QPOs during magnetar flares are not driven by mechanical normal modes of the crust

Quasi-Periodic Oscillations (QPOs) have been observed during three powerful magnetar flares, from SGR0526-66, SGR1806-20 and SGR1900+14. These QPOs have been commonly interpreted as being driven by the mechanical modes of the magnetar's solid crust which are excited during the flare. Here we show that this interpretation is in sharp contradiction with the conventional magnetar model. Firstly, we show that a magnetar crustal mode decays on the timescale of at most a second due to the emission of Alfven waves into the neutron-star interior. A possible modification is then to assume that the QPOs are associated with the magnetars' global modes. However, we argue that at the frequencies of the observed QPOs, the neutron-star core is likely to support a continuum of Magneto-Hydrodynamic (MHD) normal modes. We demonstrate this on a completely solvable toy model which captures the essential physics of the system. We then show that the frequency of the global mode of the whole star is likely to have a significant imaginary component, and its amplitude is likely to decay on a short timescale. This is not observed. Thus we conclude that either (i) the origin of the QPO is in the magnetar's magnetosphere, or (ii) the magnetic field has a special configuration: either it is expelled from the magnetar's core prior to the flares, or its poloidal component has very small coherence length.