Bulk viscosity in superfluid neutron star cores

Haensel, P.; Levenfish, K. P.; Yakovlev, D. G.

doi:10.1051/0004-6361:20010383

Cited by 94 publications

(216 citation statements)

References 12 publications

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“…(18-21) of Ref. [85]) which increases with L above saturation density, and decreases below it, as it can be seen in the inset of the figure. The dependence of ξ and η with L can be described by simple powerlaws of the type ξ = A ξ L B ξ and η = A η L B η at each density, shown by solid lines in the figure.…”

Section: Bulk and Shear Viscositiesmentioning

confidence: 65%

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Nuclear symmetry energy and ther-mode instability of neutron stars

Vidaña

2012

Phys. Rev. C

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We analyze the role of the symmetry energy slope parameter L on the r-mode instability of neutron stars. Our study is performed using both microscopic and phenomenological approaches of the nuclear equation of state. The microscopic ones include the Brueckner-Hartree-Fock approximation, the well known variational equation of state of Akmal, Pandharipande and Ravenhall, and a parametrization of recent Auxiliary Field Diffusion Monte Carlo calculations. For the phenomenological approaches, we use several Skyrme forces and relativisic mean field models. Our results show that the r-mode instability region is smaller for those models which give larger values of L. The reason is that both bulk (ξ ) and shear (η) viscosities increase with L and, therefore, the damping of the mode is more efficient for the models with larger L. We show also that the dependence of both viscosities on L can be described at each density by simple power-laws of the type ξ = A ξ L B ξ and η = A η L B η . Using the measured spin frequency and the estimated core temperature of the pulsar in the low-mass X-ray binary 4U 1608-52, we conclude that observational data seem to favor values of L larger than ∼ 50 MeV if this object is assumed to be outside the instability region, its radius is in the range 11.5 − 12(11.5 − 13) km, and its mass 1.4M ⊙ (2M ⊙ ). Outside this range it is not possible to draw any conclusion on L from this pulsar.

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Section: Bulk and Shear Viscositiesmentioning

confidence: 65%

“…(18-21) of Ref. [85]). Shear viscosity η is the main viscous dissipation at low temperatures (T < 10 9 K), and it becomes the dominant mechanism for the damping of r-modes of cooler stars.…”

Section: Bulk and Shear Viscositiesmentioning

confidence: 95%

Nuclear symmetry energy and ther-mode instability of neutron stars

Vidaña

2012

Phys. Rev. C

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“…The bulk viscosity is calculated according to Refs. [33,34]. The EOS is the same as in [33,34] (PAL I with K 0 = 180 MeV).…”

Section: Shear Viscosity In Superfluid Mattermentioning

confidence: 99%

Shear viscosity in neutron star cores

Shternin¹,

Yakovlev²

2008

Phys. Rev. D

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118

264

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We calculate the shear viscosity η ≈ ηeµ +ηn in a neutron star core composed of nucleons, electrons and muons (ηeµ being the electron-muon viscosity, mediated by collisions of electrons and muons with charged particles, and ηn the neutron viscosity, mediated by neutron-neutron and neutronproton collisions). Deriving ηeµ, we take into account the Landau damping in collisions of electrons and muons with charged particles via the exchange of transverse plasmons. It lowers ηeµ and leads to the non-standard temperature behavior ηeµ ∝ T −5/3 . The viscosity ηn is calculated taking into account that in-medium effects modify nucleon effective masses in dense matter. Both viscosities, ηeµ and ηn, can be important, and both are calculated including the effects of proton superfluidity. They are presented in the form valid for any equation of state of nucleon dense matter. We analyze the density and temperature dependence of η for different equations of state in neutron star cores, and compare η with the bulk viscosity in the core and with the shear viscosity in the crust.

