A self-consistent single-fluid framework for neutron stars admixed with mirror dark matter

Technical Summary: A Self-Consistent Single-Fluid Framework for Neutron Stars Admixed with Mirror Dark Matter

Problem Statement
The nature of dark matter (DM) remains an open question, with its mass, coupling strength, and interaction modes undetermined by direct detection experiments. While compact objects like neutron stars (NSs) serve as potential astrophysical laboratories for indirect DM detection, existing modeling approaches suffer from significant limitations.

1. Two-Fluid Formalisms: These treat DM and baryonic matter (BM) as separate fluids interacting only via gravity. This allows for DM cores or halos but fails to capture non-gravitational interactions that could alter the equation of state (EOS).
2. Existing Single-Fluid Approaches: These typically fix the DM Fermi momentum ($k_F^\chi$) as an external parameter. This results in a nearly uniform DM number density ($n_\chi$) throughout the star, causing the relative DM fraction ($n_\chi/n_B$) to decrease toward the high-density core. This profile contradicts realistic capture scenarios where scattering and thermalization should couple DM content to the local baryonic environment.
3. Neutron-Decay Equilibrium Models: Some approaches impose $\mu_\chi = \mu_n$ to determine DM populations. While useful as a limiting case, this can overestimate DM abundance by ignoring finite capture rates and scattering cross-sections, potentially leading to unphysical DM populations unless strong repulsive self-interactions are artificially introduced.

There is a need for a self-consistent framework that controls the DM content at realistic levels, allows the local DM density to track the baryonic density, and links the interaction strength directly to particle physics constraints.

Methodology
The authors develop a self-consistent single-fluid framework based on a mirror dark matter scenario, where the dark sector is an exact copy of the visible baryonic sector (identical particle content, masses, and interactions). The key methodological components include:

• Interaction Mechanism: The two sectors are coupled via a contact vector current–current interaction ($L_{DB} = \alpha (\bar{\psi}_D \gamma^\mu \psi_D)(\bar{\psi}_B \gamma^\mu \psi_B)$). This generates mutual mean-field shifts in the effective chemical potentials of both sectors: $-\alpha n_B$ for the dark sector and $-\alpha n_D$ for the baryonic sector.
• Global Constraint: Instead of fixing the Fermi momentum, the framework fixes the global DM fraction $F_D = N_D/N_B$ (the ratio of total dark to baryonic particle numbers). Since both sectors occupy the same stellar volume, this imposes a local relation $n_D = F_D n_B$, ensuring the DM density scales self-consistently with the baryon density throughout the star.
• Equations of State (EOS): The study employs four Relativistic Mean-Field (RMF) models with varying symmetry energy slopes: NL3$\omega\rho$, FSU2R, NL3, and DDME2 (a density-dependent model requiring rearrangement self-energy terms for thermodynamic consistency).
• Parameter Constraints: The coupling constant $\alpha$ is directly related to the spin-independent DM–nucleon scattering cross-section ($\sigma_{DN}$) constrained by terrestrial direct-detection experiments (specifically CRESST-III limits for $\sim 1$ GeV DM).
• Numerical Solution: The coupled mean-field equations are solved simultaneously with baryon number conservation and $\beta$-equilibrium (and charge neutrality) imposed separately for each sector. The resulting EOS is used to solve the Tolman–Oppenheimer–Volkoff (TOV) equations to determine stellar structure.

Key Contributions

1. Thermodynamic Consistency: The framework provides a physically motivated alternative to fixed-density prescriptions, allowing the local DM density to follow the baryonic matter density naturally. It avoids the artificial density profiles of fixed-$k_F$ models and the potential overestimation of DM in equilibrium-only models.
2. Micro-Macro Bridge: By relating the coupling strength $\alpha$ to $\sigma_{DN}$, the work establishes a direct quantitative link between compact star observables and particle-physics constraints from terrestrial experiments.
3. Unified Treatment: It treats DM not merely as a gravitational component but as a dynamically coupled fluid that modifies the EOS, particle composition, and global stellar properties through non-gravitational interactions.

Results
The application of this framework to mirror DM admixed with NS matter yields several systematic findings across all tested EOS models:

• Softening of the EOS: The DM–BM interaction weakens the binding of dense matter and reduces its incompressibility ($K_0$). As $F_D$ increases from 0% to 10%, the EOS shifts to lower pressures at fixed energy density.
• Macroscopic Changes:
  • Maximum Mass: The maximum supported mass ($M_{max}$) decreases by approximately 7–9% (e.g., from 2.76 to 2.56 $M_\odot$ for NL3$\omega\rho$).
  • Compactness: Neutron stars become more compact, with central densities ($n_c$) increasing and radii ($R$) decreasing by roughly 0.8–1.0 km for a 1.4 $M_\odot$ star.
  • Binding Energy: The binding energy per nucleon becomes less negative, indicating a reduction in the overall stability of the system.
• Microscopic Composition: The interaction drives the matter toward a more neutron-rich composition. The proton fraction ($Y_p$) is systematically suppressed at a given density to satisfy $\beta$-equilibrium and charge neutrality in the presence of the DM-induced chemical potential shifts.
• Direct Urca (DU) Process: The suppression of the proton fraction shifts the onset density of the direct Urca process ($n_{DU}$) to higher stellar densities.
  • For models with a stiff symmetry energy (e.g., NL3), this shift moves the onset of rapid cooling to more massive stars.
  • For models with a soft symmetry energy (e.g., NL3$\omega\rho$, FSU2R), the increased compactness can shift the onset to less massive stars, or in the case of DDME2, the DU process may not occur at all within the supported mass range.
• Observational Compatibility: The DDME2 model with DM admixture shows the most favorable agreement with multimessenger constraints (GW170817, HESS J1731-347, and massive pulsars), maintaining consistency with the $\sim 2 M_\odot$ mass limit while moving closer to radius constraints, though it requires a relatively large $F_D$ to satisfy the HESS J1731-347 region.

Significance and Claims
The paper claims that mirror DM admixtures fundamentally modify both the microscopic composition (increasing neutron richness) and the macroscopic structure (increasing compactness, reducing maximum mass) of neutron stars.

The significance of this work lies in its provision of a thermodynamically consistent, observationally constrained platform for exploring DM signatures. The authors assert that the framework allows NS measurements to be interpreted within the same parameter space probed by direct-detection experiments. The predicted signatures—specifically the simultaneous reduction in maximum mass, increase in compactness, and the shifting of the direct Urca cooling onset—constitute a potential multimessenger signature of mirror DM. This offers a promising avenue for testing dark matter physics in the extreme environments of compact stars, distinguishing this single-fluid approach from previous two-fluid or fixed-density models.