First-principles calculations of shear moduli for Monte Carlo–simulated Coulomb solids

Ogata, Shūji; Ichimaru, Setsuo

doi:10.1103/physreva.42.4867

Cited by 110 publications

(116 citation statements)

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“…The shear modulus of a Coulomb lattice of positively charged nuclei in a uniform negatively charged background in the NS crust at a baryon number density n b was determined through Monte Carlo simulation (Ogata & Ichimaru 1990;Strohmayer et al 1991;Chugunov & Horowitz 2010) and can be written as…”

Section: Variation Of K Sym − L Relationsmentioning

confidence: 99%

“…The maximum and typical size of mountains on NS crusts Haskell et al 2006) and frequencies of torsional crustal oscillations (Piro 2005;Steiner & Watts 2009;Samuelsson & Andersson 2007;Andersson et al 2009) depends on the thickness of the elastically rigid part of the crust and its shear modulus, which depends on the characteristic quantities which define the lattice: the inter-ion spacing a and nuclear charge Z (Gearheart et al 2011). The shear modulus throughout the inner crust (Ogata & Ichimaru 1990;Strohmayer et al 1991;Chugunov & Horowitz 2010) is an important quantity in determining the frequencies at which the crust might undergo global oscillations. Various transport properties within the crust will also depend somewhat on the crustal composition through the densities of the various components, the electron fraction and the lattice spacing.…”

Section: Introductionmentioning

confidence: 99%

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A Survey of the Parameter Space of the Compressible Liquid Drop Model as Applied to the Neutron Star Inner Crust

Newton

Gearheart

2012

ApJS

110

111

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We present a systematic survey of the range of predictions of the neutron star inner crust composition, crust-core transition densities and pressures, and density range of the nuclear "pasta" phases at the bottom of the crust provided by the compressible liquid drop model in light of the current experimental and theoretical constraints on model parameters. Using a Skyrme-like model for nuclear matter, we construct baseline sequences of crust models by consistently varying the density dependence of the bulk symmetry energy at nuclear saturation density, L, under two conditions: (1) that the magnitude of the symmetry energy at saturation density J is held constant, and (2) J correlates with L under the constraint that the pure neutron matter (PNM) equation of state (EoS) satisfies the results of ab initio calculations at low densities. Such baseline crust models facilitate consistent exploration of the L dependence of crustal properties. The remaining surface energy and symmetric nuclear matter parameters are systematically varied around the baseline, and different functional forms of the PNM EoS at sub-saturation densities implemented, to estimate theoretical "error bars" for the baseline predictions. Inner crust composition and transition densities are shown to be most sensitive to the surface energy at very low proton fractions and to the behavior of the sub-saturation PNM EoS. Recent calculations of the energies of neutron drops suggest that the low-proton-fraction surface energy might be higher than predicted in Skyrme-like models, which our study suggests may result in a greatly reduced volume of pasta in the crust than conventionally predicted.

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Section: Variation Of K Sym − L Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Survey of the Parameter Space of the Compressible Liquid Drop Model as Applied to the Neutron Star Inner Crust

Newton

Gearheart

2012

ApJS

110

111

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“…We have calculated the "effective" shear modulus S of the outer crust, assuming that it is made of a body-centered-cubic lattice polycrystal, using the following expression [46] :…”

Section: Elastic Propertiesmentioning

confidence: 99%

Properties of the outer crust of strongly magnetized neutron stars from Hartree-Fock-Bogoliubov atomic mass models

et al. 2012

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The equilibrium properties of the outer crust of cold nonaccreting magnetars (i.e. neutron stars endowed with very strong magnetic fields) are studied using the latest experimental atomic mass data complemented with a microscopic atomic mass model based on the Hartree-Fock-Bogoliubov method. The Landau quantization of electron motion caused by the strong magnetic field is found to have a significant impact on the composition and the equation of state of crustal matter. It is also shown that the outer crust of magnetars could be much more massive than that of ordinary neutron stars.

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“…(6), we shall see that μ must be identified with S 1212 . Alternatively, we can use the isotropisation procedure proposed by Ogata and Ichimaru [10]. Then we obtain effective shear modulus μ eff = (S 1111 − S 1122 − S 1221 + 4S 1212 )/5.…”

Section: Effective Shear Modulusmentioning

confidence: 99%

Shear Modulus of a Coulomb Crystal of Ions: Effects of Ion Motion and Electron Background Polarization

Baiko

2012

Contrib. Plasma Phys.

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Shear modulus of a body-centered cubic Coulomb crystal of ions is calculated by thermodynamic perturbation theory taking into account ion motion. Classic and quantum regimes of ion motion are considered. The calculations in the classic range of high temperatures agree well with previous Monte Carlo simulations. In this case, the shear modulus is given by a sum of a positive contribution due to the static lattice and a negative ∝ T contribution due to the ion motion. In the quantum regime of low temperatures, the contribution to the shear modulus due to the ion motion saturates at a negative constant value, determined by zero-point ion vibrations.The correction to the static lattice shear modulus due to the polarization of the electron background is also calculated. The background polarization is described by a dielectric function in the linear response formalism. We compare two dielectric functions (simple Thomas-Fermi and more realistic Jancovici) and find dependence of the correction to the shear modulus on the ion charge number and the electron degree of relativity.The numerical results are approximated by simple analytical formulas. They can be applied to matter in white dwarf cores and neutron star crusts for precise modeling of oscillations of these astrophysical objects.

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First-principles calculations of shear moduli for Monte Carlo–simulated Coulomb solids

Cited by 110 publications

References 10 publications

A Survey of the Parameter Space of the Compressible Liquid Drop Model as Applied to the Neutron Star Inner Crust

A Survey of the Parameter Space of the Compressible Liquid Drop Model as Applied to the Neutron Star Inner Crust

Properties of the outer crust of strongly magnetized neutron stars from Hartree-Fock-Bogoliubov atomic mass models

Shear Modulus of a Coulomb Crystal of Ions: Effects of Ion Motion and Electron Background Polarization

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