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“…PACS: 97.60.Jd, 95.30.Cq As one of the most important transport coefficients, bulk viscosities of simple npe matter, of hyperon matter and even of quark matter, both in normal and superfluid states, have been extensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], for more references see [19].In fact, the mechanical energy of density perturbations is not only dissipated to heat via bulk viscosity, but also is radiated away via neutrinos, this was first pointed out by Finiz and Wolf in 1968[1]. However, the damping mechanism through neutrinos is ignored for several decades, until recently, named this mechanism the radiative viscosity, and found it is 1.5 times larger than the bulk viscosity to all Urca processes in the lowest order of δµ/T , both in nuclear matter and quark matter.…”

mentioning

confidence: 99%

“…As one of the most important transport coefficients, bulk viscosities of simple npe matter, of hyperon matter and even of quark matter, both in normal and superfluid states, have been extensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], for more references see [19].…”

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confidence: 99%

Extension of Radiative Viscosity to Superfluid Matter

Pi¹,

Yang²,

Zheng³

2011

Chinese Phys. Lett.

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The radiative viscosity of superfluid npe matter is studied, and it is found that to the lowest order of δµ/T the ratio of radiative viscosity to bulk viscosity is the same as that of the normal matter. PACS: 97.60.Jd, 95.30.Cq As one of the most important transport coefficients, bulk viscosities of simple npe matter, of hyperon matter and even of quark matter, both in normal and superfluid states, have been extensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], for more references see [19].In fact, the mechanical energy of density perturbations is not only dissipated to heat via bulk viscosity, but also is radiated away via neutrinos, this was first pointed out by Finiz and Wolf in 1968[1]. However, the damping mechanism through neutrinos is ignored for several decades, until recently, named this mechanism the radiative viscosity, and found it is 1.5 times larger than the bulk viscosity to all Urca processes in the lowest order of δµ/T , both in nuclear matter and quark matter. Yang et al.[21] studied non-linear effect of radiative viscosity of npe matter in neutron stars for both direct Urca process and modified Urca process, and found that non-linear effect will decrease the ratio of radiative viscosity to bulk viscosity from 1.5 to 0.5 (for direct Urca process) and 0.375 (for modified Urca process); which means that for small oscillations of neutron star the large fraction of oscillation energy is emitted as neutrinos, but for large enough ones bulk viscous dissipation dominates.It's well known that below certain critical temperature nucleons in neutron star matter will be in superfluid states. The bulk viscosity of superfluid nucleon matter have been studied [4,5,17], and it turns out that the superfluidity may strongly reduce bulk viscosity. This paper aims to study the radiative viscosity of superfluid nucleon matter, in other words, we will give the relationship between radiative viscosity and bulk viscosity in the superfluid case.Both the bulk viscosity and the radiative viscosity of npe matter are related to direct Urca process (n → p+e+ ν e , p + e → n + ν e ) and modified Urca process (n + N → p + N + e + ν e , p + N + e → n + N + ν e ) in different conditions. As shown by [22] corresponds to n p /n > 1/9. This happens if the density is several times larger than the standard nuclear matter density ρ 0 = 2.8 × 10 14 gcm −3 . In the following, we focus on the direct Urca process. Let us first recall the formulae of radiative viscosity of simple non-superfluid npe matter [7,20]. Considering a periodic perturbation to the baryon number densityIt will lead to a deviation from β-equilibrium characterized bywhere µ n , µ p and µ e are the chemical potentials of the neutrons, protons and electrons. δµ can be expressed in terms of the variations of two independent variables δn b and δX p ,where X p = n p /n b is the proton fraction and the coefficient functions C and B are given byB = n b ∂µ p ∂n p + ∂µ e ∂n e + ∂µ n ∂n n .To the leading order, the net reaction rate and the i...

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Bulk viscosity in superfluid neutron star cores

Cited by 94 publications

References 12 publications

Nuclear symmetry energy and ther-mode instability of neutron stars

Nuclear symmetry energy and ther-mode instability of neutron stars

Shear viscosity in neutron star cores

Extension of Radiative Viscosity to Superfluid Matter

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