Abstract
We present several exact solutions of the eigenfrequency problem for torsional shear vibrations in homogeneous and non-homogeneous models of the neutron star crust governed by the canonical equation of solid mechanics with a restoring force of Hookean elasticity. Particular attention is given to the regime of large-lengthscale nodeless axisymmetric differentially rotational oscillations, which are treated in spherical polar coordinates, reflecting the real geometry of the neutron star crust. We highlight the distinction between analytic solutions, computed as a function of the multipole degree of nodeless torsional oscillations and fractional depth of the crust, caused by different boundary conditions imposed on the toroidal field of material displacements. The relevance of the considered models to quasiperiodic oscillations, recently detected during the flare of SGR 1806-20 and SGR 1900+14, is discussed. © 2007 The Authors.