Nuclear superfluidity and specific heat in the inner crust of neutron stars

We analyze the temperature dependence of pairing correlations in the inner crust matter of neutron stars. The study is done in a finite-temperature HFB approach and by using a zero range pairing force adjusted to the pairing properties of infinite neutron matter. Within the same approach we investigate how the specific heat of the inner crust depends on temperature, matter inhomogeneity, and the assumption used for the pairing force. It is shown that in a physical relevant range of densities the pairing properties of inner crust matter depend significantly on temperature. The finite-temperature HFB calculations show also that the specific heat is rather sensitive to the presence of nuclear clusters inside the inner crust. However, the most dramatic change of the specific heat is determined by the scenario used for the neutron matter superfluidity