Frequency spectrum of toroidal Alfv\'en mode in a neutron star with Ferraro's form of nonhomogeneous poloidal magnetic field

TL;DR

This paper derives the frequency spectrum of toroidal Alfvén modes in neutron stars with nonhomogeneous magnetic fields, comparing it to the homogeneous case, and discusses implications for observed X-ray oscillations.

Contribution

It introduces a model for neutron star torsional vibrations with Ferraro's nonhomogeneous magnetic field, extending previous homogeneous field models.

Findings

Frequency spectrum differs significantly from the homogeneous case.

Model explains quasi-periodic oscillations in magnetar outbursts.

Provides a framework for asteroseismic analysis of neutron stars.

Abstract

Using the energy variational method of magneto-solid-mechanical theory of a perfectly conducting elastic medium threaded by magnetic field, the frequency spectrum of Lorentz-force-driven global torsional nodeless vibrations of a neutron star with Ferraro's form of axisymmetric poloidal nonhomogeneous internal and dipole-like external magnetic field is obtained and compared with that for this toroidal Alfv\'en mode in a neutron star with homogeneous internal and dipolar external magnetic field. The relevance of considered asteroseismic models to quasi-periodic oscillations of the X-ray flux during the ultra powerful outbursts of SGR 1806-20 and SGR 1900+14 is discussed.