Unresolved dynamical properties of nuclear superfluids in the neutron-star inner crust

Investigate the dynamical properties of nuclear superfluids in the inner crust of neutron stars by determining mutual entrainment effects between neutrons and protons, characterizing vortex dynamics, and quantifying dissipation mechanisms, so as to reduce current uncertainties and enable more reliable global models of neutron-star matter.

Background

The paper highlights that extreme conditions inside neutron stars cannot be reproduced in the laboratory, and that neutron and proton superfluidity in the inner crust introduces complex dynamical phenomena. The authors emphasize that these phenomena are central to interpreting astrophysical observations and constructing global models of superfluid neutron stars.

To address such questions, the authors develop a time-dependent nuclear energy-density functional toolkit (W-BSk Toolkit) and demonstrate its capabilities on a 3D problem of a nucleus accelerating through a neutron superfluid. While the study provides new insights into effective mass and dissipation, it explicitly notes broader unresolved questions related to entrainment, vortex dynamics, and dissipation in nuclear superfluids.

References

In particular, the dynamical properties of nuclear superfluids raise many open questions concerning, for example, mutual entrainment between neutrons and protons, vortex dynamics, disspation, etc.

— Time-dependent nuclear energy-density functional theory toolkit for neutron star crust: Dynamics of a nucleus in a neutron superfluid  (2403.17499 - Pȩcak et al., 2024) in Section I (Introduction), page 041054-1

Whether the crust alone is sufficient, and how strongly entrainment reduces the effective mobile superfluid fraction, remains debated, and recent results (see \citep{urban_sf_fraction,Chamel2025}) show that, considering the current uncertainty on the neutron star equation of state and crust modelling, the angular momentum reservoir in the inner crust is typically enough to explain glitches~\citep{burrello2025PhRvC,klausner2026PhRvC}.

— Fluxtube Bouquets and Type-1.5 Clustering in Superfluid Neutron Star Cores  (2608.25943 - Karekkat et al., 26 Aug 2026) in Section 1, Introduction

A systematic treatment of the crossover between thermal and quantum creep regimes, and its dependence on vortex tension, pinning geometry, and local temperature, is still lacking and could substantially affect predicted post-glitch relaxation timescales.

— Superfluidity and Vortex Dynamics in Neutron Stars  (2609.01022 - Link et al., 1 Sep 2026) in Section “Open questions and perspectives” under “Superfluid rotation and vortex motion”

The global evolution of flux tubes remains an open problem.

— Superfluidity and Vortex Dynamics in Neutron Stars  (2609.01022 - Link et al., 1 Sep 2026) in Section “Vortex--flux-tube interactions and magnetic evolution”

It remains an open question whether or not underdamped, long-period precession can occur when pinned vortices move through the thermal activation process described in Section~\ref{thermal-effects}.

— Superfluidity and Vortex Dynamics in Neutron Stars  (2609.01022 - Link et al., 1 Sep 2026) in Section “Free precession in a superfluid neutron star”

The mechanism whereby Tkachenko modes might be excited in neutron stars has not been studied in detail.

— Superfluidity and Vortex Dynamics in Neutron Stars  (2609.01022 - Link et al., 1 Sep 2026) in Section “Open questions and perspectives” under “Precession, Tkachenko modes, and long-term rotational variability”

There is no model-independent expectation for the sign of the oblateness correction in this problem. An oblate background changes the local crustal thickness, density surfaces, vortex geometry and pinning-weighted lever arm differently between equator and pole, so competing effects can either enhance or reduce the $m=2$ response. Determining the sign requires solving the Magnus-forced perturbation on a self-consistently rotating background rather than extrapolating the spherical sequence. We do not assign a universal percentage error to these omissions because it has not been calculated for the present Magnus-forced boundary-value problem.

— Vortex pinning and the elastic response of neutron-star crusts II. Non-axisymmetric loading and Magnus mountains  (2609.02863 - Giliberti, 2 Sep 2026) in Section 3.2, subsection “Continuous-wave scale and high-spin limit”