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Rotochemical heating in millisecond pulsars with Cooper pairing

When a rotating neutron star loses angular momentum, the reduction in the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium that enhance the neutrino emissivity and produce thermal energy. This mechanism is named rotochemical heating and has previously been studied for neutron stars of non-superfluid matter, finding that they reach a quasi-steady state in which the rate that the spin-down modifies the equilibrium concentrations is the same to that of the neutrino reactions restoring the equilibrium. On the other hand, the neutron star interior is believed to contain superfluid nucleons, which affect the thermal evolution of the star by suppressing the neutrino reactions and the specific heat, and opening new Cooper pairing reactions. In this work we describe the thermal effects of Cooper pairing with spatially uniform energy gaps of neutrons and protons on rotochemical heating in millisecond pulsars (MSPs) when only modified Urca reactions are allowed. We find that the chemical imbalances grow up to a value close to the energy gaps, which is higher than the one of the nonsuperfluid case. Therefore, the surface temperatures predicted with Cooper pairing are higher and explain the recent measurement of MSP J0437-4715.