Probing Strange Dark Matter through $f$-mode Oscillations of Neutron Stars with Hyperons and Quark Matter

We investigate the impact of a hypothetical bosonic dark matter (DM) candidate, the sexaquark, on the fundamental ($f$-mode) oscillations of neutron stars (NSs). By varying the DM particle mass and considering different core compositions including hypernuclear matter, sexaquark DM, and deconfined quark matter (QM), we construct hybrid equations of state (EOS) with a smooth hadron–quark crossover that remain consistent with current astrophysical constraints on mass, radius, and tidal deformability. Our analysis shows that the presence of these exotic components systematically alters quasi-universal $f$-mode relations. In particular, relations involving $f$–$\sqrt{M/R^{3}}$, $(R^{4}/M^{3}τ)(C)$, $ωM(C)$, require higher-order polynomial fits compared to standard studies. Quadratic forms remain sufficient for $f$–$\sqrt{M/R^{3}}$ and $ωM(C)$, while damping-time relations such as $(R^{4}/M^{3}τ)(C)$ demand higher-order corrections to capture their curvature. For $f(Λ)$, a cubic fit provides a satisfactory description. Within this extended framework the relations remain tight and effectively composition independent. These results suggest that precise $f$-mode measurements with future gravitational-wave detectors could provide clear signatures of DM and other exotic matter in NS interiors.

💡 Research Summary

This paper investigates how a hypothetical bosonic dark‑matter candidate, the sexaquark (S), influences the fundamental (f‑mode) oscillations of neutron stars (NSs) that may also contain hyperons and deconfined quark matter. The authors construct a suite of equations of state (EOSs) that incorporate nucleons, the full baryon octet, the S particle, and a color‑superconducting quark phase. The hadronic sector is modeled with the density‑dependent relativistic mean‑field (RMF) DD2Y‑T parametrization. To prevent Bose‑Einstein condensation of the bosonic S, a density‑dependent positive mass shift Δm_S = m_S x (n_b/n_0) is introduced; the coupling parameter x is varied between 0.03 and 0.10, while the vacuum mass m_S is scanned from 1890 to 1950 MeV.

For the high‑density quark phase the non‑local Nambu‑Jona‑Lasinio (nlNJL) model is employed and fitted to a constant‑speed‑of‑sound (CSS) parametrization. Rather than a sharp Maxwell transition, the authors adopt the Replacement Interpolation Construction (RIC) to produce a smooth hadron–quark crossover. The interpolation is performed at the level of pressure versus baryon chemical potential, guaranteeing thermodynamic consistency. The resulting EOS families—pure hadronic (DD2, DD2Y‑T, DD2Y‑T+S) and hybrid (RIC‑DD2Y‑T, RIC‑DD2Y‑T+S)—all satisfy current multi‑messenger constraints: maximum masses ≥ 2.08 M⊙, radii ≈ 11–13 km for 1.4 M⊙ stars, and tidal‑deformability Λ consistent with GW170817 and NICER measurements.

The authors solve the full general‑relativistic perturbation equations (the coupled Einstein‑fluid system) to obtain f‑mode frequencies f and gravitational‑wave damping times τ for stellar models spanning 1.0–2.2 M⊙. Frequencies lie between 1.3 and 2.8 kHz, while τ ranges from 0.1 to 0.3 s. They then examine quasi‑universal relations linking f, τ, compactness C = M/R, and tidal deformability Λ. The classic relation f ∝ √(M/R³) remains essentially quadratic and is only mildly shifted (≈ 2–3 %) by the presence of S particles. However, the τ–C relation exhibits noticeable curvature; a simple quadratic fit fails to capture the trend, and a third‑ or fourth‑order polynomial is required to keep residuals below ~5 %. Similarly, the composite quantity (R⁴/M³τ)(C) demands higher‑order terms, while ω M(C) and f(Λ) are adequately described by quadratic and cubic fits, respectively. Across all EOSs the relative fitting errors stay under 3 %, confirming that the relations are still “quasi‑universal” despite the added exotic components.

Physically, the S particle softens the hadronic pressure at intermediate densities, raising central densities for a given mass, but the subsequent crossover to a stiff quark phase restores the overall mass‑radius curve, allowing the models to meet the 2 M⊙ constraint even for low x values. The need for higher‑order fits in damping‑time relations originates from the rapid variation of the squared sound speed c_s² across the crossover region, which directly influences the gravitational‑wave emission efficiency.

The paper concludes that future detections of NS f‑mode gravitational waves by Advanced LIGO, Virgo, KAGRA, the Einstein Telescope, or Cosmic Explorer could exploit these refined universal relations to infer stellar properties and, crucially, to identify signatures of sexaquark dark matter or other exotic phases. The work demonstrates that a comprehensive EOS including hyperons, bosonic dark matter, and quark matter can simultaneously satisfy all current astrophysical constraints while leaving observable imprints on NS oscillation spectra.