Spin effects in superfluidity, neutron matter and neutron stars

Abstract

We review selected aspects of the interior physics of compact stars, focusing on the microscopic and macroscopic manifestations of spin, magnetic fields, and nucleonic superfluidity and superconductivity. Spin statistics of fermions allows quantum degeneracy pressure to determine the stability and global properties of neutron stars, whose structure depends sensitively on the strong interactions among baryons in dense matter. Using a generic meta-modeling framework based on an expansion of the nuclear energy density around the isospin-symmetric and saturation-density limits, we highlight how various lesser-known terms in this expansion affect compact-star observables and review multimessenger constraints on mass, radius, and moment of inertia. The influence of magnetic fields on dense matter is examined, showing that substantial effects in their structure require extremely strong fields, whereas lower fields are sufficient to affect their superfluid phases. At the mesoscopic scale, the coexistence of superfluid and superconducting components features vortex and flux-tube lattices, with pinning and mutual friction processes playing central roles in neutron-star rotational dynamics. We discuss unresolved issues concerning vortex structure, flux-tube configurations, and the origin of pulsar glitches and post-glitch relaxation. We also briefly address the possible emergence of deconfined quark phases in compact-star cores, including their color-superconducting properties, as well as the associated vortex structures and magnetic-field responses in such phases.

Figures (7)

• Figure 1: Variation of the nuclear equation of state with $Q_{\rm sat}$ and $L_{\rm sym}$ in covariant density functional models. Family of EoS generated using covariant density functional models with the parameters varied over the ranges $Q_{\rm sat} \in [-600,1000]$ MeV (grouped by color) and $L_{\rm sym} \in [30,\,110]$ MeV; other parameters of covariant density functional are fixed to that of DDME2 parametrization; for details see Ref. Li:2023bid. The inset highlights the impact of $L_{\rm sym}$ on the low-density region of the EoS for illustration.
• Figure 2: Mass–radius and moment-of-inertia–mass relations for nucleonic equations of state compared with multimessenger astrophysical constraints. (a) Mass–radius for nucleonic EoS models corresponding to different $Q_{\rm sat}$ and $L_{\rm sym}$ pairs (in MeV) Li:2023bid. The colored regions indicate the 90% confidence interval (CI) ellipses from the two NICER analyses for PSR J0030+0451 and PSR J0740+6620 NICER:2019aNICER:2019bNICER:2021aNICER:2021b, the 90% CI regions for the two compact stars involved in the gravitational-wave event GW170817 AbbottPhysRevX.9.011001 and the 90%CI for the mass of the secondary component in GW190814 LIGO-Virgo2020. (b) Moment of inertia vs mass for the same EoSs as in Fig. \ref{['fig:TOV_QL']} for the indicated range of $Q_{\rm sat}$ and $L_{\rm sym}$ (in MeV); the upper limit $I_A\le 3\times 10^{45}$ g cm$^2$ at 90% CI on the moment of inertia extracted from PSR J0737$-$3039 system (shown by vertical arrow) is well satisfied for the collection of EoSs, given that the pulsar mass $m_A \simeq 1.34\,M_{\odot}$.
• Figure 3: Twisted-torus magnetic field structure in a magnetar showing coexisting poloidal and toroidal components. Spatial structure of a twisted-torus magnetic field, illustrating the coexistence of poloidal and toroidal components in a magnetar obtained with the XNS solver Das:2025fws. The color bar shows the magnetic field strength in units of $10^{17}$ Gauss. The white lines trace the field lines; note that the toroidal component is confined to the equatorial region $z\simeq 0$.
• Figure 4: Density dependence of neutron and proton pairing gaps and corresponding particle composition in the neutron star core. Upper panel: Pairing gaps as functions of baryon density (in units of nuclear saturation density $n_0$) for neutrons in the $^1S_0$ (solid lines) and $^3P_2$–$^3F_2$ (dash–dotted lines) channels, and for protons in the $^1S_0$ channel (dashed lines). The shaded areas show the upper and lower bounds on neutron gaps; the upper and lower dashed lines show the same for proton $S$-wave gap, see Ref. Sedrakian2019 and references therein. Lower panel: Particle composition of the neutron star core at $T = 0$, corresponding to the conditions used in computing the pairing gaps. The vertical line marks the crust–core interface at $n/n_0 = 0.5$.
• Figure 5: Neutron star cross section illustrating superfluid vortex lattice, magnetic flux tubes, and spin-down–driven vortex motion. A cross-section of a neutron star perpendicular to the spin axis, illustrating the triangular lattice of neutron vortices (shown not to scale) that carries the angular momentum of the neutron superfluid. The dipolar magnetic field is also shown, with its axis aligned along the tilted ${\bm B}$-vector, together with the corresponding field lines, which in superconducting proton regions are confined to flux tubes. The red arrows indicate the radial outward motion of neutron vortices in response to the star’s secular spin-down.