Extended Dark Matter Compact Objects (EDCOs)

• EDCOs are dark-sector compact objects defined by extended mass functions, finite-size structures, and dark envelopes that modify gravitational and astrophysical signatures.
• They arise from diverse formation channels—such as primordial collapse, dissipative dark-sector dynamics, and accretion processes—leading to observable effects in microlensing and transit phenomena.
• Theoretical models employ multifluid hydrostatic equilibrium and advanced lensing formalisms to predict signatures in gravitational-wave signals and exoplanet-like observations.

Extended Dark Matter Compact Objects (EDCOs) are a broad class of dark-sector compact configurations and compact-object populations in which “extended” has more than one technical meaning. In the literature considered here, it can denote a compact-object population with a non-monochromatic mass spectrum, a finite-size horizonless compact body supported by pressure or self-interactions, a compact remnant surrounded by an extended dark envelope or mini-halo, or an exotic compact object whose exterior spacetime is dressed by a back-reacting dark-matter environment (Green, 2016, Tolos et al., 2015, Raidal et al., 2018, Yang et al., 2011, Chakravarti et al., 3 Sep 2025). The subject therefore sits at the intersection of primordial compact-object cosmology, multifluid compact-star structure, dissipative dark-sector astrophysics, strong-lensing phenomenology, and gravitational-wave astronomy.

1. Conceptual scope and taxonomy

A useful way to organize the field is to separate three recurring usages. First, some studies treat dark compact objects as effectively pointlike lenses or scatterers but assign them an extended mass function rather than a delta-function spectrum. Second, other studies focus on individual finite-radius dark compact bodies, such as dark compact planets, dark white dwarfs, boson-star-like objects, or self-interacting fermion stars. Third, a further class consists of composite systems in which an ultracompact core is embedded in, or accompanied by, an extended dark component, as in neutron stars with dark mini-halos or ECOs in dark-matter halos (Green, 2016, Tolos et al., 2015, Ryan et al., 2022, Yang et al., 2011, Chakravarti et al., 3 Sep 2025).

Category	Defining feature	Representative studies
Extended-mass-function compact objects	Dark fraction distributed over mass by $\psi(M)$	(Green, 2016)
Pressure-supported dark compact stars/planets	Finite radius, horizonless equilibrium	(Tolos et al., 2015, Ryan et al., 2022, Cassing et al., 2022, Buras-Stubbs et al., 6 Feb 2026)
Primordial horizonless ECOs	PBH-like formation but suppressed evaporation	(Raidal et al., 2018)
Dark-admixed compact stars	Hadronic and dark components coexist in equilibrium	(Deliyergiyev et al., 2019, Vikiaris et al., 4 Feb 2026)
Compact objects with dark envelopes	Compact remnant plus extended DM halo or halo-dressed ECO	(Yang et al., 2011, Chakravarti et al., 3 Sep 2025)
Extended photon-coupled dark clumps	Finite-size dark objects probed by dimming rather than lensing	(Bramante et al., 2024)

This taxonomy matters because observables depend on which sense of “extended” is relevant. An extended mass spectrum modifies event-rate integrals and dynamical-heating integrals. An extended spatial structure changes transit depth, tidal response, echo cavity structure, accretion, and finite-source lensing behavior. An extended environment modifies the background spacetime itself. The same umbrella term therefore covers physically distinct sectors of parameter space rather than a single universal model.

2. Internal structure, equations of state, and equilibrium descriptions

For extended-mass-function compact dark matter, the basic object is the differential halo fraction $\psi(M)$, defined so that the total compact-object halo fraction is

$f=\int_0^\infty \psi(M)\,dM.$

A widely used inflation-motivated parameterization is

$$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$

with $M_c$ the central mass and $\sigma$ the width in $\log M$ (Green, 2016). This formalism is not a structural model of an individual object; it is a population-level EDCO description in which observables must be integrated over the full distribution.

