Shear modulus of neutron star crust

TL;DR

This paper calculates the shear modulus of neutron star crust considering ion motion, including quantum effects, providing new insights into low-temperature behavior and offering formulas for neutron star oscillation modeling.

Contribution

It introduces the first quantum calculations of shear modulus in neutron star crust and provides fitting formulas for use in stellar seismology.

Findings

Shear modulus includes static lattice and ion motion contributions.

Ion motion contribution saturates at low temperatures due to zero-point vibrations.

Quantum effects are significant for lighter elements at high densities.

Abstract

Shear modulus of solid neutron star crust is calculated by thermodynamic perturbation theory taking into account ion motion. At given density the crust is modelled as a body-centered cubic Coulomb crystal of fully ionized atomic nuclei of one type with the uniform charge-compensating electron background. Classic and quantum regimes of ion motion are considered. The calculations in the classic temperature range agree well with previous Monte Carlo simulations. At these temperatures the shear modulus is given by the sum of a positive contribution due to the static lattice and a negative $\propto T$ contribution due to the ion motion. The quantum calculations are performed for the first time. The main result is that at low temperatures the contribution to the shear modulus due to the ion motion saturates at a constant value, associated with zero-point ion vibrations. Such behavior is qualitatively similar to the zero-point ion motion contribution to the crystal energy. The quantum effects may be important for lighter elements at higher densities, where the ion plasma temperature is not entirely negligible compared to the typical Coulomb ion interaction energy. The results of numerical calculations are approximated by convenient fitting formulae. They should be used for precise neutron star oscillation modelling, a rapidly developing branch of stellar seismology.