Long-wavelength phonons in the crystalline and pasta phases of neutron-star crusts

Durel, David; Urban, Michael

doi:10.1103/physrevc.97.065805

Cited by 14 publications

(6 citation statements)

References 34 publications

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“…Observations of the magnetic field, spin evolution, bursts, flares and some rotational properties in soft gamma repeaters and anomalous X-ray pulsars provide a base for modelling of effects of the stellar magnetic field [22,23], and may be used to constrain the internal nuclear structure of neutron star crusts [24][25][26][27][28][29]. Non-relativistic treatment of the elastic forces in the pasta phases was developed in [30][31][32], and the relativistic treatment can be found in [33]; here, the focus is on a nonrelativistic model in the spirit of [34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Application of superconducting-superfluid magnetohydrodynamics to nuclear “pasta” in neutron stars

Kobyakov

2018

Phys. Rev. C

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A mixture of superconducting and superfluid nuclear liquids of protons coupled to the ultrarelativistic electron gas, and neutrons is considered. In the magnetohydrodynamic (MHD) approximation, the energy-momentum (stress) tensor is derived, and the entrainment contribution is found in the explicit form. It is shown that this contribution generates a force density, when a superfluid velocity lag and the magnetic field are simultaneously present. This force may be important in the nuclear "pasta" phase in neutron stars, if the proton and neutron Cooper pairing in the pasta phase is taken into account. It is found that if the liquid-crystalline matter of the pasta phase is superfluid and superconducting, then magnitude of the forces acting upon element of matter at typical magnetic field and the superfluid velocity lag, under certain conditions may become large enough to induce a critical stress in the neutron star crust. As an application, the necessary conditions for triggering of a starquake are found in the pasta phase of neutron stars, assuming that the nuclei are flat slabs in parallel magnetic field. The present model includes two independent local parameters: the superfluid velocity lag and the magnetic field. Possible links between the entrainment force and the magnetar starquake triggering mechanism, and some open problems are discussed.

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Section: Introductionmentioning

confidence: 99%

Application of superconducting-superfluid magnetohydrodynamics to nuclear “pasta” in neutron stars

Kobyakov

2018

Phys. Rev. C

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“…At low temperatures, longwavelength phonons are mainly responsible for the thermodynamic properties of the neutron star crust. In this regard, various lattice oscillation modes and their coupling to superfluid phonons have been studied within macroscopic effective theories [11][12][13][14]. Within the time-dependent self-consistent band theory, we will be able, in principle, to examine various oscillation modes of the crustal nuclear matter microscopically to determine, e.g., share coefficients, phonon velocities, specific heat, and so on.…”

Section: Summary and Prospectmentioning

confidence: 99%

“…Since the seminal work by Chamel, many authors considered its impact on neutron star models. For instance, the entrainment affects long-wavelength collective excitations of the inner crust such as lattice phonons, Anderson-Bogoliubov modes of neutron superfluid, and their mutual coupling [11][12][13][14]. As a result, heat capacity and thermal conductivity, and thus thermal evolution of the star can be affected.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase

Sekizawa,

Kobayashi,

Matsuo

2021

Preprint

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Background: In the solid crust of neutron stars, a variety of crystalline structure may exist. Recently the band theory of solids has been applied to the inner crust of neutron stars and significance of the entrainment between dripped neutrons and the solid crust was advocated. Since it influences interpretations of various phenomena of neutron stars, it has been desired to develop deeper understanding of the microphysics behind.Purpose: The purpose of the present article is to propose a fully self-consistent microscopic framework for describing timedependent dynamics of neutron star matter, which allows us to explore diverse properties of nuclear matter, including the entrainment effect.Methods: A fully self-consistent nuclear band theory is employed with Skyrme SLy4 energy density functional. A timedependent extension of the microscopic band theory is developed based on the time-dependent density functional theory (TDDFT). An intuitive real-time method is proposed for extracting the collective mass of a nuclear cluster immersed in a sea of dripped neutrons.Results: As the first application of the time-dependent self-consistent band theory for nuclear systems, we investigate the slab phase of nuclear matter with various proton fractions. From a dynamic response of the system to an external force, we extract the collective mass of a slab, associated with entrained neutrons as well as bound nucleons. We find that the extracted collective mass is smaller than a naive estimation based on a potential profile and single-particle energies. We show that the reduction is mainly caused by "counterflow" of dripped neutrons towards the direction opposite to the motion of the slabs. We interpret it as an "anti-entrainment" effect. As a result, the number of effectively bound neutrons is reduced, indicating an enhancement of the number density of conduction neutrons. We demonstrate that those findings are consistent with a static treatment in the band theory of solids. Conclusions:The proposed approach offers a new research possibility of investigating non-linear many-body dynamics of nuclear matter microscopically, taking full account of the periodic structure in the neutron star crusts. The fully self-consistent band theory calculations, in both static and dynamic formalisms, suggest that the mobility of dripped neutrons is larger than expected without band structure effects, at least for the slab phase of nuclear matter.

