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Magneto-elastic oscillations of neutron stars with dipolar magnetic fields

By means of two dimensional, general-relativistic, magneto-hydrodynamical simulations we investigate the oscillations of magnetized neutron star models (magnetars) including the description of an extended solid crust. The aim of this study is to understand the origin of the QPOs observed in the giant flares of SGRs. We confirm the existence of three different regimes: (a) a weak magnetic field regime B<5 x 10^13 G, where crustal shear modes dominate the evolution; (b) a regime of intermediate magnetic fields 5 x 10^13 G<B< 10^15 G, where Alfvén QPOs are mainly confined to the core of the neutron star and the crustal shear modes are damped very efficiently; and (c) a strong field regime B>10^15 G, where magneto-elastic oscillations reach the surface and approach the behavior of purely Alfvén QPOs. When the Alfvén QPOs are confined to the core of the neutron star, we find qualitatively similar QPOs as in the absence of a crust. The lower QPOs associated with the closed field lines of the dipolar magnetic field configuration are reproduced as in our previous simulations without crust, while the upper QPOs connected to the open field lines are displaced from the polar axis. Additionally, we observe a family of edge QPOs. Our results do not leave much room for a crustal-mode interpretation of observed QPOs in SGR giant flares, but can accommodate an interpretation of these observations as originating from Alfvén-like, global, turning-point QPOs in models with dipolar magnetic field strengths in the narrow range of 5 x 10^15 G < B < 1.4 x 10^16 G. This range is somewhat larger than estimates for magnetic field strengths in known magnetars. The discrepancy may be resolved in models including a more complicated magnetic field structure or with models taking superfluidity of the neutrons and superconductivity of the protons in the core into account.