Implications of Fermionic Dark Matter Interactions on Anisotropic Neutron Stars

TL;DR

We address how dark matter (DM) admixture and pressure anisotropy affect neutron-star structure, using a two-fluid formalism with three nuclear EOS (AP3, BSk22, MPA1) and a fermionic DM EOS from Yukawa-interacting self-coupled DM. The approach combines anisotropic TOV equations and tidal deformability calculations to map mass-radius and $\Lambda$ across DM subfractions and DM–BM coupling $g$, comparing results against GW170817, NICER, and pulsar data. Key findings show that increasing anisotropy and DM subfraction can still satisfy observational constraints, with DM forming either a core or halo around baryonic matter and with coupling strength $g$ driving core–halo transitions and extreme $\Lambda$ values that may be ruled out by data. The work highlights the potential of binary pulsar observations and future gravitational-wave measurements to constrain or reveal DM-admixed anisotropic NSs, and provides a framework to test DM scenarios in compact objects.

Abstract

The presence of Dark matter (DM) within a neutron star (NS) can substantially influence the macroscopic properties. It is commonly assumed that the pressure inside an NS is isotropic, but in reality, pressure is locally anisotropic. This study explores the properties of anisotropic NS with a subfraction of DM (isotropic) trapped inside. Implementing a two-fluid formalism with three Equations of State (EOS): AP3 (a realistic nucleon-nucleon interaction model), BSk22 (modeling atomic nuclei and neutron-matter), and MPA1 (considering relativistic effects in nuclear interactions). The properties of NS, such as mass ($M$), radius ($R$), and dimensionless tidal deformability ($Λ$), for various DM-anisotropic configurations, have been rigorously tested against observational constraints. These constraints include data from the binary NS merger GW170817, NICER x-ray measurements, and pulsar mass-radius observations. We observe that with increasing DM subfraction, higher anisotropies could also satisfy the observational constraints. Furthermore, increasing the coupling ($g$) between DM and its mediator leads to the formation of a core-halo structure, with a DM halo surrounding the baryonic matter (BM). Specifically, for coupling values of $g = 10^{-4}$, $10^{-3.7}$, and $10^{-3.5}$, we observe that the maximum radius ($R_{max}$) decreases with increasing anisotropy, which contrasts with the behavior at $g = 10^{-5}$ and in scenarios with no DM. Our analysis indicates that binary pulsar systems could potentially constrain the extent of admixed anisotropic NS or, more optimistically, provide evidence for the existence of DM-admixed anisotropic NS.

Figures (40)

• Figure 1: The plot compares the pressure (MeV/fm$^3$) as a function of energy density (MeV/fm$^3$) for three EOS models: AP3 (solid blue line), MPA1 (dashed red line), and BSk22 (dash-dotted black line), highlighting the variation in the stiffness of the isotropic BM across different models.
• Figure 2: The profile shows the speed of sound squared normalized by the squared speed of light as a function of radius (Km) for three EOS models (as seen in Fig. \ref{['fig:Press_VS_Energy']}). This illustrates the differences in the speed of sound within an isotropic NS, indicating how the internal structure varies depending on the chosen EOS.
• Figure 10: Mass-radius stability profile for 5% DM-admixed anisotropic NS with varying $g$-values, as labeled, and constant $m_\chi=1$GeV, and $m_\phi=1$KeV. The color contour represents the range of $\alpha$-values from $-2$ to $2$. The subplots correspond to (a) AP3 EOS, (b) BSk22 EOS, and (c) MPA1 EOS. Observational constraints are shown with deep sky blue (PSR J0952-0607), red (PSR J0740+6620), orange (PSR J0348+0432), black (PSR J1614-2230), steel-blue solid patch (GW170817 90%), steel-blue dashed patch (GW170817 50%), red and black dashed line for PSR J0030+0451.
• Figure 11: Tidal deformability-mass stability profile, with the same setup as in Fig. \ref{['g vary MvsR']}
• Figure 12: Correlation coefficients of different NS observables