Magnetar giant flare oscillations and the nuclear symmetry energy

If the observed quasi-periodic oscillations in magnetar flares are partially confined to the crust, then the oscillation frequencies are unique probes of the nuclear physics of the neutron star crust. We study crustal oscillations in magnetars including corrections for a finite Alfven velocity. Our crust model uses a new nuclear mass formula that predicts nuclear masses with an accuracy very close to that of the finite range droplet model. This mass model for equilibrium nuclei also includes shell corrections and an updated neutron-drip line. We perturb our crust model to predict axial crust modes and assign them to observed giant flare quasi-periodic oscillation frequencies from the soft gamma-ray repeater SGR 1806-20. We find magnetar crusts that match observations for various magnetic field strengths, entrainment of the free neutron gas in the inner crust, and crust-core transition densities. We find that observations can be reconciled with smaller values of the symmetry energy slope parameter, L, if there is a significant amount of entrainment of the neutrons by the superfluid or if the crust-core transition density is large. We also find neutron star masses and radii which are in agreement with expectations from what is known about low-density matter from nuclear experiment. Matching observations with a field-free model we obtain the approximate values of M = 1.35 M-circle dot and R = 11.9 km. Matching observations using a model with the surface dipole field of SGR 1806-20 ( B = 2.4 x 10(15) G) we obtain the approximate values of M = 1.25 M-circle dot and R = 12.4 km.