Properties of phonons in the neutron star crust

Neutron stars are compact objects, created in supernova explosions at the end of the life of massive stars. They contain matter under extreme conditions, in particular concerning the density : starting from a lattice of (neutron rich) nuclei in the crust one reaches nuclear matter at several times the density of atomic nuclei in the center. One way to understand this object is to confront theoretical modelisation with observations. Among observations of pulsars there is the thermal emission of its surface. This observable, which depend on the heat transport properties, is very sensitive to the superfluid and superconducting character of the different sutructures inside the star. The presentation is focussed on the inner crust, where we can find an interesting nuclear structure called the ''Pasta Phase". Its excitation spectrum within a superfluid hydrodynamics approach will be discussed in view of calculating the contribution to the heat capacity.