Quasi-periodic oscillations in superfluid, relativistic magnetars with nuclear pasta phases

We study the torsional magneto-elastic oscillations of relativistic superfluid magnetars and explore the effects of a phase transition in the crust-core interface (nuclear pasta) which results in a weaker elastic response. Exploring various models with different extension of nuclear pasta phases, we find that the differences in the oscillation spectrum present in purely elastic modes (weak magnetic field), are smeared out with increasing strength of the magnetic field. For magnetar conditions, the main characteristic and features of models without nuclear pasta are preserved. We find in general two classes of magneto-elastic oscillations which exhibit a different oscillation pattern. For B_p < 4 x 10^{14} G, the spectrum is characterised by the turning points and edges of the continuum which are confined into the star's core, and have no constant phase. Increasing the magnetic field, we find, in addition, several magneto-elastic oscillations which reach the surface and have an angular structure similar to crustal modes. These global magneto-elastic oscillations show a constant phase and become dominant when B_p > 5 x 10^{14} G. We do not find any evidence of fundamental pure crustal modes in the low frequency range (below 200 Hz) for B_p >= 10^{14} G.