F-mode Oscillations of Neutron Stars with Dark Matter from Neutron Decay: Implications for Gravitational-Wave Detectability

TL;DR

This study investigates how neutron decay into dark matter, together with dark-matter self-interactions, alters neutron-star f-mode oscillations and their gravitational-wave detectability with the Einstein Telescope. It uses the quark-meson coupling model for nucleons, augmented by a dark fermion χ coupled to a vector mediator, to generate EoSs for nucleon-only, strange-matter, and DM-admixed stars across varying DM self-interaction strengths. The authors find that strong DM self-repulsion stiffens the EoS and can reestablish stability for high-mass neutron stars, while strange matter and non-self-interacting DM show deviations from standard universal f-mode relations; f-mode frequencies and damping times largely follow universal trends except for these exotic cases. Under a benchmark GW energy release of $E = 10^{52}$ erg at a distance of $D = 25$ Mpc, the characteristic strain and SNR exceed the ET-D sensitivity below approximately $2.1$ kHz for self-interacting DM and strange matter, indicating that next-generation detectors could constrain DM interactions and the neutron lifetime anomaly via f-mode asteroseismology.

Abstract

In this study, the impact of neutron decay into dark matter and various dark matter self-interaction strengths on neutron star properties have been explored. Using the quark-meson coupling (QMC) model for nucleon-only equations of state (EoSs), the effects of different matter compositions have been compared, including strange matter and self-interacting dark matter. The results demonstrate that increasing DM-DM self-repulsion stiffens the EoS, influencing the mass-radius relationship and stability of neutron stars. Furthermore, fundamental mode (f-mode) oscillations have been analyzed, which serve as a diagnostic tool for probing neutron star interiors. The f-mode frequencies follow universal relations, reinforcing their applicability for constraining dense matter properties. It has been shown that neutron stars composed of nucleons-only and self-interacting dark matter exhibit a universal behavior in damping time and angular frequency, whereas strange matter and non-self-interacting dark matter deviate from this trend. Importantly, it has been shown that for a GW energy release of E = 10^{52} erg and a source distance of 25 Mpc, the characteristic strain and signal-to-noise ratio exceed the ET-D sensitivity threshold below 2.1 kHz for all models except the non-interacting DM case, demonstrating that neutron-to-dark matter decay scenarios, including the role of DM self-interactions, can be tested through next-generation gravitational-wave asteroseismology, offering a new probe of DM physics and the neutron lifetime anomaly.

Figures (8)

• Figure 1: Equations of state (pressure vs. energy density) for nucleonic matter (QMC), strange matter (MIT bag model), and neutron decay into dark matter for different DM–DM self-interaction strengths $G$ (fm$^2$). Higher $G$ corresponds to stronger repulsive self-interactions.
• Figure 2: Mass–radius relations for neutron stars with different equations of state (EoSs). Shown are nucleon-only (QMC), strange matter (MIT bag model), and dark-matter–admixed stars with varying self-interaction strengths $G$. The radius of light neutron stars is smaller because the EoS is not optimized in the lower energy density region (outer crust region) Husain_2020.
• Figure 3: The normalised damping time of the f-mode as a function of stellar mass. Nucleon-only stars exhibit the shortest damping times, while strange-matter stars show longer-lived oscillations.
• Figure 4: The relationship between mass-scaled angular frequency and compactness, where mass is given in solar masses and radius in given in kilometers, demonstrating a universal trend, is plotted for selected dark matter equations of state (EoSs). This analysis includes various DM-DM self-interaction strengths.
• Figure 5: The relationship between mass-scaled angular frequency and effective compactness is plotted for selected dark matter EoSs, including various DM-DM self-interaction strengths.