Nuclear superfluidity and cooling time of neutron star crusts

We analyze the effect of neutron superfluidity on the cooling time of inner crust matter in neutron stars, in the case of a rapid cooling of the core. The specific heat of the inner crust, which determines the thermal response of the crust, is calculated in the framework of HFB approach at finite temperature. The calculations are performed with two paring forces chosen to simulate the pairing properties of uniform neutron matter corresponding to the BCS approximation and to many-body techniques including polarization effects. Using a simple model for the heat transport across the inner crust, it is shown that the two pairing scenarios mentioned above give very different values for the cooling time, i.e., of about 12 and 25 yr.