The mean-field theory of superfluid-superconducting vortex states in the outer core of neutron stars
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866911672300470272 |
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| author | Kobyakov, Dmitry |
| author_facet | Kobyakov, Dmitry |
| contents | Purpose: Characterize superfluid-superconducting vortex states at arbitrary pressures with $T_{cp}\neq T_{cn}$, assuming both proton and neutron mean-fields are formed by spin-0 Cooper pairs.
Method: The existing mean-field theory is extended to account for $T_{cp}\neq T_{cn}$. The pressure dependence of the pairing gap energy $Δ_{\alpha0}$ is quantitatively established on the basis of the effective chiral field theory. To link $T_{cα}$ with $Δ_{\alpha0}$, I use the weak-coupling result $T_{cα}\approx0.57Δ_{\alpha0}$. A quadratic scaled-temperature ($T/T_{cp}$) dependence of the thermodynamic magnetic field is postulated in analogy with pure superconductors. The $T/T_{cα}$-dependence of the gap $Δ_{αT}$ is inferred from the many-body approximations for the pure neutron matter.
Results: An empirical $T/T_{cα}$-dependence for the mean-field is constructed to account for the interplay between the condensation and the magnetic energies. The superfluid entrainment is found to increase the size of the vortex core and to decrease the effective magnetic penetration depth. The size of the neutron vortex core is found to be larger than the magnetic penetration depth in the outer core.
Conclusions: The usual approximation of infinitely thin vortex line (the London's approximation) for the neutron vortex is found to be irrelevant in the entire outer core and for the proton vortex is found to be limited to vicinity of the crust-core transition. The developed mean-field theory paves the way to study the vortex microscopic structure, the angular momentum, the magnetization and the vortex-fluxtube interaction energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11216 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The mean-field theory of superfluid-superconducting vortex states in the outer core of neutron stars Kobyakov, Dmitry Nuclear Theory Solar and Stellar Astrophysics Superconductivity Purpose: Characterize superfluid-superconducting vortex states at arbitrary pressures with $T_{cp}\neq T_{cn}$, assuming both proton and neutron mean-fields are formed by spin-0 Cooper pairs. Method: The existing mean-field theory is extended to account for $T_{cp}\neq T_{cn}$. The pressure dependence of the pairing gap energy $Δ_{\alpha0}$ is quantitatively established on the basis of the effective chiral field theory. To link $T_{cα}$ with $Δ_{\alpha0}$, I use the weak-coupling result $T_{cα}\approx0.57Δ_{\alpha0}$. A quadratic scaled-temperature ($T/T_{cp}$) dependence of the thermodynamic magnetic field is postulated in analogy with pure superconductors. The $T/T_{cα}$-dependence of the gap $Δ_{αT}$ is inferred from the many-body approximations for the pure neutron matter. Results: An empirical $T/T_{cα}$-dependence for the mean-field is constructed to account for the interplay between the condensation and the magnetic energies. The superfluid entrainment is found to increase the size of the vortex core and to decrease the effective magnetic penetration depth. The size of the neutron vortex core is found to be larger than the magnetic penetration depth in the outer core. Conclusions: The usual approximation of infinitely thin vortex line (the London's approximation) for the neutron vortex is found to be irrelevant in the entire outer core and for the proton vortex is found to be limited to vicinity of the crust-core transition. The developed mean-field theory paves the way to study the vortex microscopic structure, the angular momentum, the magnetization and the vortex-fluxtube interaction energy. |
| title | The mean-field theory of superfluid-superconducting vortex states in the outer core of neutron stars |
| topic | Nuclear Theory Solar and Stellar Astrophysics Superconductivity |
| url | https://arxiv.org/abs/2605.11216 |