Bulk viscosity of superfluid neutron stars

Gusakov, M. E.

doi:10.1103/physrevd.76.083001

Cited by 69 publications

(177 citation statements)

References 42 publications

(98 reference statements)

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“…The evaluation of all the bulk viscosity coefficients arising from non-equilibrium beta processes has been recently reported in Ref. [10]. It would be interesting to evaluate the phonon contribution to these viscosity coefficients.…”

Section: Discussionmentioning

confidence: 99%

“…In the non-dissipative limit it is possible to show that all these approaches are equivalent. Unfortunately, very little is known about dissipative effects in relativistic superfluids [9,10,11]. To the best of our knowledge, the whole set of dissipative terms which enter into the relativistic hydrodynamical equations has only been derived in one of the above mentioned approaches [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Transport theory for cold relativistic superfluids from an analogue model of gravity

Mannarelli

Manuel

2008

Phys. Rev. D

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We write a covariant transport equation for the phonon excitations of a relativistic superfluid valid at small temperatures. The hydrodynamical equations for this system are derived from the effective field theory associated to the superfluid phonons. We describe how to construct the kinetic theory for the phonon quasiparticles using a relativistic generalization of the analogue model of gravity developed by Unruh. This gravity analogy relies on the equivalence between the action of a phonon field moving in a superfluid background with that of a boson propagating in a given curved space-time. Exploiting this analogy we obtain continuity equations for the phonon current, entropy and energy-momentum tensor in a covariant form, valid in any reference frame. Our aim is to shed light on some aspects of transport phenomena of relativistic superfluidity. In particular, we are interested in the low temperature regime of the color flavor locked phase, which is a color superconducting and superfluid phase of high density QCD that may be realized in the core of neutron stars.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transport theory for cold relativistic superfluids from an analogue model of gravity

Mannarelli

Manuel

2008

Phys. Rev. D

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“…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.…”

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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].…”

mentioning

confidence: 99%

“…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.…”

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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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Reaction Rates and Transport in Neutron Stars

Schmitt

Shternin

2018

Astrophysics and Space Science Library

122

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Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions. arXiv:1711.06520v3 [astro-ph.HE] 29 Oct 2018 65 References 66 I. INTRODUCTION A. ContextTransport describes how conserved quantities such as energy, momentum, particle number, or electric charge are transferred from one region to another. Such a transfer occurs if the system is out of equilibrium, for instance through a temperature gradient or a non-uniform chemical composition. Different theoretical methods are used to understand transport, depending on how far the system is away from its equilibrium state. If the system is close to equilibrium locally and perturbations are on large scales in space and time, hydrodynamics is a powerful technique. Further away from equilibrium other techniques are required, for example kinetic theory, which can also be used to provide the transport coefficients needed in the hydrodynamic equations. In any case, transport is determined by interactions on a microscopic level, and it is the resulting transport properties that we are concerned with in this review.Signals from neutron stars are sensitive to equilibrium properties such as the equation of state but also, to a large extent, to transport properties -here, by neutron stars we mean all objects with a radius of about 10 km and a mass of about 1-2 solar masses, including the possibilities of hybrid stars, which have a quark matter core, and pure quark stars. Therefore, understanding transport is crucial to interpret astrophysical observations, and, turning the argument around, we can use astrophysical observations to improve our understanding of transport in dense matter and thus ultimately our understanding of the microscopic interactions.Transport properties are most commonly computed from particle collisions. (Although, in strongly coupled systems, the picture of well-defined particles scattering off each other has to be taken with care.) These can be scattering processes in which energy and momentum is exchanged without changing the chemical composition of the system, or these can be flavor-changing processes from the electroweak interaction. Understanding transport thus amounts to understanding the rates of these processes, as a function of temperature and density. Electroweak processes are well understood, but large uncertainties arise if the strong interaction is involved in a reaction that contributes to transport. Therefore, approximations such as weak-coupling techniques or one-pion exchange for nucleon-nucleon collisions are being used, and efforts in current research aim at improving these approximations.In a neutron star, most of the particles involved in these processes are fermions: electrons, muons, neutrinos, neutrons, protons, hyperons, and quarks. Since the Fermi momenta of these fermions are typically much larger tha...

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Bulk viscosity of superfluid neutron stars

Cited by 69 publications

References 42 publications

Transport theory for cold relativistic superfluids from an analogue model of gravity

Transport theory for cold relativistic superfluids from an analogue model of gravity

Extension of Radiative Viscosity to Superfluid Matter

Reaction Rates and Transport in Neutron Stars

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