Neutron star inner crust: reduction of shear modulus by nuclei finite size effect

Abstract

ABSTRACT The elasticity of neutron star crust is important for adequate interpretation of observations. To describe elastic properties one should rely on theoretical models. The most widely used is Coulomb crystal model (system of point-like charges on neutralizing uniform background), in some works it is corrected for electron screening. These models neglect finite size of nuclei. This approximation is well justified except for the innermost crustal layers, where nuclei size becomes comparable with the inter-nuclear spacing. Still, even in those dense layers it seems reasonable to apply the Coulomb crystal result, if one assumes that nuclei are spherically symmetric: Coulomb interaction between them should be the same as interaction between point-like charges. This argument is indeed correct; however, as we point here, shear of crustal lattice generates (microscopic) quadrupole electrostatic potential in a vicinity of lattice cites, which induces deformation on the nuclei. We analyse this problem analytically within compressible liquid drop model. In particular, for ground state crust composition the effective shear modulus is reduced for a factor of $1-u^{5/3}/(2+3\, u-4\, u^{1/3})$, where u is the ratio of the nuclei volume to the volume of the cell. This result is universal, i.e. it does not depend on the applied nucleon interaction model within applied approach. For the innermost layers of inner crust u ∼ 0.2 leading to reduction of the shear modulus by $\sim 25{{\ \rm per\ cent}}$, which can be important for correct interpretation of quasi-periodic oscillations in the tails of magnetar flares.