Radial Oscillations and Stability of Neutron Stars with Antikaon Condensates

TL;DR

This paper examines how antikaon condensation in neutron-star cores modifies radial oscillations and the stellar equation of state. Using NL-RMF and DD-RMF frameworks with varied stiffness, the authors incorporate K^- and arK^0 condensation across a range of optical potentials U_barK, deriving the static TOV backgrounds and the corresponding Sturm–Liouville pulsation problem to obtain mode frequencies. They find that deeper antikaon potentials and the onset of condensation systematically soften the EoS, decrease M_max, and alter the mass–frequency relations, with K^- condensing prior to arK^0 and, in some models, producing a first-order transition. These imprints on radial spectra provide a potential diagnostic for the internal composition of neutron stars and motivate future multi-messenger and high-frequency GW observations to constrain dense-matter microphysics. The work highlights the sensitivity of radial oscillations to high-density phase transitions and strengthens the link between microphysical EoSs and observable neutron-star phenomenology, including possible constraints from NICER and GW observations.

Abstract

Radial oscillations provide a direct probe of the stability and compressibility of neutron stars and are highly sensitive to the equation of state of dense matter. In this work, we investigate the impact of antikaon condensates on the radial oscillation properties of neutron stars. We model neutron star matter using equations of state with a wide range of stiffness. For this purpose, both non-linear and density-dependent relativistic mean-field frameworks are employed to develop equations of state that are consistent with current astrophysical constraints. We further consider the emergence of antikaon condensates ($K^-$ and $\bar{K}^0$) in the stellar core, which modifies the pressure--energy density relation of dense matter. We find that the nature of the transition from nuclear matter to the condensed phase is sensitive to the antikaon optical potential depth and underlying equation of state. We compute the fundamental and higher-order radial oscillation modes for neutron stars containing antikaon condensates over a range of antikaon optical potential depths. Our results demonstrate that the antikaon optical potential depth plays a decisive role in governing the systematic shifts observed in the radial oscillation frequencies, while also significantly reducing the stability limits and maximum masses of neutron stars. These imprints of antikaon condensation on radial oscillation spectra provide a promising avenue for future multi-messenger observations and high-frequency gravitational-wave searches to directly probe and constrain the internal composition and equation of state of neutron stars.

Figures (12)

• Figure 1: (a) Pressure as a function of energy density for matter composed exclusively of nucleons ($n,p$) and leptons ($e^-,\mu^-$). (b) Corresponding mass--radius relations derived from the EoSs obtained using the NL3, GMT, IUFSU, DD2, PKDD, and DDME$\delta$ parametrizations.
• Figure 2: In-medium energies of the $K^-$ meson as a function of baryon density $\rho_B$ (normalized to the nuclear saturation density $\rho_0$) for different RMF parametrizations, shown for several values of the antikaon optical potential depth $U_{\bar{K}}$.
• Figure 3: The in-medium energies of $\bar{K^0}$ as functions of baryon density $\rho_B$ (normalized to the nuclear saturation density $\rho_0$) for various RMF parametrizations, shown for different choices of the antikaon optical potential depth $U_{\bar{K}}$.
• Figure 4: Population fractions $\rho_i/\rho_0$ of nucleons, leptons, and antikaons as functions of the baryon density $\rho_B/\rho_0$, calculated using different RMF parametrizations for an antikaon optical potential depth of $U_{\bar{K}} = -120$ MeV.
• Figure 5: Pressure as a function of energy density (EoS) for various RMF parametrizations, illustrated for different choices of the antikaon optical potential depth $U_{\bar{K}}$.