Neutron-star spindown and magnetic inclination-angle evolution

A rotating fluid star, endowed with a magnetic field, can undergo a form of precessional motion: a sum of rigid-body free precession and a non-rigid response. On secular timescales this motion is dissipated by bulk and shear viscous processes in the stellar interior and magnetospheric braking in the exterior, changing the inclination angle between the rotation and magnetic axes. Using our recent solutions for the non-rigid precessional dynamics, and viscous dissipation integrals derived in this paper, we make the only self-consistent calculation to date of these dissipation rates. We present the first results for the full coupled evolution of spindown and inclination angle for a model of a late-stage proto-neutron star with a strong toroidal magnetic field, allowing for both electromagnetic torques and internal dissipation when evolving the inclination angle. We explore this coupled evolution for a range of initial inclination angles, rotation rates and magnetic field strengths. For fixed initial inclination angle, our results indicate that the neutron-star population naturally evolves into two classes: near-aligned and near-orthogonal rotators -- with typical pulsars falling into the latter category. Millisecond magnetars can evolve into the near-aligned rotators which mature magnetars appear to be, but only for small initial inclination angle and internal toroidal fields stronger than roughly $5\times 10^{15}$ G. Once any model has evolved to either an aligned or orthogonal state, there appears to be no further evolution away from this state at later times.