From the standard Neutron Star cooling theory after we expect that after ~10 million years the initially very hot stars have to cooled down to temperatures below ~10^4 K. However, the likely thermal emission MSPJ0437-4715 of age ~7 Gyrs implies a temperarure of ~10^5 K. This naturally suggests that a heating mechanism needs to be incorporated in the cooling models in order to explain this object.
Figure: Thermal evolution of the MSP J0437-4715 using a superfluidity gap of 0.1 MeV.
In Petrovich & Reisenegger (2010, 2011) we investigate a previously proposed mechanism named Rotochemical Heating (Reisenegger 1995) and incorporated the effect of having superfluid neutrons and protons in the interior, as it is expected at this very high densities. Using a wide set of equations of state, we show that this model reproduces the thermal emission from MSP J0437 only when superfluidity is incorporated with energy gaps in the interesting range of ~0.1-1 MeV, roughly consistent with constraints obtained from cooling models of young NSs (e.g. Cass A).