The Elasticity of the Neutron Star Mantle: The Improved Compressible Liquid Drop Model for Cylindrical Phases

Abstract

Neutron stars are the densest objects in the Universe. They have a microscopically homogeneous core and heterogeneous crust. In particular, there may be a specific layer inside neutron stars, the mantle, which consists of substantially non-spherical nuclei immersed in a background of relativistic degenerate electrons and quasi-free neutrons. In this paper, we reconsider the transverse shear modulus for cylindrical phases of the mantle within the framework of the compressible liquid drop model. We demonstrate that transverse shearing affects the shape of nuclear clusters: their cross-section becomes elliptical. This effect reduces the respective elastic constant. Using a simple model, we perform all derivations analytically and obtain the expression for the transverse shear modulus, which can be useful for astrophysical applications.