Strong-field magnetohydrodynamics for neutron stars

Abstract

We present a formulation of magnetohydrodynamics which can be used to describe the evolution of strong magnetic fields in neutron star interiors. Our approach is based on viewing magnetohydrodynamics as a theory with a one-form global symmetry and developing an effective field theory for the hydrodynamic modes associated with this symmetry. In the regime where the local velocity and temperature variations can be neglected, we derive the most general constitutive relation consistent with symmetry constraints for the electric field in the presence of a strong magnetic field. This constitutive relation not only reproduces the phenomena of Ohmic decay, ambipolar diffusion, and Hall drift derived in a phenomenological model by Goldreich and Reisenegger, but also reveals new terms in the evolution of the magnetic field which cannot easily be seen from such microscopic models. This formulation gives predictions for novel diffusion behaviors of small perturbations around a constant background magnetic field, and for the two-point correlation functions among various components of the electric and magnetic fields.