Magnetar Oscillations II: spectral method

TL;DR

This paper develops a spectral computational framework to study magnetar oscillations, enabling fast, detailed simulations of crust-core coupling and revealing rapid energy drainage of high-frequency modes, which challenges existing explanations for observed QPOs.

Contribution

It introduces a relativistic spectral method for modeling magnetar oscillations, allowing precise and efficient simulation of crust-core interactions and mode localization.

Findings

High-frequency crustal modes localize in nearly horizontal magnetic field regions.

Localized modes have reduced coupling to the core Alfven continuum.

Energy drains from these modes in less than one second, questioning their role in observed QPOs.

Abstract

The seismological dynamics of magnetars is largely determined by a strong hydro-magnetic coupling between the solid crust and the fluid core. In this paper we set up a "spectral" computational framework in which the magnetar's motion is decomposed into a series of basis functions which are associated with the crust and core vibrational eigenmodes. A general-relativistic formalism is presented for evaluation of the core Alfven modes in the magnetic-flux coordinates, as well for eigenmode computation of a strongly magnetized crust of finite thickness. By considering coupling of the crustal modes to the continuum of Alfven modes in the core, we construct a fully relativistic dynamical model of the magnetar which allows: i) Fast and long simulations without numerical dissipation. ii) Very fine sampling of the stellar structure. We find that the presence of strong magnetic field in the crust results in localizing of some high-frequency crustal elasto-magnetic modes with the radial number n>1 to the regions of the crust where the field is nearly horizontal. While the hydro-magnetic coupling of these localized modes to the Alfven continuum in the core is reduced, their energy is drained on a time-scale much less than 1 second. Therefore the puzzle of the observed QPOs with frequencies larger than 600 Hz still stands.