Using the energy variational method of magnetosolid-mechanical theory of a perfectly conducting elastic medium threaded by magnetic field, the frequency spectrum of Lorentz-force-driven global torsional nodeless vibrations of a neutron star with Ferraro's form of axisymmetric poloidal nonhomogeneous internal and dipole-like external magnetic field is obtained and compared with that for this toroidal Alfvén mode in a neutron star with homogeneous internal and dipolar external magnetic field. The relevance of considered asteroseismic models to quasi-periodic oscillations of the X-ray flux during the ultra powerful outbursts of SGR 1806−20 and SGR 1900+14 is discussed.
The fluid-dynamical model of a self-gravitating mass of viscous liquid with singular density at the center vibrating in fundamental mode is considered in juxtaposition with that for Kelvin fundamental mode in a homogeneous heavy mass of incompressible inviscid liquid. Particular attention is given to the difference between spectral formulae for the frequency and lifetime of f -mode in the singular and homogeneous models. The newly obtained results are discussed in the context of theoretical asteroseismology of pre-white dwarf stage of red giants and stellar cocoons -spherical gas-dust clouds with dense star-forming core at the center.
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