Nucleon superfluidity vs. observations of cooling neutron stars

Cooling simulations of neutron stars (NSs) are performed assuming that stellar cores consist of neutrons, protons and electrons and using realistic density proles of superfluid critical temperatures Tcn( )a ndTcp( )o f neutrons and protons. Taking a suitable prole of Tcp( )w ith maximum5 10 9 K one can obtain smooth transition from slow to rapid cooling with increasing stellar mass. Adopting the same prole one can explain the majority of observations of thermal emission from isolated middle{aged NSs by cooling of NSs with dierent masses either with no neutron superfluidity in the cores or with a weak superfluidity, Tcn < 10 8 K. The required masses range from1:2 M for (young and hot) RX J0822{43 and (old and warm) PSR 1055{52 and RX J1856- 3754 to1:45 M for the (rather cold) Geminga and Vela pulsars. Observations constrain the Tcn( )a ndTcp() proles with respect to the threshold density of direct Urca process and maximum central density of NSs.