For finite-size EDCOs, the dominant structural framework is multifluid general-relativistic hydrostatic equilibrium. Dark compact planets and the broader class of dark compact objects studied by Tolos, Schaffner-Bielich, and collaborators are modeled as two gravitating fluids—ordinary matter and non-self-annihilating fermionic dark matter—interacting only through gravity. The ordinary component uses neutron-star, crust, and white-dwarf-like equations of state, whereas the dark component is an interacting degenerate Fermi gas parameterized by $y=m_f/m_I$. In this setup, a new stable branch of dark compact planets appears: for $y=10^{-1}$, masses are $M\sim10^{-4}-10^{-7}\,M_\odot$ with radii from a few km to a few hundred km; for $\psi(M)$0, masses are $\psi(M)$1 with radii of a few hundred km (Tolos et al., 2015).

The same multifluid logic extends to broader dark-admixed compact stars. In the “dark compact objects” overview, the total structure is set by separate hydrostatic equations for ordinary and dark fluids sharing a common metric potential, with the control parameters given by the dark particle mass $\psi(M)$2, the self-interaction strength $\psi(M)$3 or $\psi(M)$4, and the central pressure ratio $\psi(M)$5 to $\psi(M)$6 (Deliyergiyev et al., 2019). This framework produces ordinary-looking neutron-star and white-dwarf branches at small dark fractions, but also exotic branches including Earth-like and Jupiter-like compact configurations.

A more explicitly dark-only route is provided by compact stars made of two dark fluids. The scale-invariant treatment of two-fluid dark stars allows both core-shell and homogeneously mixed configurations composed of incompressible matter, free or interacting Fermi gases, and self-bound matter with a vacuum term. In this class, some core-shell combinations approach the causality compactness limit $\psi(M)$7, but not beyond it if the dark-matter equations of state remain causal (Cassing et al., 2022). This result places multicomponent dark stars among the most compact horizonless EDCO candidates in the surveyed literature.

Dark white dwarfs are a particularly clean fermionic EDCO realization. They are modeled as cold, self-gravitating, two-component degenerate Fermi systems of heavy and light dark fermions $\psi(M)$8 and $\psi(M)$9, with approximate bulk neutrality $f=\int_0^\infty \psi(M)\,dM.$0. Their scaling relations are especially transparent: $f=\int_0^\infty \psi(M)\,dM.$1 and over the explored parameter space the maximum mass ranges from $f=\int_0^\infty \psi(M)\,dM.$2 to $f=\int_0^\infty \psi(M)\,dM.$3, while the compactness at maximum mass ranges from $f=\int_0^\infty \psi(M)\,dM.$4 to $f=\int_0^\infty \psi(M)\,dM.$5 and approaches $f=\int_0^\infty \psi(M)\,dM.$6 near the single-particle fermion-star limit (Ryan et al., 2022). These objects are horizonless, highly deformable, and occupy mass-radius territory distinct from ordinary white dwarfs, neutron stars, and black holes.

Another finite-size EDCO family is built entirely from self-interacting asymmetric fermionic dark matter with a repulsive Yukawa interaction. In the slow-rotation study based on the Hartle-Thorne formalism to second order, the equilibrium equation of state is a degenerate Fermi gas plus an interaction term proportional to $f=\int_0^\infty \psi(M)\,dM.$7, with $f=\int_0^\infty \psi(M)\,dM.$8. For benchmark masses $f=\int_0^\infty \psi(M)\,dM.$9 and $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$0, the sequences are tuned to maximum masses around $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$1, but their radii are generally larger and their compactness lower than for SLy4 neutron stars at fixed mass (Buras-Stubbs et al., 6 Feb 2026). This suggests a class of extended dark stars that can mimic neutron-star masses while remaining structurally more diffuse.

Bosonic EDCOs also appear in the form of dark boson stars. In the binary-merger study of dark boson stars, each star is described by an independent complex scalar field, so the two stars interact only through gravity. The resulting objects have finite radii, nonzero tidal Love numbers $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$2–$$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$3, and a contact phase absent in black-hole mergers, which makes them unambiguously extended compact bodies rather than pointlike or horizon-dominated objects (Bezares et al., 2018).

3. Formation channels and evolutionary pathways

EDCO formation is heterogeneous. One channel assumes primordial collapse from large curvature perturbations, but into horizonless exotic compact objects rather than black holes. In that case, the crucial physical ingredient is not a novel collapse threshold but the assumption that the post-collapse object is horizonless and radiates much less efficiently than a black hole. The survival condition is

$$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$4

where $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$5 parameterizes evaporation suppression. Under favorable assumptions, primordial horizonless ECO dark matter can survive to the present day well below the usual PBH evaporation scale, potentially down to $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$6 (Raidal et al., 2018).

