Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus

Andrey Chugunov

doi:10.1093/mnrasl/slaa173

paper

Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus

arXiv:2010.08398 · doi:10.1093/mnrasl/slaa173

Abstract

I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modeled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress-strain tensor has additional symmetry: contraction $B_{ij i l} = 0$ . It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to $- 2/15$ of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus: $\sum_{Z} 0.12 n_{Z} Z^{5/3} e^{2} / a_{e}$ . Here summation is taken over ion species, $n_{Z}$ is number density of ions with charge $Z e$ . 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.

arXiv comment5 pages, accepted for publication in MNRAS:Letters

Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus

Abstract

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