Updated gravitational-wave upper limits on the internal magnetic field strength of recycled pulsars

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 μ 0. 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 ~μ 0/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 Gravitation..