Elastic or magnetic? A toy model for global magnetar oscillations with implications for QPOs during flares

We use a simple toy-model to discuss global MHD modes of a neutron star, taking into account the magnetic coupling between the elastic crust and the fluid core. Our results suggest that the notion of pure torsional crust modes is not useful for the coupled system, all modes excite Alfven waves in the core. However, we also show that the modes that are most likely to be excited by a fractured crust, eg. during a magnetar flare, are such that the crust and the core oscillate in concert. For our simple model, the frequencies of these modes are similar to the ``pure crustal'' frequencies. In addition, our model provides a natural explanation for the presence of lower frequency ($< 30$~Hz) QPOs seen in the December 2004 giant flare of SGR 1806-20.