A second channel is dissipative dark-sector structure formation. In the two-particle dark-electron–dark-photon model, perturbations grow, become nonlinear, and form dense dark halos. Bremsstrahlung cooling then drives fragmentation into clumps ranging from a few to millions of solar masses, and in part of the parameter space the endpoints are asymmetric dark stars or black holes (Chang et al., 2018). This sequence is especially important conceptually because it explicitly contains extended intermediate stages—virialized dark halos, fragmenting clumps, and protostar-like configurations—that function as EDCO progenitors before any ultracompact endpoint is reached.

A third route is primordial dark seeds plus later baryonic accretion. For dark compact planets, direct accretion of dark matter onto neutron stars and white dwarfs is estimated to be too weak to build the required dark cores: $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$7 and $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$8. The favored scenario is therefore primordial formation of dark compact seeds followed by later accretion of white-dwarf-like ordinary matter (Tolos et al., 2015). This leaves the existence of the object class intact while shifting the burden to an early-universe dark-fragmentation mechanism.

A fourth mechanism is environment-dependent capture into compact stars. In the extended overview of dark compact objects, smooth local-halo capture yields only $$\psi(M)=N\exp\!\left[-\frac{(\log M-\log M_c)^2}{2\sigma^2}\right],$$9 in neutron stars and $M_c$0 in white dwarfs, but dense clumps, ultra-compact minihalos, and Galactic-center environments can raise the accumulated dark mass to $M_c$1–$M_c$2 (Deliyergiyev et al., 2019). This suggests that EDCO populations may inherit a strong environmental dependence even when the underlying stellar equilibrium equations are local.

A fifth route is collapse-induced dark mini-halos around compact remnants. In the inelastic dark matter scenario of Sandin and Ciarcelluti, DM captured by a progenitor star can redistribute during core collapse so that an extended dense mini-halo remains outside the neutron star. The successful case is specific: inelastic DM with very suppressed elastic scattering. The resulting halo has radius $M_c$3, nascent number density $M_c$4, and long-term annihilation-driven decline roughly

$M_c$5

for $M_c$6 years (Yang et al., 2011). This is a genuine compact-remnant-plus-extended-dark-envelope configuration.

A sixth mechanism is in-situ generation of dark matter inside neutron stars through neutron dark decay. In the neutron-dark-decay compact-star scenario, the star manufactures its dark fermion component through $M_c$7, rather than capturing it from the halo. The resulting equilibrium is a mixed hadronic–dark configuration, and a key conclusion is that dark conversion must be suppressed above densities of order a few times saturation density if one is to retain both low-mass exotic compact stars and the $M_c$8 limit (Vikiaris et al., 4 Feb 2026). This mechanism differs qualitatively from ordinary admixed-star models because the dark component is generated endogenously.

4. Observational signatures and experimental access

Microlensing remains one of the central probes, but the relevant formalism depends strongly on whether one is dealing with a pointlike lens population or a finite-size extended object. For extended-mass-function compact dark matter, the key observable is not a pointwise comparison to monochromatic exclusion curves; one must recompute the full event count

$M_c$9

for the actual $\sigma$0 (Green, 2016). This is the methodological core of the extended-mass-function literature.

Strong-lensing cluster caustics provide a different lensing channel. Supermagnified stars near cluster critical lines constrain any additional surface density in compact perturbers because such perturbers broaden the micro-critical-line network. The half-width scales as

$\sigma$1

and the positional likelihood of observed stars around the macro-critical line limits additional dark compact lenses. This method constrains compact objects above $\sigma$2 to contribute only a few percent of the dark matter, provided they are compact enough in projection to generate microcritical perturbations (Müller et al., 2024). This applicability to some extended lenses is explicitly noted in the paper, but only if the object is sufficiently concentrated.

A non-gravitational transit signature appears for photon-coupled extended dark clumps. In the dimming formalism, a spherical dark object of radius $\sigma$3 and optical-depth scale $\sigma$4 transmits

$\sigma$5

at projected distance $\sigma$6 from its center (Bramante et al., 2024). Such objects act as partially transparent “lampshades” rather than lenses, and the event timescale is set by the physical transit diameter rather than the Einstein radius. This directly probes EDCOs that are too large or too diffuse for standard microlensing.

