Radial oscillations of pulsating neutron stars: The UCIa equation-of-state case

Abstract

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, $β$-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 $σ$-cut scheme by adding a regulator potential $U_{\rm cut}(σ)$ [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 $σ$-cutoff suppresses the growth of the scalar field at supranuclear density, increases the pressure, and shifts the maximum mass, radii, and $Λ_{1.4}$ accordingly, while systematically raising the radial-mode frequencies at fixed mass. Using the sign change of $ω_0^2$ 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.

Figures (8)

• Figure 1: The pressure of pure nucleonic neutron star matter as a function of nucleon number density $n_N$ (in units of $n_0$) is shown for the original UCIa and UCIa with $f_{s}$= 0.58. Additional constraints (as mentioned in the text) are represented by shaded regions.
• Figure 2: Mass-to-radius relationships for the two viable equations-of-state considered in this work (original UCIa and UCIa with $f_s$=0.58). They are in agreement with current astrophysical constraints from NICER results Riley:2019Miller:2019Choudhury:2024xbkMiller:2021qhaRiley:2021pdl and the HESS J1731-347 compact object Doroshenko:2022nwp. Furthermore, they are capable of accommodating massive stars at two solar masses Demorest:2010Antoniadis:2013Cromartie:2019, while at the same time satisfy the stringent constraints for the canonical star at 1.4 solar masses obtained in Capano:2019eae.
• Figure 3: Large frequency separations for the purely nucleonic EoS without cuts. Top: Spectrum considering $M=1.4~M_{\odot}$ (blue color). Bottom: Spectrum considering $M=2.0~M_{\odot}$ (red color).
• Figure 4: Large frequency separations for the purely nucleonic EoS with $f_s=0.58$. Top: Spectrum considering $M=1.4~M_{\odot}$ (blue color). Bottom: Spectrum considering $M=2.0~M_{\odot}$ (red color).
• Figure 5: Radial profiles of the eigenfunctions $\xi(r), \eta(r)$ versus dimensionless radial coordinate for the case $f_s=0, M=1.4~M_{\odot}$. Shown are the fundamental and first excited mode ($n=0,1$) in black and blue, intermediate excited modes ($n=5,6$) in red and magenta as well as highly excited modes ($n=9,10$) in brown and orange.