Dark-Matter-Admixed Neutron Stars

• Dark-matter-admixed neutron stars are compact objects where a dark component coexists with neutron-star matter, forming cores, halos, or mixed configurations.
• Different modeling approaches—two-fluid formulations, effective one-fluid EOS, and dark-decay setups—yield varied predictions for mass, radius, and tidal deformability.
• Observational probes such as gravitational waves, pulse profiles, and thermal evolution offer practical tests to constrain the dark-sector properties in neutron stars.

Dark-matter-admixed neutron stars are compact stars in which ordinary neutron-star matter coexists with a dark component inside the same gravitationally bound object. In much of the literature, they are modeled as genuinely two-fluid relativistic stars with separate equations of state and separate hydrostatic-balance equations in a common spacetime, although some works instead use a single effective equation of state or a chemically equilibrated dark-decay framework (Leung et al., 2011, Kain, 2021, Cipriani et al., 25 Feb 2025, Shirke et al., 23 Jun 2025). Depending on the dark-sector microphysics, particle mass, self-interaction strength, dark fraction, and rotational state, the dark component can form a compact core, an extended halo, or a mixed configuration, and can alter masses, visible radii, moments of inertia, tidal deformabilities, oscillation spectra, pulse profiles, and thermal evolution (Miao et al., 2022, Jockel, 2023, karan et al., 4 Jul 2026).

1. Relativistic formulation and model classes

A standard starting point is the additive stress-energy tensor

$$T^{\mu\nu}_{\rm tot}=T^{\mu\nu}_{\rm BM}+T^{\mu\nu}_{\rm DM},$$

together with separate conservation laws for the two fluids when baryonic matter and dark matter interact only through gravity,

$$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$

In this framework, each fluid satisfies its own hydrostatic equilibrium equation in the common metric generated by the sum of both components (Cipriani et al., 25 Feb 2025). Static configurations are then obtained from a two-fluid Tolman-Oppenheimer-Volkoff system in which the total pressure and total enclosed mass source the geometry, while each fluid retains its own pressure gradient equation (Kain, 2021, Scordino et al., 2024).

A representative spherically symmetric realization writes

$$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$

$$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$

with separate component radii defined by the vanishing of each pressure and total radius given by $R=\max\{R_{\rm OM},R_{\rm DM}\}$ (Scordino et al., 2024). In the Carter-Comer formulation, the same physics can be expressed through a two-fluid master function $\Lambda(n^2,p^2,x^2)$; in the gravity-only limit the master function is taken independent of $x^2$, so there is no entrainment and the equation of state is separable (Leung et al., 2011).

The term “dark-matter-admixed neutron star” is not restricted to this gravity-only two-fluid tradition. One line of work uses a unified, one-fluid equation of state in which hadronic, leptonic, and dark contributions are summed and then inserted into the ordinary TOV equations, as in Higgs-portal-inspired heavy-fermion models for ultracompact objects (Lopes et al., 2024). Another line uses chemical equilibrium between neutrons and a dark fermion produced by a neutron-dark decay channel, so that the stellar core contains an equilibrated dark component rather than a separately conserved second fluid (Shirke et al., 23 Jun 2025). A further thermal-evolution literature treats captured dark matter inside a finite-temperature relativistic mean-field equation of state, again not as a gravity-only two-fluid system (Kumar et al., 2022). The shared subject is therefore the existence of a dark component in neutron stars; the dynamical implementation differs across subliteratures.

2. Dark-sector microphysics and equation-of-state landscape

The dark sector has been modeled in several distinct ways, ranging from free fermions to self-interacting bosons, lattice-informed strongly interacting dark baryons, and explicitly agnostic sound-speed interpolations.

Model class	Dark-sector description	Representative papers
Free fermionic or mirror DM	Free Dirac Fermi gas; mirror matter uses the same EOS as ordinary matter	(Kain, 2021, Leung et al., 2011, Scordino et al., 2024)
Self-interacting bosonic condensate	Quartic self-coupling, often Bose-Einstein condensed	(Cipriani et al., 25 Feb 2025, Santos et al., 26 Aug 2025)
Bosonic field configurations	Scalar fermion-boson stars and vector fermion Proca stars	(Jockel, 2023)
Strongly interacting dark baryons	Lattice-informed one-flavor $G_2$-QCD dark EOS	(Dengler et al., 25 Mar 2025)
Agnostic dark sector	Low-density Fermi gas plus causal speed-of-sound interpolation	(karan et al., 4 Jul 2026)

In the free-fermion tradition, dark matter is modeled as a zero-temperature relativistic Fermi gas with particle mass $m_f$, while mirror dark matter is represented macroscopically by the same equation of state as ordinary matter. Static equilibria then form a two-parameter family in the central-pressure plane, and $m_f\sim 1$ GeV emerges as a transitional mass scale separating qualitatively different behavior: lighter fermions favor extended halos, while heavier fermions favor compact cores (Kain, 2021). In a later two-fluid study with a realistic chiral nuclear EOS, the same qualitative distinction appears more sharply: $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$0 decreases the stellar maximum mass, whereas $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$1 increases it relative to ordinary neutron stars (Scordino et al., 2024).

