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Neutron star magnetic field evolution is mediated through the Hall effect andOhmic dissipation in the crust while ambipolar diffusion is taking place in thecore. These effects have been studied in detail in either part of the star,however, their combined, simultaneous evolution and interplay has not beenexplored in detail yet. Here, we present simulation results of the simultaneousevolution of the magnetic field in the core due to ambipolar diffusion and thecrust due to Hall effect and Ohmic decay, under the assumption of axialsymmetry. We find that a purely poloidal field generates a toroidal field inthe crust, due to the Hall effect, that sinks into the core. A purely toroidalfield remains toroidal and spreads into the core and the crust. Finally, for amixed poloidal-toroidal field, the north-south symmetry is broken due to theHall effect in the crust, however, ambipolar diffusion, tends to restore it. Weexamine the role of ambipolar diffusion to the magnetic field decay and wecompare the rate of the conversion of magnetic field energy into heat, findingthat it enhances the magnetic field decay in neutron stars.

Combined magnetic field evolution in neutron star cores and crusts: Ambipolar diffusion, Hall effect and Ohmic dissipation