The evolution of the core and surface magnetic fields in isolated neutron stars

We apply the model of flux expulsion from the superfluid and superconductiv e core of a neutron star, developed by Konenkov & Geppert, both to neutron star models based on different equations of state and to different initial magnetic field structures. Initially, when the core and the surface magneti c field are of the same order of magnitude, the rate of flux expulsion from the core is almost independent of the equation of state, and the evolution of the surface field decouples from the core field evolution with increasi ng stiffness. When the surface field is initially much stronger than the co re field, the magnetic and rotational evolution resembles that of a neutron star with a purely crustal field configuration; the only difference is the occurrence of a residual field. In the case of an initially submerged fiel d, significant differences from the standard evolution only occur during th e early period of the life of a neutron star, until the field has been re-d iffused to the surface. The reminder of the episode of submergence is a cor relation of the residual field strength with the submergence depth of the i nitial field. We discuss the effect of the re-diffusion of the magnetic fie ld on the difference between the real and the active age of young pulsars a nd on their braking indices. Finally, we estimate the shear stresses built up by the moving fluxoids at the crust-core interface and show that these s tresses may cause crust cracking, preferentially in neutron stars with a so ft equation of state.