Universal relation involving fundamental modes in two-fluid dark matter admixed neutron stars

TL;DR

The paper investigates whether universal asteroseismic relations known from standard neutron stars persist when dark matter is admixtured into the star. Using a two-fluid relativistic framework in the Cowling approximation, it analyzes self-interacting fermionic dark matter that interacts with normal matter only via gravity, across multiple nuclear EOSs and DM fractions. The key finding is that while the universal relations involving the tidal deformability $\Lambda_t$ and the mass-scaled $f$-mode frequency $f_f M$ break down in dark-matter-admixed stars, the $f_f M$–$M/R$ relation for normal matter in dark-core configurations and for dark matter in dark-halo configurations remains largely universal across DM parameters. This provides a potential observational signature of DM in neutron stars, suggesting that joint measurements of compactness and tidal deformability could help distinguish DM-admixed stars from ordinary neutron stars; the study also points to extending the analysis beyond the Cowling approximation for more precise asteroseismology.

Abstract

We systematically investigate the fundamental oscillation frequencies of dark matter admixed neutron stars, focusing on models with self-interacting fermionic dark matter that couples to normal matter solely through gravity. The analysis is carried out within a two-fluid formalism under the relativistic Cowling approximation, where the perturbation equations follow from the linearized energy-momentum conservation laws of both components. We find that the mass-scaled fundamental frequencies of the nuclear (dark) fluid in dark core (halo) configurations exhibit a remarkably tight correlation with the total stellar compactness. This universality persists across the dark matter parameter space explored in this study and is largely insensitive to the choice of nuclear equation of state. In contrast, we also find the breakdown of such universality with the tidal deformability, i.e, the same frequencies show substantial deviations from universality when expressed in terms of the tidal deformability. These contrasting behaviors highlight possible observational imprints of dark matter in neutron star interiors.

Figures (12)

• Figure 1: Mass-radius relations for dark matter admixed neutron star models constructed using the QMC-RMF4 EOS for baryonic matter. Left panel: Results for fixed interaction strength $g_\chi/m_v=0.04$ MeV$^{-1}$, with varying dark matter mass fractions $M_{\rm DM}/M=0.1$, 0.2, 0.4, 0.6, and 0.8. Right panel: Results for fixed dark matter mass fraction $M_{\rm DM}/M=0.2$, with varying interaction strengths $g_\chi/m_v=0.02$, 0.04, 0.06, 0.08, and 0.10 MeV$^{-1}$. In both panels, the stellar radius, $R$, is defined as the outermost surface, i.e., $R={\rm max}(R_{\rm NM}, R_{\rm DM})$. Solid lines correspond to dark-core configurations where $R_{\rm DM}<R_{\rm NM}$, while open circles represent dark-halo configurations with$R_{\rm DM}>R_{\rm NM}$. For reference, the mass-radius relation for neutron star models without dark matter is also shown with the dotted line, and several astronomical constraints from PSR J0740+6620, PSR J0030+0451, GW170817, and GRB 200415A are also included (see text for details).
• Figure 2: Top panels: Relation between the dimensionless tidal deformability ($\Lambda_t$) and stellar compactness ($M/R$) for various dark matter admixed neutron star models with dark core configurations. The left, middle, and right panels correspond to stellar models with fixed dark matter mass fractions of $M_{\rm DM}/M=0.2$, 0.4, and 0.6, respectively. Different interaction strengths are indicated by symbols: circles $(g_\chi/m_v=0.02\ \rm{MeV}^{-1})$, diamonds $(g_\chi/m_v=0.04\ \rm{MeV}^{-1})$, squares $(0.06\ \rm{MeV}^{-1})$, triangles $(0.08\ \rm{MeV}^{-1})$, and inverted triangles $(0.10\ \rm{MeV}^{-1})$. The thick solid line in each panel represents the empirical relation between $\Lambda_t$ and $M/R$ for standard neutron star models without dark matter, as given by Eq. (\ref{['eq:C_Lam']}). Bottom panels: Relative deviation of the calculated $\Lambda_t$ from the empirical estimate $\Lambda_t^{\rm em}$, defined as $\Delta \Lambda_t/\Lambda_t=(\Lambda_t^{\rm em}-\Lambda_t)/\Lambda_t$. An enlarged view of this deviation for $M_{\rm DM}/M=0.2$ is shown in the inset of the bottom-left panel.
• Figure 3: Same as Fig. \ref{['fig:DC-C-Lam']}, but for dark halo configurations.
• Figure 4: The $f$- and $p_1$-mode frequencies associated with normal (dark) matter, $f_f^{\rm NM}$ ($f_f^{\rm DM}$) and $f_{p_1}^{\rm NM}$ ($f_{p_1}^{\rm DM}$) are shown as a function of the total mass for the dark matter admixed neutron stars with a fixed DM mass fraction of $M_{\rm DM}/M=0.2$ and interaction strength $g_\chi/m_v=0.02$, adopting QMC-RMF4 as normal matter EOS. For reference, the $f$- and $p_1$-mode frequencies of standard neutron stars without dark matter are also shown, denoted by double-circles and double-squares markers.
• Figure 5: The $f$- and $p_1$-mode frequencies are shown in the top and bottom panels, respectively, as a function of the total stellar mass for dark matter admixed neutron stars with three different dark matter mass fractions: $M_{\rm DM}/M = 0.2$, 0.4, and 0.6. The results are computed using QMC-RMF4 as the EOS for normal matter. The left, middle, and right panels correspond to interaction strengths of $g_\chi/m_v = 0.02$, 0.04, and 0.06 MeV$^{-1}$, respectively. In each panel, mode frequencies associated with normal (dark) matter are labeled as N 0.2, N 0.4, N 0.6 (D 0.2, D 0.4, D 0.6), where 0.2, 0.4, and 0.6 denote adopted dark matter mass fractions. For reference, the $f$- and $p_1$-mode frequencies excited in the neutron star models without dark matter are also shown with double-square markers.