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Low-energy collective excitations in the neutron star inner crust

We study the low-energy collective excitations of the neutron star inner crust, where a neutron superfluid coexists with a Coulomb lattice of nuclei. The dispersion relation of the modes is calculated systematically from a microscopic theory including neutron band structure effects. These effects are shown to lead to a strong mixing between the Bogoliubov-Anderson bosons of the neutron superfluid and the longitudinal crystal lattice phonons. In addition, the speed of the transverse shear mode is greatly reduced as a large fraction of superfluid neutrons are entrained by nuclei. Not only does the much smaller velocity of the transverse mode increase the specific heat of the inner crust, but it also decreases its electron thermal conductivity. These results may impact our interpretation of the thermal relaxation in accreting neutron stars. Due to strong mixing, the mean free path of the superfluid mode is found to be greatly reduced. Our results for the collective mode dispersion relations and their damping may also have implications for neutron star seismology.