Nucleon superfluidity versus thermal states of isolated and transiently accreting neutron stars

The properties of superdense matter in neutron star (NS) cores control NS thermal states by affecting the efficiency of neutrino emission from NS interiors. To probe these properties we confront the theory of thermal evolution of NSs with observations of their thermal radiation. Our observational basis includes cooling isolated NSs (INSs) and NSs in quiescent states of soft X-ray transients (SXTs). We find that the data on SXTs support the conclusions obtained from the analysis of INSs: strong proton superfluidity with T_{cp,max} >= 10^9 K should be present, while mild neutron superfluidity with T_{cn,max} =(2*10^8 -- 2*10^9) K is ruled out in the outer NS core. Here T_{cn,max} and T_{cp,max} are the maximum values of the density dependent critical temperatures of neutrons and protons. The data on SXTs suggest also that: (i) cooling of massive NSs is enhanced by neutrino emission more powerful than the emission due to Cooper pairing of neutrons; (ii) mild neutron superfluidity, if available, might be present only in inner cores of massive NSs. In the latter case SXTs would exhibit dichotomy, i.e. very similar SXTs may evolve to very different thermal states.