Abstract
Within the framework of Newtonian magneto-solid mechanics, relying on equations appropriate for a perfectly conducting elastic continuous medium threaded by a uniform magnetic field, the asteroseismic model of a neutron star undergoing axisymmetric global torsional nodeless vibrations under the combined action of Hooke's elastic and Lorentz magnetic forces is considered with emphasis on a toroidal Alfvén mode of differentially rotational vibrations about the dipole magnetic-moment axis of the star. The obtained spectral equation for frequency is applied to ℓ-pole identification of quasi-periodic oscillations (QPOs) of the X-ray flux during the giant flares of SGR 1806-20 and SGR 1900+14. Our calculations suggest that detected QPOs can consistently be interpreted, within the framework of this model, as being produced by global torsional nodeless vibrations of a quaking magnetar if they are considered to be restored by the joint action of bulk forces of shear elastic and magnetic field stresses. © 2009. The American Astronomical Society. All rights reserved..