Bosonic dark sectors have been treated in two different languages. One is an effective self-interacting bosonic-fluid description based on a quartic scalar field,

$$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$2

with condensed-limit relations for $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$3, $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$4, $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$5, and $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$6, often interpreted as self-interacting bosonic dark matter in a Bose-Einstein condensate (Cipriani et al., 25 Feb 2025). Another is a fully self-consistent Einstein-Klein-Gordon or Einstein-Proca treatment, where the dark sector is a complex scalar or vector field with quartic self-interaction and the mixed objects are fermion-boson stars and fermion Proca stars (Jockel, 2023).

A distinct development is the use of a first-principles dark-sector EOS from one-flavor $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$7-QCD. There the dark matter candidate is the lightest absolutely stable fermionic dark baryon, and the dense-matter EOS is constructed from finite-density lattice data, piecewise polytropes, and controlled extrapolations. This furnishes a strongly interacting dark-matter EOS that is neither a free-gas ansatz nor a mean-field toy model (Dengler et al., 25 Mar 2025).

The most deliberately model-independent construction is the agnostic framework in which the dark matter is characterized only by a bare mass $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$8, a low-density free-Fermi-gas anchor, and a causal, thermodynamically consistent high-density speed-of-sound interpolation. In that approach, the hadronic sector is itself agnostic, anchored to chiral effective theory at low density and perturbative QCD at high density (karan et al., 4 Jul 2026). Collectively, these model classes show that “DMANS” is not a single microphysical hypothesis but a family of compact-star scenarios sharing a hidden-matter component.

3. Core, halo, and mixed morphologies

The most persistent morphological distinction is between dark cores and dark halos. In the simplest geometric definition,

$$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$9

and this criterion is used across free-fermion, bosonic, and agnostic studies (Kain, 2021, Miao et al., 2022, karan et al., 4 Jul 2026). Heavy dark particles tend to concentrate centrally, while lighter ones tend to remain more extended. In the free-fermion literature, $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$0 GeV favors halos and $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$1 GeV favors cores (Kain, 2021). In the realistic chiral-nuclear study, $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$2 produces core-like behavior and reduces $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$3, whereas $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$4 produces halo-like behavior and increases $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$5 (Scordino et al., 2024). In the agnostic framework, $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$6 yields only halos in the sampled stable solutions, $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$7 yields only cores, and intermediate masses admit Core, Halo, Core-Halo, and Halo-Core sequences (karan et al., 4 Jul 2026).

A particularly sharp analytic result comes from the self-interacting asymmetric-fermion model. There the relative distribution is controlled by the ratio of the central enthalpies of the two components: $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$8 For the critical case $$\frac{dP_j}{dr} = -G\,\frac{m_{\rm tot}(r)\,\varepsilon_j(r)}{c^2 r^2} \left(1+\frac{P_j(r)}{\varepsilon_j(r)}\right) \left(1+\frac{4\pi r^3 P_{\rm tot}(r)}{c^2 m_{\rm tot}(r)}\right) \left(1-\frac{2Gm_{\rm tot}(r)}{c^2 r}\right)^{-1},$$9, the paper derives

$$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$0

together with the asymptotic scalings $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$1 for $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$2 and $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$3 for $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$4 (Miao et al., 2022). This provides a compact criterion connecting microscopic dark-sector parameters to the core-halo transition.

The observational consequences of morphology can be extreme. In the original two-fluid study of non-self-annihilating fermionic dark matter with $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$5, large dark fractions yield a new class of compact stars consisting of a small normal-matter core of radius only a few km embedded in a $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$6 km dark halo (Leung et al., 2011). In the mirror-dark-matter case, stable halo solutions include $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$7–$$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$8 stars with visible radii $$\frac{dm_j(r)}{dr}=\frac{4\pi}{c^2}r^2\varepsilon_j(r), \qquad m_{\rm tot}=m_{\rm OM}+m_{\rm DM}, \qquad P_{\rm tot}=P_{\rm OM}+P_{\rm DM},$$9–$R=\max\{R_{\rm OM},R_{\rm DM}\}$0 km (Kain, 2021). A Higgs-portal one-fluid model for XTE J1814-338 interprets that source as requiring a substantially dark-compressed branch with $R=\max\{R_{\rm OM},R_{\rm DM}\}$1, giving $R=\max\{R_{\rm OM},R_{\rm DM}\}$2 in the nucleonic case and $R=\max\{R_{\rm OM},R_{\rm DM}\}$3 in the hyperonic case (Lopes et al., 2024).

