Magnetar Oscillations I: strongly coupled dynamics of the crust and the core

Quasi-Periodic Oscillations (QPOs) observed at the tail end of Soft Gamma Repeaters giant flares are com-monly interpreted as the torsional oscillations of magnetars. From a theoretical perspective, the oscillatory motion is influenced by the strong interaction between the shear modes of the crust and magnetohydro-dynamic Alfven-like modes in the core. We study the dynamics which arises through this interaction, and present several new results: (1) We show that discrete edge modes frequently reside near the edges of the core Alfven continuum, and explain using simple models why these are generic and long-lived. (2) We compute the magnetar’s oscillatory motion for realistic axisymmetric magnetic field configurations and core density profiles, but with a simplified model of the elastic crust. We show that one may generically get multiple gaps in the Alfven continuum. One obtains strong discrete gap modes if the crustal frequencies belong to the gaps; the resulting frequencies do not coincide with, but are in some cases close to the crustal frequencies. (3) We deal with the issue of tangled magnetic fields in the core by developing a phenomenological model to quantify the tangling. We show that field tangling enhances the role of the core discrete Alfven modes and reduces the role of the core Alfven continuum in the overall oscillatory dynamics of the magnetar. (4) We demonstrate that the system displays transient QPOs when parts of the spectrum of the core Alfve