Symmetry of the neutron and proton superfluidity effects in cooling neutron stars

We investigate the combined effect of neutron and proton superfluidities on the cooling of neutron stars whose cores consist of nucleons and electrons. We consider the singlet state paring of protons and the triplet pairing of neutrons in the cores of neutron stars. The critical superfluid temperatures Tc are assumed to depend on the matter density. We study two types of neutron pairing with different components of the total angular momentum of a Cooper pair along the quantization axis (|mJ|=0 or 2). Our calculations are compared with the observations of thermal emission from isolated neutron stars. We show that the observations can be interpreted by using two classes of superfluidity models: (1) strong proton superfluidity with a maximum critical temperature in the stellar core Tcmax≳4×109 K and weak neutron superfluidity of any type (Tcmax≲2×108 K); (2) strong neutron superfluidity (pairing with mJ=0) and weak proton superfluidity. The two types of models reflect an approximate symmetry with respect to an interchange of the critical neutron and proton pairing temperatures.