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When a rotating neutron star loses angular momentum, the progressivereduction of the centrifugal force makes it contract. This perturbs each fluidelement, raising the local pressure and originating deviations from betaequilibrium, inducing reactions that release heat (rotochemical heating). Thiseffect has previously been studied by Fern\'andez & Reisenegger (2005) fornon-superfluid neutron stars and by Petrovich & Reisenegger (2010) forsuperfluid millisecond pulsars. Both studies found that pulsars reach aquasi-steady state in which the compression driving the matter out of betaequilibrium is balanced by the reactions trying to restore the equilibrium. Weextend previous studies by considering the effect of density-dependence andanisotropy of the superfluid energy gaps, for the case in which the dominantreactions are the modified Urca processes, the protons are non-superconducting,and the neutron superfluidity is parametrized by models proposed in theliterature. By comparing our predictions with the surface temperature of themillisecond pulsar PSR J0437-4715 and upper limits for twenty-one classicalpulsars, we find the millisecond pulsar can be only explained by the modelswith the effectively largest energy gaps (type B models), the classical pulsarsrequire with the gap models that vanish for some angle (type C) and twodifferent envelope compositions. Thus, no single model for neutronsuperfluidity can simultaneously account for the thermal emission of allavailable observations of non-accreting neutron stars, possibly due to ourneglect of proton superconductivity.

Rotochemical heating of millisecond and classical pulsars with anisotropic and density-dependent superfluid gap models