Rapid rotation makes the morphology problem dynamical rather than merely geometric. In self-interacting bosonic two-fluid stars, a nominally halo-like distribution can become a mixed configuration once rapid rotation is included. For the displayed $R=\max\{R_{\rm OM},R_{\rm DM}\}$4 halo sequence, the transition occurs around

$R=\max\{R_{\rm OM},R_{\rm DM}\}$5

where

$R=\max\{R_{\rm OM},R_{\rm DM}\}$6

The same study notes that a rapidly rotating nominal halo with $R=\max\{R_{\rm OM},R_{\rm DM}\}$7 MeV can become more like a very large core with $R=\max\{R_{\rm OM},R_{\rm DM}\}$8 (Cipriani et al., 25 Feb 2025). Collectively, these results indicate that “core” and “halo” are not immutable labels; they depend on mass, microphysics, and, in rotating stars, on the global equilibrium sequence.

4. Rotation, stability, and oscillation spectra

Rotation introduces additional degrees of freedom absent from static two-fluid stars. In Hartle-type slow-rotation formalisms, each fluid may rotate uniformly with its own angular velocity $R=\max\{R_{\rm OM},R_{\rm DM}\}$9, and the first-order dynamics is governed by frame dragging and separate angular-momentum contributions $\Lambda(n^2,p^2,x^2)$0 (Cronin et al., 2023). The fully relativistic rapid-rotation treatment goes further by allowing two independently rotating fluids in the same axisymmetric spacetime, with local velocity

$\Lambda(n^2,p^2,x^2)$1

so that even a formally nonrotating component can acquire nonzero local linear velocity through frame dragging (Cipriani et al., 25 Feb 2025).

This independent-rotation freedom leads to qualitatively new phenomena. In rapidly spinning bosonic DM-admixed stars, the dark component may be nonrotating, co-rotating, or counter-rotating relative to baryonic matter. For a representative $\Lambda(n^2,p^2,x^2)$2, $\Lambda(n^2,p^2,x^2)$3, $\Lambda(n^2,p^2,x^2)$4 GeV core model with $\Lambda(n^2,p^2,x^2)$5, the dark-matter shape differs sharply between the two cases: $\Lambda(n^2,p^2,x^2)$6 The interpretation given is that frame dragging assists co-rotation but opposes counter-rotation, so counter-rotating dark matter becomes much more oblate (Cipriani et al., 25 Feb 2025).

Moments of inertia are also nontrivial in two-fluid stars. In the slow-rotation study of fermionic DM-admixed stars, two definitions are contrasted: a straightforward total-fluid generalization using total $\Lambda(n^2,p^2,x^2)$7 and total $\Lambda(n^2,p^2,x^2)$8, and an observationally motivated definition using only the ordinary-matter quantities $\Lambda(n^2,p^2,x^2)$9 and $x^2$0, since electromagnetic measurements probe the visible surface rather than the dark sector (Cronin et al., 2023). With the latter choice, the standard I-Love-Q universality can break down strongly. An earlier slow-rotation two-fluid analysis already showed that the scaled moment of inertia $x^2$1 of DM-dominated objects can deviate strongly from the Bejger-Haensel relation for ordinary neutron stars (Leung et al., 2011).

Stability in two-fluid stars is not governed by the ordinary one-parameter maximum-mass criterion. For static multi-fluid stars, the onset of instability becomes a critical curve in the two-central-pressure plane $x^2$2, and the literature evaluates it either by solving the coupled radial-pulsation problem or by a turning/constraint criterion based on simultaneous stationarity of $x^2$3, $x^2$4, and $x^2$5 (Kain, 2021). A striking result is that stable equilibria can exist even when both central pressures exceed the isolated one-fluid critical values, so a naive sector-by-sector stability test fails (Kain, 2021).

