The stability of global non-radial pulsations of neutron stars

A neutron star is the cosmic nuclear object in which the energy of gravitational pull is brought to equilibrium by elastic energy stored in the neutron Fermi-continuum. Evidence for the viscoelastic behaviour of a stellar nuclear matter provides a seismological model of pulsar glitches interpreted as a sudden release of the elastic energy. In laboratory nuclear physics, the signatures of viscoelasticity of nuclear matter are found in the current investigations on the collective nuclear dynamics, in which a heavy nucleus is modelled by a spherical piece of viscoelastic Fermi-continuum compressed to the normal nuclear density. It is plausible to expect, therefore, that the motions of self-gravitating nuclear matter constituting the interior of neutron stars should be governed by the equations of an elastic solid, rather than by hydrodynamic equations describing the behaviour of gaseous plasma inside the main sequence stars. In this paper, we present arguments that elastodynamic equations, originally introduced in the context of nuclear collective dynamics, can provide a proper account of elasticity in the large scale motions of neutron matter under its own gravity. Emphasis is placed on mathematical physics underlying the constructive description of the continuum mechanics and the rheology of macroscopic nuclear matter. The capability of the elastodynamic approach is examined by analysis of oscillatory dynamics of a neutron star in the standard homogenous model, operating with a spherical mass of self-gravitating degenerate neutron matter whose viscoelastic behaviour is described in terms of the spheroidal and torsional gravitational-elastic eigenmodes, inherenly related to viscoelasticy. The energy variational principle is utilized to compute the frequencies of viscoelastic gravitational pulsations and their relaxation time. The method is demonstrated for both the idealized homogeneous model and the neutron star models constructed on realistic equations of state. Finally, we derive analytic conditions for the stability of a neutron star to linear elastic deformations accompanying the non-radial pulsations, and discuss the fingerprints of these pulsations in the electromagnetic activity of radiopulsars.