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

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 $B_{ijil}=0$. 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: ${\sum }_{Z}0.12n_Z{Z}^{5/3}{e}^2/a_{\mathrm{e}}$. Here summation is taken over ion species, $n_Z$ is number density of ions with charge $Ze$. Finally $a_{\mathrm{e}}=(4\pi n_{\mathrm{e}}/3{)}^{-1/3}$ is electron sphere radius. Quasineutrality condition $n_{\mathrm{e}}={\sum }_{Z}Z{n}_Z$ is assumed.

5 pages, accepted for publication in MNRAS:Letters

References in corpus (17)

• The Breaking Strain of Neutron Star Crust and Gravitational Waves
• Models of Pulsar Glitches
• Mountains on Neutron Stars: Accreted vs. Non-Accreted crusts
• Gravitational-wave constraints on the equatorial ellipticity of millisecond pulsars
• Thermoplastic waves in magnetars
• Crystallization of the inner crust of a neutron star and the influence of shell effects
• Crystallization of the outer crust of a non-accreting neutron star
• Binary and ternary ionic compounds in the outer crust of a cold nonaccreting neutron star
• Elastic properties of polycrystalline dense matter
• Minimum Glitch of the Crab Pulsar and the Crustquake as a Trigger Mechanism
• Deformed crystals and torsional oscillations of neutron star crust
• Superfluidity in Disordered Neutron Stars Crusts
• Vortex unpinning due to crustquake initiated neutron excitation and pulsar glitches
• Pulsar glitch activity as a state-dependent Poisson process: parameter estimation and epoch prediction
• Elastic properties of multicomponent crystals in neutron stars and white dwarfs
• Electrostatic energy and phonon properties of Yukawa crystals
• Averaging of elastic constants for polycrystals

Cited by in corpus (7)

• Mountain formation by repeated, inhomogeneous crustal failure in a neutron star
• Neutron star inner crust: reduction of shear modulus by nuclei finite size effect
• Elastic properties of nuclear pasta in a fully three-dimensional geometry
• Oscillations and tidal deformations of crystallized white dwarfs
• Elastic properties of Yukawa crystals
• Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus
• Constraining shear modulus of polycrystalline neutron star crust: Hashin-Shtrikman variational approach