Time-dependent evolutions confirm that the equilibrium and perturbative analyses have nonlinear content. The first dynamical GR evolutions of fermionic DM-admixed stars showed that linearly stable two-fluid equilibria remain bounded and oscillatory, unstable ones collapse to black holes, and a neutron star embedded in a dark-matter cloud can relax to a more massive, more compact DMANS. In the displayed formation run, the system evolves from

$x^2$6

to

$x^2$7

while forming a dark-matter core (Gleason et al., 2022).

Oscillation studies show that dark matter alters not only equilibrium but mode spectra. The comprehensive static-stability paper found that the fundamental radial frequency of two-fluid stars can exceed the maximum frequency of either corresponding one-fluid star (Kain, 2021). A more recent study of $x^2$8-modes in DMANSs built from neutron-dark decay concluded that the effect on the principal $x^2$9-mode frequency and its first overtone depends predominantly on the dark-matter fraction, and presented an equation-of-state-independent constraint for that fraction in the Cowling approximation (Shirke et al., 23 Jun 2025). This suggests that composition-sensitive oscillation modes may provide a probe complementary to mass-radius and tidal measurements.

5. Multimessenger phenomenology

The most developed observables are mass-radius relations, tidal deformability, binary tidal response, pulse profiles, and cooling. In all of them, the central theme is that the dark component changes the radial mass distribution rather than merely adding inert mass.

For tides, the essential relation is

$G_2$0

Core-like dark matter tends to increase compactness and lower $G_2$1, whereas halo-like dark matter can increase the effective radius and raise $G_2$2 (Jockel, 2023, karan et al., 4 Jul 2026). The agnostic two-fluid study makes this point especially sharply: light, halo-dominated dark matter increases tidal deformability and is therefore constrained primarily by the GW170817 bound, while heavy, core-dominated dark matter lowers $G_2$3 and is instead constrained more strongly by NICER mass-radius data (karan et al., 4 Jul 2026). In the chiral-nuclear free-fermion study, the same sign reversal appears at the level of maximum masses: $G_2$4 GeV lowers $G_2$5, whereas $G_2$6 GeV raises it (Scordino et al., 2024).

Binary calculations confirm that the dark morphology changes inspiral behavior. The first constraint-solved quasi-equilibrium initial data for DMANS binaries showed that core-confined dark matter makes stars less deformable than ordinary neutron stars of the same total rest mass, while a dilute halo is tidally stretched early. In the halo benchmark with $G_2$7 and DM fraction $G_2$8, the DM mass-shedding parameter reaches about $G_2$9 already at $m_f$0, and halo contact or shedding occurs around $m_f$1–$m_f$2. In the dark-core benchmark with $m_f$3 and DM fraction $m_f$4, $m_f$5 is reached only at $m_f$6, and baryonic mass shedding occurs near $m_f$7 (Rüter et al., 2023). These results are the binary analogue of the isolated-star core-versus-halo distinction.

Current gravitational-wave data have already been used to bound specific DMANS models. In a Bayesian reanalysis of GW230529, GW200115, GW200105, and GW190814 using a bosonic self-interacting scalar-field model, GW200105 gave the strongest standard-NSBH constraint: $m_f$8 for SLy4, favoring a DM core. GW190814 was different: with SLy4 or APR4, it required a halo-dominated interpretation with

$m_f$9

for SLy4, whereas with the stiffer MPA1 EOS it instead admitted

$m_f\sim 1$0

again a core scenario (Santos et al., 26 Aug 2025). The same paper emphasized that waveform differences from tides alone are small for present detector sensitivity, so present constraints are driven mainly by model-consistent stellar structure rather than by visually large phase shifts.

Pulse-profile modeling adds a complementary halo probe. For self-interacting asymmetric-fermion DANSs with a dark halo, the extra light bending outside the visible baryonic surface modifies the observed X-ray pulse amplitude. The relevant control parameter is

$m_f\sim 1$1

and the peak-flux deviation obeys the empirical relation

$m_f\sim 1$2

with $m_f\sim 1$3. Compact halos with $m_f\sim 1$4 can generate roughly $m_f\sim 1$5 peak-flux deviations (Miao et al., 2022). By contrast, diffuse halos of the same mass can be observationally negligible.

Thermal evolution provides yet another window in models where dark matter is built into the finite-temperature EOS rather than treated as a second gravity-only fluid. In a Higgs-portal relativistic mean-field study, canonical stars with $m_f\sim 1$6 enter a fast-cooling regime because the dark component increases the proton and lepton fractions enough to open direct Urca processes. The same work found that the thermal relaxation time of a canonical star decreases from about $m_f\sim 1$7 yr for $m_f\sim 1$8 to about $m_f\sim 1$9 yr for $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$00 GeV (Kumar et al., 2022). In such models, dark matter is not directly emitting the dominant neutrinos; it is changing the hadronic composition and reaction thresholds.

