Passively cooling neutron stars would reach very low surface temperatures $T_s < 10^4$ K within $<10^7$ yr. However, likely thermal UV emission has been detected in HST observations of 4 much older neutrons stars (2 “classical” and 2 millisecond pulsars), implying $T_s ∼ 10^5$ K.
We computed their evolution with different heating mechanisms, finding that the relevant ones are rotochemical heating and vortex creep. The former consists of non-equilibrium beta reactions induced by the continuous spin-down of the NS. If there are superfluid nucleons in its core, chemical energy is stored until a threshold is reached. Then, part of the energy is rapidly released, raising the temperature. If the protons in the core are superconducting, the magnetic flux is concentrated in quantized flux tubes. Outside the flux tube cores, protons are superconducting, while inside they remain non-superconducting, so reactions occur mostly inside. Vortex creep is the friction of the quantized neutron vortices moving through the NS crust.
We find that all the observations can be explained by rotochemical heating with superconducting protons and suitable internal magnetic fields, or by a combination of vortex creep and rotochemical heating with superfluid neutrons.