Long-lasting accretion-powered chemical heating of millisecond pulsars

We analyse the effect of magnetic field in superconducting neutron star (NS) cores on the chemical heating of millisecond pulsars (MSPs). We argue that the magnetic field destroys proton superconductivity in some volume fraction of the stellar core, thus allowing for unsuppressed non-equilibrium reactions of particle mutual transformations there. The reactions transform the chemical energy, accumulated by an NS core during the low-mass X-ray binary stage, into heat. This heating may keep an NS warm at the MSP stage (with the surface temperature $\sim 10^5\, \rm K$) for more than a billion of years after ceasing of accretion, without appealing to the rotochemical heating mechanism.