Radial oscillations of pulsating neutron stars: The UCIa equation-of-state case
Radial oscillations provide a clean dynamical test of the high-density stiffness of neutron-star equations of state. We study spherically symmetric pulsations of nonrotating relativistic stars built from cold, charge-neutral, $\beta$-equilibrated pure nucleonic matter described within relativistic mean-field theory. As a baseline we adopt the UCIa parameter set [Astron. Astro-phys. 689, A242 (2024)], and we implement high-density stiffening via the $\sigma$-cut scheme by adding a regulator potential $U_{\rm cut}(\sigma)$ [Phys. Rev. C 92, no.5, 052801 (2015), Phys. Rev. C 106, no.5, 055806 (2022)]. For representative choices $f_s=0$ (no cutoff) and $f_s=0.58$ (stiffened), we solve the Tolman-Oppenheimer-Volkoff and tidal perturbation equations to obtain equilibrium sequences, mass-radius relations, and tidal deformabilities. We then derive and solve the linear general-relativistic radial pulsation equations to compute the eigenfrequencies and eigenfunctions of the fundamental and overtone modes. The $\sigma$-cutoff suppresses the growth of the scalar field at supranuclear density, increases the pressure, and shifts the maximum mass, radii, and $\Lambda_{1.4}$ accordingly, while systematically raising the radial-mode frequencies at fixed mass. Using the sign change of $\omega_0^2$ as a stability criterion, we identify stiffened models that remain radially stable up to the observed $\sim 2M_\odot$ mass scale and are consistent with current multimessenger constraints, demonstrating how radial spectra complement static EoS tests.