Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus

Andrey I. Chugunov

doi:10.1093/mnras/stac2157

paper

Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus

arXiv:2207.14649 · doi:10.1093/mnras/stac2157

Abstract

The main contribution to the effective shear modulus of neutron star crust can be calculated within Coulomb solid model and can be approximated by simple analytical expression for arbitrary (even multicomponent) composition. Here I consider correction associated with electron screening within Thomas-Fermi approximation. In particular, I demonstrate that for relativistic electrons (density $ρ > 1 0^{6}$ g\,cm $^{- 3}$ ) this correction can be estimated as $δ μ_{eff}^{V} = - 9.4 \times 1 0^{- 4} \sum_{Z} n_{Z} Z^{7/3} e^{2} / a_{e}$ , where summation is taken over ion species, $n_{Z}$ is number density of ions with charge $Z e$ , $k_{TF}$ is Thomas-Fermi screening wave number. Finally, $a_{e} = (4 π n_{e} /3)^{- 1/3}$ is electron sphere radius. Quasineutrality condition $n_{e} = \sum_{Z} Z n_{Z}$ is assumed. This result holds true for arbitrary (even multicomponent and amorphous) matter and can be applied for neutron star crust and (dense) cores of white dwarfs. For example, the screening correction reduces shear modulus by $\sim 9$ \% for $Z \sim 40$ , which is typical for inner layers of neutron star crust.

arXiv comment6 pages, Accepted in MNRAS

Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus

Abstract

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