Stratification, superfluidity and magnetar QPOs

The violent giant flares of magnetars excite QPOs which persist for hundreds of seconds, as seen in the X-ray tail following the initial burst. Recent studies, based on single-fluid barotropic magnetar models, have suggested that the lower-frequency QPOs correspond to magneto-elastic oscillations of the star. The higher frequencies, however, in particular the strong 625 Hz peak, have proved harder to explain, except as high mode multipoles. In this work we study the time evolutions of non-axisymmetric oscillations of two-fluid Newtonian magnetars with no crust. We consider models with superfluid neutrons and normal protons, and poloidal and toroidal background field configurations. We show that multi-fluid physics (composition-gradient stratification, entrainment) tends to increase Alfven mode frequencies significantly from their values in a single-fluid barotropic model. The higher-frequency magnetar QPOs may then be naturally interpreted as Alfven oscillations of the multi-fluid stellar core. The lower-frequency QPOs are less easily explained within our purely fluid core model, but we discuss the possibility that these are crustal modes.