational set (a), and enhanced r-mode dissipation at the red-shifted internal temperatures T ∞ ∼ 10 8 K is required to stabilize the observed NSs. Here, we argue that models with enhanced bulk viscosity can hardly lead to a self-consistent explanation of observational set (a) due to strong neutrino emission, which is typical for these models (unrealistically powerful energy source is required to keep NSs at the observed temperatures). We also demonstrate that the observational set (b) , combined with the theory of internal heating and NS cooling, provides evidence of enhanced r-mode dissipation at low temperatures, T ∞ ∼ 2×10 7 K. Observational set (c) allows us to set an upper limit on the internal temperatures of MSPs, T ∞ < 2 × 10 7 K (assuming a canonical NS with the accreted crust). Recycling scenario can produce MSPs at these temperatures only if r-mode instability is suppressed in the whole MSP spin frequency range (ν 750 Hz) at temperatures 2 × 10 7 T ∞ 3 × 10 7 K, providing thus a new constraint on the r-mode instability window. These observational constraints are analysed in more details in application to the resonance uplift scenario of Gusakov et al. (2014b,a).

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“…We then obtain (after an approximate algebraic simplification) The third term arises from the bulk viscosity produced by out-of-equilibrium hyperon reactions (which dominate that produced by direct and modified Urca reactions). This has been studied by Jones (2001aJones ( , 2001b and Lindblom & Owen (2002) for normal nuclear matter and by Haensel, Levenfish, & Yakovlev (2002) for superfluids. We employ the results of Lindblom & Owen (2002) for .…”

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confidence: 99%

“…These hyperons n ϩ n O n ϩ L should be present at densities , which 14 Ϫ3 r տ (5-8) # 10 g cm are achieved over a large fraction of the core of relevant mass ( ) neutron star models for many nuclear equa-M ഡ 1.3-1.6 M , tions of state (which are softened by their presence; Balberg, Lichtenstadt, & Cook 1999). Employing the superfluid reduction factor of Haensel et al (2002) …”

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confidence: 99%

Conditions for Steady Gravitational Radiation from Accreting Neutron Stars

Wagoner

2002

The Astrophysical Journal

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The gravitational wave-and accretion-driven evolution of the angular velocity, core temperature, and (small) amplitude of an r-mode of neutron stars in low-mass X-ray binaries and similar systems is investigated. The conditions required for evolution to a stable equilibrium state (with gravitational wave flux proportional to average X-ray flux) are determined. In keeping with conclusions derived from observations of neutron star cooling, the core neutrons are taken to be normal while the core protons and hyperons and the crust neutrons are taken to be singlet superfluids. The dominant sources of damping are then hyperon bulk viscosity (if much of the core is at least 2-3 times nuclear density) and (e-e and n-n) shear (and possibly magnetic) viscosity within the corecrust boundary layer. It is found that a stable equilibrium state can be reached if the superfluid transition temperature of the hyperons is sufficiently small (Շ K), allowing the gravitational radiation from Sco X-1 and several 9 2 # 10 other neutron stars in low-mass X-ray binaries to be potentially detectable by the second-generation LIGO (and VIRGO) arrays.

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Bulk viscosity in superfluid neutron star cores

Cited by 97 publications

References 29 publications

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

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

R modes and neutron star recycling scenario

Conditions for Steady Gravitational Radiation from Accreting Neutron Stars

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