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A recipe is presented to construct an analytic, self-consistent model of anon-barotropic neutron star with a poloidal-toroidal field of arbitrarymultipole order, whose toroidal component is confined in a torus around theneutral curve inside the star, as in numerical simulations of twisted tori. Therecipe takes advantage of magnetic-field-aligned coordinates to ensurecontinuity of the mass density at the surface of the torus. The densityperturbation and ellipticity of such a star are calculated in general and forthe special case of a mixed dipole-quadrupole field as a worked example. Thecalculation generalises previous work restricted to dipolar, poloidal-toroidaland multipolar, poloidal-only configurations. The results are applied, as anexample, to magnetars whose observations (e.g., spectral features and pulsemodulation) indicate that the internal magnetic fields may be at least oneorder of magnitude stronger than the external fields, as inferred from theirspin downs, and are not purely dipolar.

Neutron star deformation due to poloidal-toroidal magnetic fields of arbitrary multipole order: a new analytic approach