Effects of Mirror Dark Matter on Neutron-Star Structure and Tidal Deformability

Abstract: Mirror dark matter (MDM) can modify neutron-star structure and tidal response through gravitational coupling. In this work, we construct an ordinary-matter equation of state (EOS) by comparing hadronic matter described by the relativistic mean-field NL3(ωρ) model, and quark matter in the framework of the Nambu--Jona-Lasinio (NJL) model. The stable branch is determined through a Maxwell construction, which serves to connect distinct phases of matter. For the parameter sets considered here, (m_u=5.2~{\rm MeV}) is the lowest light current-quark mass in the scanned range that satisfies the (2M_\odot) maximum-mass requirement, while (m_u>5.2~{\rm MeV}) all yield stable neutron-star configurations without a resolved macroscopic quark core. The small-radius inferences for PSR J0437--4715 and XTE J1814--338, together with the tidal-deformability constraint from GW170817, are sensitive to the dark-matter mass fraction (f_D). The commonly used GW170817 interval (70\lesssimΛ_{1.4}\lesssim580) corresponds approximately to (0.12\lesssim f_D\lesssim0.88) in the present model. These results indicate that, even without a macroscopic quark core, MDM can provide an important mechanism for reducing the visible radius and modifying the tidal response of neutron stars.

• The paper demonstrates that mirror dark matter compresses ordinary matter in neutron stars, reducing visible radii and modifying tidal deformability.
• It employs a two-fluid TOV framework with a unified EOS to model phase transitions and the interplay of nucleonic, hyperonic, and quark matter.
• Observational constraints from GW170817 and NICER map to a wide range of mirror dark matter fractions, revealing unique nonmonotonic tidal signatures.

Mirror Dark Matter and Its Impact on Neutron-Star Structure and Tidal Deformability

Equation of State Construction and Phase Transitions

This study investigates how mirror dark matter (MDM), when coupled only gravitationally, fundamentally modifies the macroscopic observables of neutron stars. The approach begins by constructing a unified ordinary-matter EOS incorporating nucleonic matter, hyperonic matter, and quark matter (both two- and three-flavor) within the NL3$\omega\rho$ mean-field and NJL effective models, respectively. First-order hadron--quark transitions are handled self-consistently using Maxwell construction, not presupposing the nature of the compact object (neutron star, hybrid star, or quark star).

Analysis of the pressure envelope $P(\mu_B)$ for several representative quark masses (Fig. 1) shows the stable phase is dictated by maximal pressure at each baryon chemical potential among nucleonic, hyperonic, and quark phases.

Figure 1: Pressure envelope $P(\mu_B)$ resulting from Maxwell construction across several light-quark masses, with highlighted phase transitions.

The Maxwell construction reveals that, for light current-quark masses $m_u \geq 5.2$ MeV, the core of stable stellar configurations is dominated by hyperonic matter, with the transition to deconfined three-flavor quark matter occurring only at high density, and the appearance of macroscopic quark cores is absent. The two-flavor quark phase is never selected as stable for these parameter choices.

The ordinary-matter EOS in the $\epsilon-P$ plane (Fig. 2) exhibits a sharp energy-density discontinuity marking the hyperon-to-three-flavor quark transition, but in the relevant density regime for canonical neutron-star radii and masses, the EOS is hadronically dominated. The squared sound speed $c_s^2$ further emphasizes the microphysical differences only at high pressure (Fig. 3).

Figure 2: EOS in the $\epsilon$-$P$ plane showing phase transitions resolved by Maxwell construction, with energy-density jump.

Figure 3: Squared sound speed $c_s^2$ as a function of pressure, indicating the EOS's microphysical phase structure.

Two-Fluid Stellar Structure with Mirror Dark Matter

MDM is postulated to be governed by identical microphysical laws as ordinary matter, yielding an EOS $\epsilon_D(P) = \epsilon_Q(P)$, but is coupled exclusively via gravity. Stellar equilibrium is described in the two-fluid TOV framework. Each configuration is specified by central pressures $P(\mu_B)$0, resulting in a two-dimensional family of equilibrium solutions parameterized by the MDM mass fraction $P(\mu_B)$1.

