Creation of magnetic spots at the neutron star surface

According to the partially screened gap scenario, an efficient electron-positron pair creation, a general precondition of radio-pulsar activity, relies on the existence of magnetic spots, i.e., local concentrations of strong and small scale magnetic field structures at the surface of neutron stars. They have a strong impact on the surface temperature, which is potentially observable. Here we reinforce the idea that such magnetic spots can be formed by extracting magnetic energy from the toroidal field that resides in deep crustal layers, via Hall drift. We study and discuss the magneto-thermal evolution of qualitatively different neutron star models and initial magnetic field configurations that lead to the creation of magnetic spots. We find that magnetic spots can be created on a timescale of $10^4$ years with magnetic field strengths $\gtrsim 5\times 10^{13}$ G, provided almost the whole magnetic energy is stored in its toroidal component, and that the conductivity in the inner crust is not too large. The lifetime of the magnetic spots is at least $\sim$one million of years, being longer if the initial field permeates both core and crust.