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

A recipe is presented to construct an analytic, self-consistent model of a non-barotropic neutron star with a poloidal-toroidal field of arbitrary multipole order, whose toroidal component is confined in a torus around the neutral curve inside the star, as in numerical simulations of twisted tori. The recipe takes advantage of magnetic-field-aligned coordinates to ensure continuity of the mass density at the surface of the torus. The density perturbation and ellipticity of such a star are calculated in general and for the special case of a mixed dipole-quadrupole field as a worked example. The calculation generalises previous work restricted to dipolar, poloidal-toroidal and multipolar, poloidal-only configurations. The results are applied, as an example, to magnetars whose observations (e.g., spectral features and pulse modulation) indicate that the internal magnetic fields may be at least one order of magnitude stronger than the external fields, as inferred from their spin downs, and are not purely dipolar.Comment: 14 pages, 6 figures, 1 table. Accepted for publication in the Monthly Notices of the Royal Astronomical Societ

A Check on the Validity of Magnetic Field Reconstructions

We investigate a method to test whether a numerically computed model coronal magnetic field B departs from the divergence-free condition (also known as the solenoidality condition). The test requires a potential field B0 to be calculated, subject to Neumann boundary conditions, given by the normal components of the model field B at the boundaries. The free energy of the model field may be calculated using the volume integral of (B-B0)^2, where the integral is over the computational volume of the model field. A second estimate of the free energy is provided by calculating the difference between the volume integral of B^2 and the volume integral of B0^2. If B is divergence-free, the two estimates of the free energy should be the same. A difference between the two estimates indicates a departure from div B = 0 in the volume. The test is an implementation of a procedure proposed by Moraitis et al. (Sol. Phys. 289, 4453, 2014) and is a simpler version of the Helmholtz decomposition procedure presented by Valori et al. (Astron. Astrophys. 553, A38, 2013). We demonstrate the test in application to previously published nonlinear force-free model fields, and also investigate the influence on the results of the test of a departure from flux balance over the boundaries of the model field. Our results underline the fact that, to make meaningful statements about magnetic free energy in the corona, it is necessary to have model magnetic fields which satisfy the divergence-free condition to a good approximation.Australian Research Counci