A numerical model of a neutron star’s outer core found that, for attractive couplings, a neutron vortex and a proton fluxtube favored an overlapped arrangement. In related calculations, several fluxtubes gathered around a vortex, while the force between separate fluxtubes was repulsive at short distances and attractive at intermediate ones. The study used that non-monotonic pattern as a local type-1.5-like diagnostic.
The document is an arXiv preprint, version 1, dated 26 Aug 2026.
Inside the calculation
The authors used a two-component Ginzburg–Landau free energy to represent a neutron superfluid coupled to a proton superconductor. It included local couplings but no genuine phase-gradient entrainment, meaning it omitted a coupling tied to how the condensates’ phases vary through space.
The numerical domain was a two-dimensional cross-section, with neutron vortices and proton fluxtubes locally aligned along the z-axis. Defect configurations were relaxed with quasi-periodic boundary conditions, while constrained phase imprinting was used to determine vortex–fluxtube interaction energies at fixed separations. Fiducial parameters were κ = 1.44, R = 0.4 and ϵ = 0.1.
Overlap and bouquets
For attractive couplings, the pinning energy Epin increased as separation grew. At d = 0, the overlapped arrangement was energetically preferred, indicating local pinning between the vortex and fluxtube.
When the calculation examined vortex-centred aggregates, several fluxtubes concentrated around the vortex. Different initial guesses yielded different bouquet arrangements, but all considered runs contained between 6 and 9 fluxtubes.
No stable multiply charged fluxtube was identified in the explored simulations, even where several fluxtubes occupied the same vortex-centred bouquet.
A binding-energy proxy reached its asymptotic regime by a separation of about d ≈ 20 in representative cases. In the uncoupled reference, where α = g = 0, the proxy was zero by construction.
A force pattern with a preferred scale
Separate fluxtubes did not simply repel or attract across all distances. Their coupled-system force was non-monotonic—repulsive at short range and attractive at intermediate range—and the study treated this as a type-1.5-like diagnostic.
Without a neutron vortex, sufficiently strong couplings were associated with many-fluxtube states described as type-1.5-like clusters. Their nearest-neighbor spacing was consistent with the preferred distance d⋆ from the two-fluxtube interaction, but the study did not treat it as an exact lattice constant.
The reported type-1.5-like regime survived in the zero-entrainment regime considered by the study. In this reduced calculation, that behavior was present without genuine phase-gradient entrainment.
A narrow astrophysical reading
The paper presents the astrophysical implications as qualitative. It did not calculate Urca reaction rates or electron transport coefficients in realistic neutron-star matter.
For average bouquets with P = 9, a model-based estimate gave a global magnetic-field change of only about 10−6 G. The estimate assumed co-motion and a spatially uniform magnetic response, and the direct effect on the global field during a glitch seemed unobservable.
Taken together, the calculations describe local interaction mechanisms within the explored numerical setup: overlap was preferred for attractive couplings, bouquets contained 6 to 9 fluxtubes, and a type-1.5-like clustering signal survived without phase-gradient entrainment. The paper keeps the astrophysical implications qualitative.
Paper data and sources
Original title: Fluxtube Bouquets and Type-1.5 Clustering in Superfluid Neutron Star Cores
Authors: Adarsh Karekkat, Gabriele Montefusco, Marco Antonelli
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text