Revealing Dark Matter's Role in Neutron Stars Anisotropy: A Bayesian Approach Using Multi-messenger Observations

TL;DR

The paper develops a two-fluid Bayesian framework to study dark matter admixture in neutron stars by coupling a pressure-anisotropic baryonic EOS with a self-interacting fermionic DM component and solving the two-fluid TOV equations. It jointly analyzes NICER mass–radius constraints and GW170817 tidal deformability to infer DM parameters $(m_\chi,g,f_\chi)$ and baryonic anisotropy $\alpha$ across three BM EOSs, finding DM fractions up to $\sim10\%$ are compatible and that DM generally softens high-density matter, reducing $R$ and $\Lambda$ while requiring only moderate $\alpha$. A key innovation is the introduction of the DM radius span $\Delta R_\chi$ as a robust diagnostic of DM distributions, which shows strong correlations with DM parameters and offers a path to break degeneracies with future measurements of DM halos or cores in NSs. Overall, the work demonstrates that DM admixture can be accommodated by current multimessenger data, with implications for constraining DM microphysics and guiding next-generation observations such as advanced x-ray and gravitational-wave instruments.

Abstract

Dark matter (DM) continues to evade direct detection, but neutron stars (NSs) serve as natural laboratories where even a modest DM component can alter their structure. While many studies have examined DM effects on NSs, they often rely on specific choices of equations of state (EOS) models, assume isotropy, and lack a Bayesian statistical framework, limiting their predictive power. In this work, we present a Bayesian framework that couples pressure-anisotropic nuclear EOS to a self-interacting fermionic DM component, constrained by NICER and GW170817 data. Our results show that DM mass fractions up to $\sim10\%$ remain consistent with current data, which softens the high-density EOS, leading to reduced stellar radii and tidal deformabilities while requiring negligible pressure anisotropy. Bayesian model comparison reveals no statistically significant preference between pure baryonic and DM-admixed NSs, indicating that DM inclusion enhances physical realism without complexity penalties. However, existing data cannot tightly constrain the DM parameters, and our empirical radius definition introduces a systematic bias toward the DM core configurations. To address this, we therefore introduce the DM radius span $ΔR_χ\equiv R_{χ,\mathrm{max}} - R_{χ,\mathrm{min}}$ as a unified diagnostic for DM distributions. This parameter simultaneously characterizes core-halo transition features while exhibiting strong linear correlations ($ΔR_χ< 4\,\mathrm{km}$) with both DM and BM parameters, providing a clear avenue for future constraints. Our approach bridges current limitations and future potential in probing DM through compact star observations.

Figures (13)

• Figure 1: The DM EOS as a function of $m_\chi$ (upper) and $g$ (lower) while fix $\log_{10}g=-4$ ($m_\chi=[parse-numbers=false]{10^3}{MeV}$)
• Figure 2: Corner plot showing the 1D marginalized posteriors and 2D joint distributions of DM properties, anisotropy parameter, and central densities in the DANS framework, obtained via Bayesian inference using combined x-ray and GW data. The densities labeled from $\rho_{c,1}$ to $\rho_{c,4}$ correspond to the central densities of J0030, J0740, J0437, and the lighter NS in GW170817, respectively. Color-coded contours represent DM admixed with different BM EOS: BSk22 (yellow), MPA1 (blue), and AP3 (red). Darker and lighter regions correspond to 68% and 99% credible regions respectively. In the 1D corner plots, the two dashed lines mark the 15.87th and 84.13th percentiles of the parameter distributions. The titles display the median value along with these percentile bounds for each parameter.
• Figure 3: The posterior distributions of DM parameters under the isotropic BM constraint ($|\alpha|< 0.001$), derived from the resampling of the full DANS parameter space. The shaded contours, dashed lines, and numerical annotations follow the same conventions as described for Figure \ref{['fig:param_all']}
• Figure 4: Heatmap illustrating pairwise model comparisons via Bayes' factors, where all values follow the definition in \ref{['eq:Bayes_factor']}. Model labels on the vertical axis (left) denote the numerator (Model-I), and those on the horizontal axis (bottom) denote the denominator (Model-II) in the Bayes' factor ratio. A dashed line divides the matrix into upper and lower triangles, which exhibit reciprocal values ($\mathcal{B}_{\mathrm{I-II}} = 1/\mathcal{B}_{\mathrm{II-I}}$) as required by the definition of Bayes' factor. Each label commences with the EOS abbreviation (e.g., BSk22, MPA1, AP3), succeeded by suffixes indicating physical modifications. The '-DM' suffix indicates DANS, while '-$\alpha$' signifies the inclusion of pressure anisotropy. Labels without hyphens represent the pure isotropic benchmark cases. Deep blue (red) regions highlight that Model-I (-II) is significantly favored, with values exceeding 3.2 (or falling below $1/3.2=0.3125$).
• Figure 5: The posterior distributions of the characteristic radii $R_\chi$, $R_B$ and $R$ each versus $M$ for the BSk22-DM EOS, shown as a representative case. The shaded regions indicate the 68% and 99% credible regions, with yellow, blue, and red corresponding to $R_\chi$, $R_B$ and $R$, respectively. The dashed cyan line with a marker represents the $M$-$R$ relation for the corresponding isotropic solution.