Shear modulus of neutron star crust

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.Comment: 10 pages, 3 figures, accepted to MNRA

Breaking properties of neutron star crust

“…It is a widely employed approximation in NS literature (e.g., Haensel et al 2007;Chamel & Haensel 2008). In particular, it is known to predict elastic properties of the crust with reasonable accuracy (Baiko 2011(Baiko , 2015. Chugunov & Horowitz (2012) have analysed effects of electron screening on the breaking stress for the shear deformation and have demonstrated that screening reduced strength, but not very much.…”

“…Crystallisation of NS crust is an extremely slow and uniform process with plenty of time to anneal out any defects. Additionally, if a large-scale sufficiently strong magnetic field is present, crystallisation may proceed in a way that favours a particular orientation of crystal axes with respect to the magnetic field (Baiko 2011). As discussed in Subsection 3.3, merging of the crystallites may occur in the course of the plastic deformation.…”

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

“…The expressions for the coefficients Φ in terms of rapidly converging lattice sums are given in [4]. The Hamiltonian variation δĤ 2 naturally causes variation of the crystal thermodynamic functions.…”

“…Variation of the oscillatory part of the crystal Hamiltonian can also be expanded in powers of the displacement gradient and written as [4,6] …”

“…We discuss the effect of ion vibrations (see also [4]) and present new calculations of the contribution to the shear modulus due to the finite polarizability of the actual electron background.…”