Masters Thesis

Thesis Title:

Stability of interlinked neutron vortex and proton flux tubes tube arrays in a neutron star 

Supervisor:

Professor Andrew Melatos, School of Physics, University of Melbourne

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Structure of a three-dimensional ground state featuring a vortex tangle. (a) Vortex structure. Blue shading denotes the condensate volume. Red shading traces out vortices. (b) Close up vortices in (a). (c) Cross-section of neutron density through z = 0. (d) Flux tube array.

Abstract (Abridged):

The outer core of a neutron star is believed to consist of three interpenetrating fluids: superfluid neutrons, superconducting protons and viscous electrons. The protons, electrons and rigid crust corotate, while the angular velocity of the neutrons is determined by the number and disposition of the superfluid vortices, each of which carries a quantum of circulation. The proton superconductor is usually regarded as type II in at least part of the outer core, implying that the magnetic field is concentrated into flux tubes, each carrying a magnetic flux quantum. Even though protons constitute 5% of the outer core by mass, they play an important role in the stellar rotational dynamics by coupling to the neutrons. For example, neutron vortices may pin to flux tubes, thereby storing angular momentum for later release in rotational glitches.

In this report, we investigate the complex microscopic interaction between neutron vortices and proton flux tubes in detail. We investigate the way in which the the vortex array rearranges and deforms geometrically in equilibrium and under far-from-equilibrium conditions. We couple the neutron fluid to the proton superconductor through density and current-current interactions. For the idealised model presented in this paper, we find that an initially rectilinear vortex array bends macroscopically and tangles microscopically in certain regimes, challenging the conventional picture of the outer core of the neutron star. The non-trivial geometry of these states arises naturally from this model due to the “frustration” of the system caused by the competing forces on the superfluid. The vortices lie broadly parallel to the rotation axis and form a tangled, frustrated equilibrium as they seek a compromise between aligning with the rotation axis globally and pinning to the flux tubes locally. The frustration results in a “glassy” relaxation to equilibrium.