Internal heating mechanisms in neutron stars

The cooling of neutron stars (hereafter NS) has the potential to reveal important features of superdense matter. Their surface temperatures are known for a fair sample of NS with ages $\leq 10^{6} \, {\it{yr}}$, and with a few exceptions, can be accommodated by standard cooling mechanisms (neutrino+photon emission without internal heating). However, for the older objects it is necessary to consider some internal heating to explain surface temperatures higher than expected. We revisit in this paper the kinetic heating by fermionic dark matter, rotochemical heating and magnetic field decay. We found that NS slightly older than $\sim 10^{6} \, {\it{yr}}$ can be explained by them, but the older ``black widow'' systems are much hotter than the values predicted by these three mechanisms, pointing towards a yet unknown heating factor for old NS.