From the waveform-modeling side, the prototype framework Darksuite connects two-fluid TOV solutions to LAL/LALSuite infrastructure by building interpolation banks in $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$01 and inserting DM-modified tidal information into NRTidal-based inspiral models. Its structural inputs include self-interacting bosonic and ideal fermionic dark sectors, and its purpose is explicitly to propagate DMANS microphysics into gravitational-wave phasing (Anh et al., 30 Jul 2025).

6. Constraints, degeneracies, and unresolved issues

A recurrent result is that dark-matter effects are often degenerate with ordinary equation-of-state effects. Rapid-rotation studies state this explicitly: dark matter can mimic changes in the baryonic EOS, so measuring only radius at a given mass may not suffice to distinguish DM-admixed stars from ordinary neutron stars (Cipriani et al., 25 Feb 2025). The waveform-modelling literature makes the same point in gravitational-wave language: a DMANS may look like an ordinary neutron star with an apparently softer or stiffer baryonic EOS, depending on whether the dark component forms a core or a halo (Anh et al., 30 Jul 2025). The slow-rotation I-Love-Q study adds that once $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$02, $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$03, $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$04, and $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$05 probe different sectors asymmetrically, ordinary one-parameter universality is lost (Cronin et al., 2023).

Large dark fractions also depend strongly on the assumed formation channel. One static two-fluid study argues that late-time capture typically yields only a negligible dark mass, of order $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$06, and therefore focuses on progenitor admixture instead (Kain, 2021). By contrast, the $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$07-mode study invokes neutron-dark decay precisely because it can produce much larger dark fractions in the core than halo capture can (Shirke et al., 23 Jun 2025). Some one-fluid applications adopt phenomenological dark Fermi momenta or fixed dark segments without a dynamical accumulation history (Lopes et al., 2024, Kumar et al., 2022). This suggests that structural predictions and observational bounds cannot be cleanly separated from assumptions about how the dark component enters the star in the first place.

Methodological limitations remain substantial. Many analyses are static and nonrotating (Kain, 2021, Scordino et al., 2024, Dengler et al., 25 Mar 2025), whereas the rapid-rotation study shows that spin can qualitatively change topology and oblateness (Cipriani et al., 25 Feb 2025). The binary-initial-data construction does not yet achieve ordinary one-fluid spectral convergence because the inner fluid surface is not grid-fitted, so Gibbs-type errors remain near the inner-fluid boundary (Rüter et al., 2023). The Darksuite framework is explicitly a proof of concept; it provides no interpolation-error analysis, convergence study, runtime benchmark, or formal validation against independent codes (Anh et al., 30 Jul 2025). The first GW constraints are prior sensitive in low-SNR events, although the core-versus-halo morphological inference appears more robust than the precise upper bounds (Santos et al., 26 Aug 2025).

Several broad observational conclusions nonetheless recur. In the agnostic framework, current data at $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$08 give

$$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$09

for light, halo-forming dark matter, and the authors highlight neutron stars with similar masses but very different tidal deformabilities as a potential smoking-gun signature (karan et al., 4 Jul 2026). In the strongly interacting $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$10-QCD framework, dark baryon masses from a few hundred MeV to a few GeV remain consistent with current neutron-star observations (Dengler et al., 25 Mar 2025). In rapidly rotating bosonic models, neutron-star observations can exclude parts of the $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$11 parameter space because large compact cores can drive the maximum mass below the $$\nabla_\mu T^{\mu\nu}_{\rm BM}=0,\qquad \nabla_\mu T^{\mu\nu}_{\rm DM}=0.$$12 threshold (Cipriani et al., 25 Feb 2025). These are not universal bounds on “dark matter in neutron stars,” but they do show that dark-sector structure is already constrained by the combination of pulsar masses, NICER radii, and gravitational-wave tides.

Higher-SNR gravitational-wave detections with better tidal measurements are repeatedly identified as the key next step for turning morphology-based arguments into sharper constraints (Santos et al., 26 Aug 2025). More rigorous stability analyses for rapidly rotating and binary configurations, improved treatment of formation channels, and systematic exploration of model-agnostic dark sectors beyond low-density fermionic anchors remain open problems (karan et al., 4 Jul 2026). The central lesson of the present literature is therefore not that dark matter changes neutron stars in one universal way, but that it introduces a family of core, halo, and mixed compact-star configurations whose phenomenology is structurally rich and observationally testable.