Mass And Radius Constraints Using Magnetar Giant Flare Oscillations. (arXiv:1303.3270v1 [astro-ph.HE])

Mass And Radius Constraints Using Magnetar Giant Flare Oscillations. (arXiv:1303.3270v1 [astro-ph.HE]):
We study crustal oscillations in magnetars including corrections for a finite
Alfv\'en 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 recent
developments in the nuclear physics, in particular, 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 (QPO)
frequencies from SGR 1806-20. The QPOs associated with the fundamental and
first harmonic can be used to constrain magnetar masses and radii. We use these
modes and the phenomenological equations of state from Steiner et al. to find a
magnetar crust which reproduces observations of 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. Matching observations with a field-free model we obtain
the approximate values of M =1.35 Msun and R = 11.9 km. Matching observations
using a model with the surface dipole field of SGR 1806-20 (B=2.4x10^15 G) we
obtain the approximate values of M = 1.25 Msun and R = 12.4 km. Without
significant entrainment of the free neutron gas the magnetar requires a larger
mass and radius to reproduce observations. If the crust-core transition occurs
at a lower density the magnetar requires a lower mass and a larger radius to
reproduce observations.