Abstract:The electromagnetic fields and magnetosphere of a slowly rotating magnetized neutron star subject to toroidal oscillations in the relativistic regime are studied. We analyze the Goldreich–Julian charge density and derive the modification induced by stellar toroidal oscillations on the accelerating electric field and on the charge density in the polar cap. We also find that, after decomposing the oscillation velocity in terms of spherical harmonics, the first few modes with m = 0, 1 are responsible for energy losses that are almost linearly dependent on the amplitude of the oscillation and that, for the mode (l,m) = (2, 1), can be a factor about 8 larger than the rotational energy losses, even for a velocity oscillation amplitude at the star surface small. The results obtained clarify the extent to which stellar oscillations are reflected in the time variation of the physical properties at the surface of the rotating neutron star, mainly by showing the existence of a relation between spindown and the oscillation amplitude. We propose a qualitative model for the explanation of the phenomenology of intermittent pulsars. The idea is that stellar oscillations, periodically excited by star glitches, can create relativistic winds of charged particles because of the additional electric field. When the stellar oscillations damp, the pulsar shifts below the death line in the P–B diagram, thus entering the OFF invisible state of intermittent pulsars. The conditions for radio emission in rotating and oscillating magnetars by focusing on the main physical processes determining the position of their death lines, i.e. of those lines that separate the regions where the neutron star may be radio loud or radio quiet. We find that larger compactness parameters of the star as well as larger inclination angles between the rotation axis and the magnetic moment produce death lines well above the majority of known magnetars. This is consistent with the observational evidence of no regular radio emission from the magnetars in the frequency range typical for the ordinary pulsars. On the contrary, when oscillations of the magnetar are taken into account, the death lines shift downward and the conditions necessary for the generation of radio emission in the magnetosphere are met. Present observations showing a close connection between the burst activity of magnetars and the generation of the radio emission in the magnetar magnetosphere are naturally accounted within our interpretation.