Context: 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 nonsuperfluid matter, finding that they reach a quasi-steady configuration
in which the rate at which the spin-down modifies the equilibrium
concentrations is the same at which neutrino reactions restore the equilibrium.
Aims: We describe the thermal effects of Cooper pairing with spatially uniform
energy gaps of neutrons \Delta_n and protons \Delta_p on the rotochemical
heating in millisecond pulsars (MSPs) when only modified Urca reactions are
allowed. By this, we may determine the amplitude of the superfluid energy gaps
for the neutron and protons needed to produce different thermal evolution of
MSPs. Results: We find that the chemical imbalances in the star grow up to the
threshold value \Delta_{thr}= min(\Delta_n+ 3\Delta_p, 3\Delta_n+\Delta_p),
which is higher than the quasi-steady state achieved in absence of
superfluidity. Therefore, the superfluid MSPs will take longer to reach the
quasi-steady state than their nonsuperfluid counterparts, and they will have a
higher a luminosity in this state, given by L_\gamma ~ (1-4)
10^{32}\Delta_{thr}/MeV \dot{P}_{-20}/P_{ms}^3 erg s^-1. We can explain the UV
emission of the PSR J0437-4715 for 0.05 MeV<\Delta_{thr}<0.45 MeV.Comment: (accepted version to be published in A&A
