Superfluid Density in Linear Response Theory: Pulsar Glitches from the Inner Crust of Neutron Stars

The question of whether there are enough superfluid neutrons in the inner crust of neutron stars to explain pulsar glitches remains a topic of debate. Previous band structure calculations suggest that the entrainment effect significantly reduces the superfluid density. In this Letter, a new derivation of the BCS expression for the superfluid density is given. We compute it in the superfluid band theory framework through linear response theory, for a small relative velocity between superfluid and normal components, under the assumption that the pairing gap in the rest frame of the superfluid is constant and not affected by the perturbation. Our result suggests that a formula extensively used in neutron star physics is incomplete. Numerical evaluations for two realistic configurations reveal that the previously neglected contribution drastically alters the picture of the superfluid reservoir in the inner crust of neutron stars, suggesting that about 90% of the neutrons are effectively superfluid.