Spheroidal and torsional modes of quasistatic shear oscillations in the solid globe models of nuclear physics and pulsar astrophysics

Abstract

The past three decades of investigation on nuclear physics and pulsar astrophysics have seen gradual recognition that elastodynamic approach to the continuum mechanics of nuclear matter provides proper account of macroscopic motions of degenerate Fermi-matter constituting interior of the nuclear material objects, the densest of all known today. This paper focuses on one theoretical issue of this development which is concerned with oscillatory behavior of a viscoelastic solid globe in the regime of quasistatic, force-free, non-compressional oscillations less investigated in the literature compared to oscillations in the regime of standing shear waves. We show that in this case the problem of computing frequency and lifetime of spheroidal and torsional modes of non-radial shear vibrations damped by viscosity can be unambiguously resolved by working from the energy balance equation and taking advantage of the Rayleigh's variational method. The efficiency of this method is demonstrated by solid globe models of nuclear physics and pulsar astrophysics dealing with oscillations of a spherical mass of a viscoelastic Fermi-solid with homogeneous and non-homogeneous profiles of the bulk density, the shear modulus, and the shear viscosity.