Probing the inner disk edge of rotating neutron stars with dipole excitations in finite nuclei

Technical Summary: Probing the Inner Disk Edge of Rotating Neutron Stars with Dipole Excitations in Finite Nuclei

Problem Statement
The structure of rapidly rotating neutron stars and the orbital dynamics within their surrounding spacetime are governed by the nuclear equation of state (EOS). A critical uncertainty in current models involves the transition point where the innermost stable circular orbit (ISCO) reaches the stellar surface. This "surface–ISCO transition" determines whether the inner edge of an accretion disk is set by the stellar surface or by orbital instability (an external ISCO). This boundary dictates the maximum Keplerian frequency and the orbital binding energy available for release. However, predictions for the mass and radius at which this transition occurs are currently limited by uncertainties in the EOS, particularly the density dependence of the symmetry energy. While astrophysical observations constrain high-density behavior, there is a need to quantify how nuclear measurements near saturation density can refine these predictions for rotating configurations.

Methodology
The authors model uniformly rotating neutron stars within the framework of general relativity using the RNS code. They employ a family of equations of state derived from relativistic energy density functionals with density-dependent point-coupling (DD–PC) interactions. This family systematically varies the symmetry energy at saturation density ($J$) from 29 to 36 MeV, with corresponding slope parameters ($L$) ranging from 29 to 94.1 MeV. All functionals are calibrated to nuclear ground-state data and support maximum non-rotating masses of at least $2 M_\odot$.

To constrain this family, the authors utilize measurements of the electric dipole polarizability ($\alpha_D$) in neutron-rich nuclei: $^{48}$Ca, $^{68}$Ni, $^{120}$Sn, and $^{208}$Pb (collectively the CNSP-4 set). Previous work by Koliogiannis et al. (2026a) inferred a symmetry energy of $J = 31.34 \pm 0.79$ MeV from these data. The study compares the full DD–PC family against the subset consistent with the CNSP-4 constraints. For each configuration, the authors locate the prograde ISCO relative to the stellar surface to define the transition mass $M_{tr}(f)$ and equatorial radius $R_{eq}$. They further calculate the orbital frequency ($\nu_{in}$) and binding efficiency ($\eta_{in}$) at the disk's inner edge.

Key Results

1. Reduction of Uncertainty: The application of the dipole polarizability constraint significantly reduces the spread in predicted transition properties. Across the considered spin frequencies, the constraint reduces the uncertainty in the transition mass by factors of approximately seven to ten (from spreads of 0.12–0.2 $M_\odot$ to below 0.025 $M_\odot$) and the transition radius by similar factors (from 0.5–1 km to below 0.15 km). This represents an 85–90% reduction in the EOS-dependent spread.
2. Orbital Frequency Constraints: Along the surface–ISCO transition, the CNSP-4 constraint confines the inner-edge orbital frequency to a band narrower than 20 Hz at each spin frequency. In contrast, the full DD–PC family yields widths of approximately 38–134 Hz.
3. Specific Case (716 Hz): For the fastest known neutron star (PSR J1748−2446ad, $f=716$ Hz), the transition mass range contracts from $1.586–1.731 M_\odot$ (full family) to $1.620–1.635 M_\odot$ (CNSP-4 constrained). The equatorial radius range contracts from $12.58–13.46$ km to $12.70–12.80$ km.
4. Application to 4U 0614+09: Combining the spin measurement ($f \approx 414$ Hz) and a lower limit on the highest kHz QPO frequency ($\nu_{in} \ge 1267$ Hz) for the low-mass X-ray binary 4U 0614+09, the authors derive allowed mass and radius intervals. Without the nuclear constraint, the lower mass boundary ranges from 0.81 to 1.23 $M_\odot$; with the CNSP-4 constraint, this narrows to 0.91–0.98 $M_\odot$ (an 82% reduction in spread). The upper mass boundary remains nearly EOS-independent at $\approx 1.97 M_\odot$. The nuclear constraint tightens the equatorial radius bounds by approximately 82–95%.

Significance and Claims
The paper demonstrates that the electric dipole response of finite nuclei provides a powerful, independent constraint on the structure of rotating neutron stars and the orbital properties of their inner accretion disks. By linking nuclear observables to the dynamics of the inner accretion disk, the authors show that dipole polarizability measurements can:

• Sharply define the mass and radius at which the surface–ISCO transition occurs.
• Confine the predicted orbital frequency at the disk inner edge to a narrow window, facilitating the interpretation of kilohertz quasi-periodic oscillations (kHz QPOs).
• Allow for an independent mass estimate of accreting neutron stars when combined with measured spin frequencies and QPO data.

The authors conclude that these nuclear constraints inform both the stellar structure and the orbital mechanics of the inner disk, offering a pathway to test the symmetry-energy constraint through astrophysical observations of rotating neutron stars. They note that further accurate measurements of dipole responses and higher-frequency QPOs (e.g., via future X-ray missions) could further refine these predictions.