Limits on dark matter existence in neutron stars from recent astrophysical observations and mass correlation analysis

TL;DR

The paper investigates the existence and extent of dark matter in neutron stars by modeling dark matter admixed neutron stars (DANSs) with twelve covariant density functional (CDF) nuclear matter EoS and a self‑interacting fermionic DM EoS, solving two‑fluid TOV equations to capture gravitational coupling. By applying multimessenger observational constraints from NICER and GW170817, it derives upper limits on the DM content and uncovers a strong linear correlation between the DM fraction and the maximum mass of a pure neutron star, enabling a model‑independent posterior for the DM mass in DANSs. The authors construct posterior distributions for DM content, e.g., $M_ ext{χ}^{ ext{max}}=0.150^{+0.070}_{-0.051} obreak ext{M}_ ext{⊙}$ at 68% CL, and provide DM mass fraction priors under TycM and MaxM scenarios, which can serve as priors for interpreting potential DANS observational signatures such as anomalous tidal deformabilities and gravitational‑wave features. Overall, the work offers a robust framework to constrain DM in NSs by linking global NS properties to DM content, reducing model dependences from the NM EoS choices, and enabling informed interpretations of future multimessenger signals.

Abstract

Dark matter admixed neutron stars (DANSs) serve as a specific astrophysical laboratory for probing the features of dark matter (DM) and have emerged as a promising candidate for interpreting recent astrophysical observations (e.g., by NICER and LIGO/Virgo). Accurately constraining the internal DM content of DANSs is therefore of critical importance. In this work, we construct the equations of state (EoS) for DANS matter by employing twelve nuclear matter (NM) models within the covariant density functional (CDF) theory and a self-interacting fermionic model for DM. Using these EoSs as input, we solve the two-fluid Tolman-Oppenheimer-Volkov (TOV) equations to systematically investigate the influence of DM on the global properties of neutron stars (NSs). By incorporating recent observational constraints on NS properties, the maximum DM mass fraction $f_χ^{\mathrm{max}}$ in DANSs is determined for each NM EoS model. Our analysis reveals a strong linear correlation (Pearson coefficient $r=0.98$) between $f_χ^{\mathrm{max}}$ and the maximum mass of a pure NS, $M_{\rm{NS}}^{\mathrm{max}}$, described by $f_χ^{\mathrm{max}} = 0.22 M_{\mathrm{NS}}^{\mathrm{max}} - 0.44$. Leveraging this correlation and the observed NS maximum mass distribution, $P(M_{\text{NS}}^{\max} \mid \text{EM})$, we derive the probability distribution function (PDF) for the maximum DM mass, $P(M_χ^{\max} \mid \text{EM})$, in DANSs. We find that at the 68\% confidence level, $M_χ^{\mathrm{max}}=0.150^{+0.070}_{-0.051}\ M_{\odot}$. This quantitative constraint on the DM mass provides a critical prior for interpreting potential observational signatures of DANSs, such as anomalous tidal deformabilities and distinctive gravitational-wave signals.

Figures (6)

• Figure 1: The pressure as a function of the energy density for both $\beta$-equilibrated nuclear matter ($P_{\rm{N}}$ vs $\varepsilon_{\rm{N}}$) and the fermionic dark matter ($P_{\chi}$ vs $\varepsilon_{\chi}$). The CDF models are selected from DDRHF models (blue), DDRMF models (olive green), and NLRMF models (red). The dark matter model (labeled as DM) takes the value of $m_{\chi}=1000$ MeV, and the dimensionless self-interaction strength $y=0.1$.
• Figure 2: Mass-radius relations of pure neutron stars obtained by the selected CDF equations of state. The shaded regions indicate several astrophysical observational constraints, including the distribution of the pulsar mass limit (green) from electromagnetic observations romani2022psr, the mass-radius measurements from the NICER mission for PSR J0030+0451 (yellow) Vinciguerra_2024 and the brightest known millisecond pulsar PSR J0437-4715 (blue) Choudhury_2024, the gravitational wave event GW170817 (red) Abbott2017PhysRevLett.
• Figure 3: Mass-radius relations (the total mass $M_{\rm{T}}$ vs the observable radius $R_{\rm{T}}$) of dark matter admixed neutron stars with different dark matter fraction $f_{\chi}$ (dashed lines with graduated colors), using the CDF model PKO3. For comparison, the case of pure neutron stars is given by the solid line. The dash-dotted line marks the fixed mass of $M_{\rm{T}}=1.4~M_{\odot}$.
• Figure 4: For a DANSs with fixed total mass of $M_{\rm{T}}=1.4\,M_\odot$, the mass of the dark matter component $M_\chi$ as a function of DM radius $R_\chi$, which is evolved with increasing DM mass fraction $f_{\chi}$, the results are given by different CDF models. The maximum DM masses which are permissible from TycM constraints $M_{\mathrm{\chi}}^{\mathrm{*1.4}}$ (open circles) and constrained by the MaxM$M_{\mathrm{\chi}}^{1.4}$ (solid circles) are marked.
• Figure 5: Linear correlation between the maximum dark matter mass fraction (derived from $1.4\,M_\odot$ DANSs) and the maximum mass of a pure neutron stars. The dashed line represents the TycM constraints limit $f_{\chi}^{\mathrm{*max}}$, with a Pearson correlation coefficient of $r_1 = \mathrm{0.97}$. The blue shaded area denotes the confidence interval. The dotted line represents the MaxM constraints limit $f _{\chi}^{\mathrm{max}}$, with a Pearson correlation coefficient of $r_1 = \mathrm{0.98}$. The red shaded area denotes the confidence interval. Bottom panel: the probability distribution function of maximum mass limit $P(M_{\text{NS}}^{\max} \mid \text{EM})$ for a pure neutron star constrained by MaxMromani2022psr. Left panel: the posterior probability distribution function $P(f_{\chi}^{\max}|\text{EM})$ of the DM mass fraction limit is derived via the linear correlation between $f_{\mathrm{\chi}}^{\max}$ and $M_{\mathrm{NS}}^{\mathrm{max}}$ in combination with $P(M_{\text{NS}}^{\max} \mid \text{EM})$.