Dark matter in neutron stars: two-fluid $f$-mode oscillations in full general relativity

A dark-matter core and a soft nuclear equation of state can produce similar mass--radius signatures, motivating a complementary probe through the $f$-mode spectrum. We compute quadrupolar $f$-mode frequencies and gravitational-wave damping times in full general relativity for cold, nonrotating neutron stars admixed with self-interacting bosonic dark matter (DM). Our two-fluid survey spans 21 nuclear equations of state covering nucleonic, hyperonic, $Δ$-admixed, and combined hyperon--$Δ$ compositions at $F_{\rm DM}=1$--$20\%$. The main sequences use $λ=π$ and boson masses of $500$ and $100\,\mathrm{MeV}$ for the core and halo studies, respectively. Independent normal-matter (NM) and DM displacements couple through the metric, yielding NM-led and DM-led $f$-mode branches whose radiative damping is determined by outgoing-wave boundary conditions. At $1.4\,M_\odot$, the core DM-led damping time decreases from order $10^3\,\mathrm{s}$ at $F_{\rm DM}=1\%$ to order $1\,\mathrm{s}$ at $20\%$, approximately following an empirical $F_{\rm DM}^{-2}$ dependence, while NM-led damping times remain within $0.12$--$0.33\,\mathrm{s}$. Halo DM-led damping instead increases with dark fraction: at the same stellar mass and $F_{\rm DM}=20\%$, dark radii approach $88\,\mathrm{km}$, frequencies fall to $0.14\,\mathrm{kHz}$, and damping times reach approximately $450\,\mathrm{s}$. Selected high-mass core sequences exhibit strong DM-led damping-time upturns not reproduced by the leading mass-quadrupole diagnostic. Representative core calculations show greater DM-led sensitivity to the bosonic self-coupling and retain both branches at $\ell=3$. Under the adopted nonrotating, circular-binary prescriptions, no evaluated configuration satisfies all geometric and perturbative conditions for a controlled linear tidal resonance.

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Authors

Prashant Thakur; Ishfaq Ahmad Rather; Y. Lim

Published

Oct 3, 2026

Paper type

preprint

Source

Arxiv