Collective modes and hydrodynamics in the inner crust of neutron stars

Neutron stars have been extensively studied since Baade and Zwicky have proposed their existence in 1934. Their description is at the interface of numerous domains of physics, e.g., X-ray astrophysics, pulsar signal observation, general relativity and nowadays gravitational waves, solid state physics, and also nuclear physics. In this thesis we will concentrate on the nuclear physics description, especially of the inner crust. These stars are characterized by their large mass from one to two solar masses, in a radius of 10 km. Their inner structure can be divided in three major layers: the outer crust, the inner crust and the core. The outer crust consists of nuclei coexisting with an electron gas to ensure charge neutrality. If one goes deeper into the crust, the ratio of neutrons with respect to the total nucleon number increases. Eventually, the excess of neutrons in the nuclei gets so high that they drip out from the nuclei and create a dilute neutron gas. From now on, we will speak of nuclear clusters instead of nuclei. This phenomenon defines the limit between the outer crust and the inner crust. This complicated structure and composition is at the origin of many characteristic properties of neutron stars. Hence, we will construct our work in three major parts. First, we start to account for the neutron gas surrounding the clusters, which we treat as uniform. Here, the neutron gas is assumed to be superfluid, and one can expect a Goldstone mode. This description will be done in the framework of QRPA. Second, we will focus on the study of properties of the clusters contained in the inner crust. Under these conditions we expect to see crystal of spheres, rods and plates of bound nucleons, that we will describe with the help of the ETF approximation. Third, we will finish by treating the interaction between the clusters and the gas with hydrodynamics. The results will be applied to astrophysics and in particular to glitches. (author)