Nodeless differentially rotational Alfv\'en oscillations of crustal solid-state plasma in quaking neutron star

TL;DR

This paper models nodeless, differentially rotational Alfvén oscillations in the crust of neutron stars, linking these vibrations to observed X-ray flux oscillations during magnetar flares.

Contribution

It introduces a two-parametric spectral formula for torsional Alfvén modes that explains rapid X-ray oscillations in magnetar flares, based on a core-crust neutron star model.

Findings

The spectral formula accurately predicts observed oscillation frequencies.

The oscillations are driven by magnetic Lorentz forces in the crust.

The model supports the link between crustal vibrations and X-ray flux variations.

Abstract

The two-component, core-crust, model of a neutron star with homogenous internal and dipolar external magnetic field is studied responding to quake-induced perturbation by substantially nodeless differentially rotational Alfv\'en oscillations of the perfectly conducting crustal matter about axis of fossil magnetic field frozen in the immobile core. The energy variational method of the magneto-solid-mechanical theory of a viscoelastic perfectly conducting medium pervaded by magnetic field is utilized to compute the frequency and lifetime of nodeless torsional vibrations of crustal solid-state plasma about the dipole magnetic-moment axis of the star. It is found that obtained two-parametric spectral formula for the frequency of this toroidal Alfven mode provides fairly accurate account of rapid oscillations of the X-ray flux during the flare of SGR 1806-20 and SGR 1900+14, supporting the investigated conjecture that these quasi-periodic oscillations owe its origin to axisymmetric torsional oscillations predominately driven by Lorentz force of magnetic field stresses in the finite-depth crustal region of the above magnetars.