Journal of Physics G: Nuclear and Particle Physics vol. 29, no. 4, pp. 683 - 695
A macroscopic model of the dissipative magneto-elastic dynamics of viscous spin polarized nuclear matter is discussed in the context of seismic activity of a paramagnetic neutron star. The source of the magnetic field of such a star is attributed to Pauli paramagnetism of baryon matter promoted by a seed magnetic field frozen into the star in the process of gravitational collapse of a massive progenitor. Particular attention is given to the effect of shear viscosity of incompressible stellar material on the timing of non-radial torsional magnetoelastic pulsations of the star triggered by starquakes. By accentuating the fact that this kind of vibration is unique to the seismology of a paramagnetic neutron star we show that the high-frequency modes decay faster than the low-frequency modes. The obtained analytic expressions for the period and relaxation time of this mode, in which the magnetic susceptibility and viscosity enter as input parameters, are then quantified by numerical estimates for these parameters taken from early and current works on transport coefficients of dense matter. It is found that the effect of viscosity is crucial for the lifetime of magnetotorsion vibrations but it does not appreciably affect the periods of this seismic mode which fall in the realm of periods of pulsed emission of soft gamma-ray repeaters and anomalous x-ray pulsars - young super-magnetized neutron stars, radiating, according to the magnetar model, at the expense of the magnetic energy release. Finally, we present arguments that the long periodic pulsed emission of these stars in a quiescent regime of radiation can be interpreted as a manifestation of weakly damped seismic magneto-torsion vibrations exhibiting the field induced spin polarization of baryon matter.