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Observations of magnetars and some of the high magnetic field pulsars haveshown that their thermal luminosity is systematically higher than that ofclassical radio-pulsars, thus confirming the idea that magnetic fields areinvolved in their X-ray emission. Here we present the results of 2D simulationsof the fully-coupled evolution of temperature and magnetic field in neutronstars, including the state-of-the-art kinetic coefficients and, for the firsttime, the important effect of the Hall term. After gathering and thoroughlyre-analysing in a consistent way all the best available data on isolated,thermally emitting neutron stars, we compare our theoretical models to a datasample of 40 sources. We find that our evolutionary models can explain thephenomenological diversity of magnetars, high-B radio-pulsars, and isolatednearby neutron stars by only varying their initial magnetic field, mass andenvelope composition. Nearly all sources appear to follow the expectations ofthe standard theoretical models. Finally, we discuss the expected outburstrates and the evolutionary links between different classes. Our resultsconstitute a major step towards the grand unification of the isolated neutronstar zoo.

Unifying the observational diversity of isolated neutron stars via magneto-thermal evolution models