SPECIFIC-HEAT OF SUPERFLUID MATTER IN THE INNER CRUST OF NEUTRON-STARS

The superfluid properties of matter in the inner crust of a neutron star (4.3 x 10(11) g cm(-3) < rho < 2.4 x 10(14) g cm (-3)), where a Coulomb lattice of neutron-rich nuclei is permeated by a gas of unbound neutrons, are studied by making use of a semiclassical model to determine the spatial behavior of the neutron pairing gap. A strong variation of this quantity as a function of position in the Wigner-Seitz, cell is found, the gap being small inside the nucleus, attaining its maximum at the nuclear surface and then saturating to an intermediate value outside the nucleus. While the specific heat of this superfluid system is obviously reduced as compared to that associated with the normal phase, in a physically relevant range of densities-and temperatures (rho/rho(0) > 0.03 and T > 0.08 MeV), its value is considerably larger than that associated with a uniform neutron superfluid, and of the same order of magnitude as the electronic specific heat.