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Role of nuclear physics in oscillations of magnetars

Strong magnetic fields have important effects on the crustal properties of magnetars. Here we study the magneto-elastic oscillations of magnetars taking into consideration the effect of strong magnetic fields on the crustal composition (magnetised crust). We calculate global magneto-elastic (GME) modes as well as modes confined to the crust (CME) only. The composition of the crust directly affects its shear modulus which we calculate using three different nucleon-nucleon interactions: SLy4, SkM and Sk272. The shear modulus of the crust is found to be enhanced in strong magnetic fields $\geq 10^{17}$ G for all those Skyrme interactions. It is noted that the shear modulus of the crust for the SLy4 interaction is much higher than those of the SkM and Sk272 interactions in presence of magnetic fields or not. Though we do not find any appreciable change in frequencies of fundamental GME and CME modes with and without magnetised crusts, frequencies of first overtones of CME modes are significantly affected in strong magnetic fields $\geq 10^{17}$ G. However, this feature is not observed in frequencies of first overtones of GME modes. As in earlier studies, it is also noted that the effects of crusts on frequencies of both types of maneto-elastic modes disappear when the magnetic field reaches the critical field ($B > 4 \times 10^{15}$ G). Frequencies of GME and CME modes calculated with magnetised crusts based on all three nucleon-nucleon interactions, stellar models and magnetic fields, are compared with frequencies of observed quasi-periodic oscillations (QPOS) in SGR 1806-20 and SGR1900+14. As in earlier studies, this comparison indicates that GME modes are essential to explain all the frequencies as CME modes can explain only the higher frequencies.