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“…The latter effect is called the entrainment effect. The notable change of neutron effective mass turned out to affect various interpretations of astrophysical phenomena of neutron stars such as pulsar glitches [21][22][23] and thermal as well as crustal properties [24][25][26][27][28], it has attracted increasing interests over the years. (See, Ref.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase

Sekizawa

Kobayashi

2022

Phys. Rev. C

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Background: The inner crust of neutron stars consists of a Coulomb lattice of neutron-rich nuclei, immersed in a sea of superfluid neutrons with background relativistic electron gas. A proper quantum mechanical treatment for such a system under a periodic potential is the band theory of solids. The effect of band structure on the effective mass of dripped neutrons, the so-called entrainment effect, is currently in a debatable situation, and it has been highly desired to develop a nuclear band theory taking into account neutron superfluidity in a fully self-consistent manner.Purpose: The main purpose of the present work is twofold: 1) to develop a formalism of the time-dependent self-consistent band theory, taking full account of nuclear superfluidity, based on time-dependent density functional theory (TDDFT) extended for superfluid systems, and 2) to quantify the effects of band structure and superfluidity on crustal properties, applying the formalism to the slab phase of nuclear matter in the β equilibrium.Methods: The fully self-consistent time-dependent band theory, proposed in a previous work [K. Sekizawa, S. Kobayashi, and M. Matsuo, Phys. Rev. C 105, 045807 (2022)], is extended for superfluid systems. To this end, superfluid TDDFT with a local treatment of pairing, known as time-dependent superfluid local density approximation (TDSLDA), is formulated in the coordinate space with a Skyrme-type energy density functional and the Bloch boundary condition. A real-time method is employed to extract the collective mass of a slab and that of protons, which in turn quantifies conduction neutron number density and the neutron effective mass, i.e., the entrainment effect.Results: Static calculations have been performed for a range of baryon (nucleon) number density (nb = 0.04-0.07 fm −3 ) under the β-equilibrium condition with and without superfluidity, for various inter-slab spacings. From the results, we find that the system gains energy through the formation of Cooper pairs for all densities examined, which validates the existence of superfluidity in the inner crust of neutron stars. From a dynamic response to an external potential, we extract the collective mass of a slab and that of protons immersed in neutron superfluid. From the results, we find that the collective mass of a slab is substantially reduced by 57.5-82.5% for nb = 0.04-0.07 fm −3 , which corresponds to an enhancement of conduction neutron number density and, thus, to a reduction of the neutron effective mass, which we call the anti-entrainment effect. A comparison of results with and without superfluidity reveals that superfluid effects slightly enhance the anti-entrainment effects for the slab phase of neutron-star matter. We discuss novel phenomena associated with superfluidity, quasiparticle resonances in the inner crust, which are absent in normal systems.Conclusions: Our fully self-consistent, microscopic, superfluid band calculations based on (TD)DFT showed that the effective mass of dripped neutrons is reduced by about 20-40% for nb = 0.04-0...

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Long-wavelength phonons in the crystalline and pasta phases of neutron-star crusts

Cited by 14 publications

References 34 publications

Application of superconducting-superfluid magnetohydrodynamics to nuclear “pasta” in neutron stars

Application of superconducting-superfluid magnetohydrodynamics to nuclear “pasta” in neutron stars

Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase

Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase

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