Magnetars: super(ficially) hot and super(fluid) cool
We examine to what extent the inferred surface temperature of magnetars in quiescence can constrain the presence of a superfluid in the neutron star core and the role of magnetic field decay in the core. By performing detailed simulations of neutron star cooling, we show that extremely strong heating from field decay in the core cannot produce the high observed surface temperatures nor delay the onset of neutron superfluidity in the core. We verify the results of Kaminker et al., namely that the high magnetar surface temperatures require heating in the neutron star crust, and crust heating is decoupled from cooling/heating in the core. Therefore, because crust heating masks core heating, it is not possible to conclude that magnetar cores are in a non-superfluid state purely from high surface temperatures. From our interior temperature evolutions and after accounting for proton superconductivity in the core, we find that neutron superfluidity in the core occurs less than a few hundred years after neutron star formation. This onset time is unaffected by heating due to core field decay at fields < 10^16 G. Thus all known neutron stars, including magnetars, without a core containing exotic particles, should have a core of superfluid neutrons and superconducting protons.