Exploring Interplays Between $^3\text{P}_2$ Neutron Superfluid Vortices and $^1\text{S}_0$ Proton Fluxtubes in the Outer Core of Neutron Stars

TL;DR

This paper addresses how $^3P_2$ neutron superfluid vortices interact with $^1S_0$ proton fluxtubes in the outer core of neutron stars, a regime relevant to glitch dynamics. It develops a coupled microscopic framework using a spin-2 GPE for neutrons and a GL equation for protons, augmented by a fluxtube-like magnetic field and neutron–proton interactions to study vortex–fluxtube configurations. The authors present 2D and 3D simulations showing that spin polarization and magnetic-field effects can reshape vortex topologies, enabling HQV-to-IQV transitions and causing vortices to bend or migrate toward fluxtubes. This work establishes a foundation for self-consistent magnetic-field treatment and dynamical studies, with potential implications for understanding outer-core contributions to pulsar glitches and neutron-star phenomenology.

Abstract

In the outer core of neutron stars, $^3$P$_2$ superfluid neutrons and $^1$S$_0$ superconducting protons are deemed to exist, forming quantum vortices and magnetic fluxtubes, respectively. Those quantum vortices and fluxtubes play an important role in explaining observed sudden changes of rotational frequency, known as pulsar ``glitches.'' While the most of conventional glitch models rely on pinning/unpinning dynamics of neutron $^1\text{S}_0$ superfluid vortices in the inner crust, contributions of the outer core have not been ruled out. However, the latter possibility has been less explored so far and further thorough investigations are desired. In this study, we are thus developing a microscopic model based on spin-2 Gross-Pitaevskii equation (GPE) for neutron $^3$P$_2$ superfluid vortices coupled with Ginzburg-Landau equation (GLE) for fluxtubes associated with superconducting $^1\text{S}_0$ protons. In this contribution, we outline our theoretical framework and report tentative results showing how shape of quantum vortices could be affected by the presence of a proton fluxtube.

Figures (3)

• Figure 1: Results of 2D calculations for the case with two or four $^3\text{P}_2$ vortices (see texts for details) and a single fluxtube-like magnetic field. Figures \ref{['fig:2d_mag_0_vortex_change']}(a) and \ref{['fig:2d_mag_0_vortex_change']}(b) show phase and density of $\psi_0$ components of $^3P_2$ superfluid without any interaction with the fluxtube, while Figs. \ref{['fig:2d_mag_0_vortex_change']}(c) and \ref{['fig:2d_mag_0_vortex_change']}(d) are those with an interaction with the fluxtube. In this case, we neglect the proton-neutron interaction: i.e., $\xi=0$ and $\eta=0$ in Eq. \ref{['effective_interaction']}.
• Figure 2: 2D calculation of $^3P_2$ vortices and a tube-like magnetic field. Spin polarization of neutron makes $|\psi_2|$ and $|\psi_{-2}|$ density differences. Here we neglect proton-neutron interaction term:$\xi=0,\eta=0$.
• Figure 3: A result of 3D calculation for $^3\text{P}_2$ vortices and a fluxtube-like magnetic field (indicated by a yellow tube). Red, blue, green isosurfaces indicate vortex core positions of $\psi_0$, $\psi_2$, and $\psi_{-2}$ components, respectively. In this case, we neglect the proton-neutron interaction: i.e., $\xi=0$ and $\eta=0$.