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Keywords:

  • gravitational waves;
  • MHD;
  • stars: interiors;
  • stars: magnetic field;
  • stars: neutron

ABSTRACT

Recent calculations of the hydromagnetic deformation of a stratified, non-barotropic neutron star are generalized to describe objects with superconducting interiors, whose magnetic permeability μ is much smaller than the vacuum value μ0. It is found that the star remains oblate if the poloidal magnetic field energy is ≳40 per cent of the total magnetic field energy, that the toroidal field is confined to a torus which shrinks as μ decreases and that the deformation is much larger (by a factor of ∼μ0/μ) than that in a non-superconducting object. The results are applied to the latest direct and indirect upper limits on the gravitational-wave emission from the Laser Interferometer Gravitational Wave Observatory (LIGO) and radio pulse timing (spin-down) observations of 81 millisecond pulsars, to show how one can use these observations to infer the internal field strength. It is found that the indirect spin-down limits already imply astrophysically interesting constraints on the poloidal–toroidal field ratio and the diamagnetic shielding factor (by which accretion reduces the observable external magnetic field e.g. by burial). These constraints will improve following gravitational-wave detections, with implications for accretion-driven magnetic field evolution in recycled pulsars and the hydromagnetic stability of these objects’ interiors.