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

The nuclear equation of state shapes both the structure of rapidly rotating neutron stars and the orbital motion in their surrounding spacetime. Its uncertainty affects the mass and radius at which the innermost stable circular orbit reaches the stellar surface, a condition that defines the transition between disks whose inner edge is set by the surface and those truncated by orbital instability. We quantify how measurements of the electric dipole polarizability of neutron-rich nuclei reduce the uncertainty in this transition and in the orbital properties at the disk inner edge. We compute uniformly rotating neutron stars in general relativity for a family of equations of state that systematically vary the symmetry energy, derived from relativistic energy density functionals with density-dependent point-coupling interactions. We compare the results for the full family with those for the subset consistent with the measured dipole polarizabilities of finite nuclei. The dipole polarizability constraint reduces the spread in transition mass and equatorial radius by factors of about seven to ten across the spin frequencies considered. Along this transition, it also confines the orbital frequency at the disk inner edge to a band narrower than $20$~Hz at each spin. Combined with a measured neutron-star spin, a kilohertz quasi-periodic oscillation interpreted as disk orbital motion further restricts the mass--radius region, allowing an independent mass estimate to probe the symmetry-energy constraint. The dipole response of finite nuclei thus informs both the structure of rotating neutron stars and the orbital properties of their inner accretion disks.