Tilted torus magnetic fields in neutron stars and their gravitational wave signatures

Gravitational-wave diagnostics are developed for discriminating between varieties of mixed poloidal-toroidal magnetic fields in neutron stars, with particular emphasis on differentially rotating protoneutron stars. It is shown that tilted torus magnetic fields, defined as the sum of an internal/external poloidal component, whose axis of symmetry is tilted with respect to the rotation axis, and an internal toroidal component, whose axis of symmetry is aligned with the rotation axis, deform the star triaxially, unlike twisted torus fields, which deform the star biaxially. Utilizing an analytic tilted torus example, we show that these two topologies can be distinguished by their gravitational wave spectrum and polarization phase portraits. For example, the relative amplitudes and frequencies of the spectral peaks allows one to infer the relative strengths of the toroidal and poloidal components of the field, and the magnetic inclination angle. Finally, we show how a tilted torus field arises naturally from magnetohydrodynamic simulations of differentially rotating neutron stars, and how the gravitational wave spectrum evolves as the internal toroidal field winds up. These results point to the sorts of experiments that may become possible once gravitational wave interferometers detect core-collapse supernovae routinely.