The global distribution of stable configurations exhibits a wide spanning in radius for fixed mass, determined by $P(\mu_B)$2 (Fig. 4), independent of the EOS branch changes that only affect the highest-mass regime. The $P(\mu_B)$3 relation (Fig. 5) demonstrates that as $P(\mu_B)$4 increases, the ordinary-matter (visible) radius $P(\mu_B)$5 decreases for a fixed total mass.

Figure 4: Population of stable neutron star models in the $P(\mu_B)$6 plane as a function of MDM mass fraction $P(\mu_B)$7.

Figure 5: Mass--radius relations for several fixed values of $P(\mu_B)$8 compared with X-ray and NICER constraints.

Configurations are further characterized by whether MDM occupies a central "core" ($P(\mu_B)$9) or an extended "halo" ($P(\mu_B)$0), impacting the relation between the visible and gravitational radii (Fig. 6).

Figure 6: Schematic illustrating the evolution of ordinary-matter and MDM boundaries as a function of $P(\mu_B)$1 at fixed total mass.

Tidal Deformability and Astrophysical Constraints

The dimensionless tidal deformability $P(\mu_B)$2 is computed for the two-fluid models, where the relevant compactness uses the total gravitational radius $P(\mu_B)$3. The $P(\mu_B)$4 relation (Fig. 7) shows a strong dependence on $P(\mu_B)$5, due to the strong scaling $P(\mu_B)$6, enhancing even modest changes in stellar compactness.

Figure 7: Dimensionless tidal deformability $P(\mu_B)$7 as a function of mass, showing strong dependence on MDM fraction $P(\mu_B)$8.

The GW170817 constraint $P(\mu_B)$9 maps to a broad range of MDM mass fractions, $m_u \geq 5.2$0, within this model. The model exhibits symmetry under $m_u \geq 5.2$1 owing to the identical EOSs for the two fluids.

Nonmonotonicity and Diagnostic Implications

The maximum mass $m_u \geq 5.2$2 and $m_u \geq 5.2$3, after stability filtering, depend nonmonotonically on $m_u \geq 5.2$4 (Fig. 8). Both approach the single-fluid ordinary-matter value at $m_u \geq 5.2$5 or 1, peaking/deviating maximally for intermediate $m_u \geq 5.2$6 where the two fluids have comparable gravitational influence. This nonmonotonic behavior is a unique signature of two-fluid, MDM-admixed models, enabling observational distinction from pure hadron-quark transition scenarios.

Figure 8: Maximum mass $m_u \geq 5.2$7 and tidal deformability $m_u \geq 5.2$8 as functions of MDM mass fraction $m_u \geq 5.2$9, highlighting the nonmonotonic behavior induced by two-fluid coupling.

Theoretical and Observational Implications

The principal theoretical result is that inclusion of a gravitating MDM component enables the reduction of visible radii and the modification of tidal response in neutron stars—without requiring a resolved quark core—by gravitationally compressing the ordinary-matter sector. This provides an alternative mechanism to hybrid or pure-quark EOS models for matching small-radius and low-$\epsilon-P$0 emission, such as that inferred for PSR J0437–4715, XTE J1814–338, and GW170817. Importantly, the EOS parameter space (e.g., $\epsilon-P$1) considered always fulfills the $\epsilon-P$2 maximum-mass constraint, and MDM effects decouple radius and tidal deformability observably from the EOS's intrinsic stiffness.

From a phenomenological perspective, small-radius inferences favor nonzero $\epsilon-P$3, while GW170817 tidal constraints are mapped to significant intervals in $\epsilon-P$4. Simultaneous electromagnetic and gravitational wave observations have enhanced discriminatory power: the two-fluid MDM scenario predicts a symmetry and broad allowed region in $\epsilon-P$5, which is challenging to reconcile within single-fluid EOS frameworks exhibiting stiff, hadron-only matter.

Conclusion

The model developed here demonstrates that gravitationally coupled mirror dark matter, even in the absence of macroscopic quark cores, has a pronounced impact on neutron-star mass–radius and tidal deformability relations. These effects are quantifiable, nonmonotonic functions of the MDM mass fraction, offering rich observational tests. Future research should consider alternative microphysical inputs (e.g., NJL vector interactions, phase coexistence phenomena), possible non-gravitational interactions in the MDM sector, and statistical inference with multimessenger data to further constrain or detect MDM contributions in neutron-star populations.