Shear waves and giant-flare oscillations from soft gamma-ray repeaters

Recent observations of giant flares from soft gamma-ray repeaters have exhibited multiple similar to 25-150 Hz oscillations. Frequencies in this range are expected for toroidal shear waves in a neutron star (NS) crust, lending support to Duncan's proposal that such modes may be excited in these events. This motivates a reassessment of how these waves reflect the NS structure and what role the magnetic field plays in setting their frequencies. We calculate the eigenfrequencies and eigenfunctions of toroidal oscillations for a realistic NS crust, including a vertical magnetic field at magnetar strengths (B similar to 10(14)-10(15) G). The lowest radial-order mode has a redshifted frequency of approximate to 28 Hz[l(l + 1)/6](1/2) with the prefactor depending on the NS's mass and radius and its crust's depth and composition. This mode is independent of the magnetic field for B less than or similar to 4 x 10(15) G, a limit much greater than the inferred dipole magnetic fields for these objects. Although this is a good fit to the observed oscillations, only rather loose constraints can be made for the NSs' properties because all that can be fit is this prefactor ( a single parameter). Modes with shorter radial wavelengths are more sensitive to the magnetic field starting at and have higher frequencies (similar to 600-2000 Hz). The discovery of these modes, coupled with the oscillations observed thus far, would provide a powerful probe to the NS crustal structure.