Superfluid dynamics in the outer core of neutron stars

Abstract

The consensus between observations and theory is that neutron star shows a layered structure determined by an increasing density and temperature with depth. Quantum degeneracy of nuclear matter lays at the basis of the existence of these exotic objects, and the Bose condensation of neutron and proton pairs leads to the emergence of superfluidity in the star interior. However, the precise equation of state of nuclear matter under such extreme conditions, relating its pressure and density, are yet unknown, and many proposals compete to provide a plausible picture compatible with the observational constrains. Currently, the study of neutron stars is becoming an interdisciplinary subject which is receiving an increasing attention due to more available data from precise observations and the possibility of making realistic computational simulations of the superfluid dynamics. This latter feature is crucial to account for the observed low moment of inertia and for the cooling down of the neutron star. It also allows us to understand the extraordinarily regular rotation of pulsars or even their observed, sudden speed-ups (glitches). Hydrodynamical models including the coupling of a normal fluid and a superfluid, or two coupled superfluids (neutronic superfluid and protonic superconductor) are being used to find dynamical instabilities that could explain the astronomical observations. Our work belongs to the latter group and models the macroscopic structure of the outer core, with typical densities around the nuclear saturation density and temperatures of the order of 108 K. The coupling between the two overlapped condensates of fermionic pairs is due to the entrainment of neutron and protons, which results from the Galilean invariance of the whole system. An equation of state based on the short range interactions between nucleons (Skyrme type) is assumed in order for the model to be consistent with observations. The resulting nonlinear equations of motion are linearized and the modes, obtained in the long wavelength regime, which allows to neglect the proton-electron interaction, are analytically derived as a function of the nuclear matter density. Comparison between the analytical predictions and numerical simulations of the original nonlinar equations are made, and relations with astronomical observations are discussed.