Superfluid fraction in the Lasagne phase of the inner crust of neutron stars
ABSTRACT :
The inner crust of neutron stars is made of a periodic lattice of nuclei surrounded by a superfluid neutron gas. The presence of the lattice reduces the superfluid density of the neutron gas, as it happens in supersolids that were recently real ized in Bose-Einstein condensates of dipolar atoms. In the field of neutron stars, the reduction of the superfluid density is also known as entrainment effect, and it has important consequences for the understanding of pulsar glitches, i.e., sudden changes of the rotation frequency of the neutron star. Previous calculations in normal band theory (analogous to the one in solid state physics) predicted a very strong entrainment, i.e., a very strong reduction of the superfluid density, whereas a simple, idealized hydrodynamic model [1] predicted only weak entrainment, consistent with glitch observations. In this seminar, I will present a new analysis [2] for the "lasagne" phase, i.e., for a periodic lattice of slabs, as it is expected in the deep layers of the crust. We solve the full Hartree-Fock-Bogoliubov equations in the presence of a stationary relative flow between the lattice and the superfluid neutrons, employing Bloch boundary conditions in order to well describe the interplay between the band structure and superfluidity. Our results for the superfluid fraction are slightly larger than those obtained in normal band theory, suggesting that normal band theory overestimates the entrainment effect.