3-D Evolution of the Crustal Magnetic Field in Neutron Stars

The evolution of the crustal magnetic field in neutron stars is mediated by two processes: Hall drift and Ohmic dissipation. Hall drift is the advection of the magnetic field lines by freely moving electrons in the rigid crust and dominates the evolution for magnetic fields above 10^13 G. While the Hall effect conserves energy, it has been suggested that it can accelerate Ohmic dissipation; however axially symmetric calculations so far have found only a modest increase in the decay rate when the Hall effect is included, compared to pure Ohmic dissipation. We find that, unlike the axially symmetric calculations, the magnetic field evolution in 3-D is susceptible to instabilities, provided that ~50% of the magnetic field energy is in the toroidal component of the field. These instabilities severely deform the large-scale structure of the field and lead to the formation of kilometer-sized structures where the magnetic field intensity is an order of magnitude higher than the spin-down dipole field. These localised magnetic fields are sites of efficient dissipation generating heat. Furthermore, the strong Maxwell stresses developed can trigger magnetar activity. Thus, we suggest that the Hall effect is capable of rearranging the magnetic field in a neutron star crust creating "magnetic spots" where the intensity is above 10^15 G while the dipole field is ~10^14. This makes magnetar theory more economical as it removes the need for extremely strong concealed magnetic fields while it provides a natural mechanism for the creation of hotspots suggested by observations .

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