Exoplanet-style observables are also relevant. Dark compact planets could appear as exoplanet candidates with planetary masses but exceptionally small radii, accessible in principle through radial-velocity and transit methods; their distinctive signature is an impossibly high mean density for an ordinary planet (Tolos et al., 2015). This is one of the few EDCO channels where a visible ordinary-matter component may coexist with a dark compact core.

Precision gravimetry probes a different regime. A compact dark object moving inside the Earth would generate a narrow-band gravimeter signal near $\sigma$7, corresponding to an orbital period of about $\sigma$8 minutes in the inner core. Superconducting-gravimeter data imply

$\sigma$9

for such an object, under the paper’s assumptions of weak baryonic coupling and coherent Earth-interior motion (Horowitz et al., 2019). For EDCO reinterpretation, this bound is reliable only when the object behaves effectively as a point mass on the relevant scales.

Gravitational-wave measurements probe finite size, tides, spin response, and post-merger dynamics. Dark boson star mergers show a threshold between long-lived non-BH remnants and prompt collapse, with $\log M$0, and low-compactness cases radiate $\log M$1 and $\log M$2, exceeding a typical equal-mass BH benchmark and earning the label “super-emitters” (Bezares et al., 2018). Dark white dwarfs can merge across a very large frequency range and are detectable in different bands depending on dark particle masses; they also obey universal relations analogous to the compactness–Love and binary Love relations (Ryan et al., 2022). Purely dark fermion stars studied in slow rotation exhibit distinctive tidal deformabilities and spin-induced quadrupoles relative to SLy4 neutron stars, which the authors frame as a gravitational-wave classification problem for systems without electromagnetic counterparts (Buras-Stubbs et al., 6 Feb 2026). For halo-dressed ECOs, the dark environment can also modify axial echoes and tidal Love numbers by shifting the effective light ring and cavity structure, especially in the non-relativistic halo model (Chakravarti et al., 3 Sep 2025).

5. Constraints, exclusions, and competing viability claims

A central negative result concerns the idea that an extended mass function can rescue all-dark-matter compact-object scenarios that are excluded in the monochromatic approximation. For the inflation-motivated Gaussian-in-$\log M$3 family, microlensing and dynamical heating pull the width in opposite directions: microlensing can require a minimum width, while dynamical heating imposes a maximum width. In the surveyed family there is no overlap, and the specific axion-curvaton and running-mass PBH distributions give $\log M$4 and $\log M$5, both above the EROS-2 exclusion threshold $\log M$6 (Green, 2016). Under those assumptions, extending the mass function does not evade the compact-dark-matter bounds.

A contrasting positive result appears for horizonless primordial ECOs. If the Hawking-like temperature is suppressed according to

$\log M$7

then evaporation is weakened by $\log M$8, and large regions below the ordinary PBH evaporation bound reopen. In favorable exponential-suppression cases and for a low gravity scale $\log M$9, masses as low as $y=m_f/m_I$0 can survive to the present and constitute all of the dark matter (Raidal et al., 2018). This is not a general theorem about all EDCOs, but it shows that horizonlessness can invalidate PBH evaporation exclusions.

CMB anisotropy constraints impose a major high-mass restriction on extended, baryon-accreting dark objects. In the conservative accretion framework with spherical flow and collisional ionization only, the Bondi scale

$y=m_f/m_I$1

and the associated luminosity from the accretion flow lead to strong limits on the dark-matter fraction. Objects as large as $y=m_f/m_I$2 are restricted to subpercent abundances in broad regions of parameter space (Croon et al., 2024). This shows that finite size weakens, but does not erase, accretion-driven exclusions.

Cluster-lensing caustic data furnish another stringent bound: for compact perturbers above roughly $y=m_f/m_I$3, the inferred extra convergence is $y=m_f/m_I$4, corresponding to about $y=m_f/m_I$5 of the total convergence and approximately $y=m_f/m_I$6 of the dark matter after accounting for hot gas (Müller et al., 2024). The paper emphasizes that this applies straightforwardly to pointlike compact objects and more cautiously to extended lenses that become effectively supercritical near the macro-critical line.

Compact-star observations constrain dark admixture in stellar interiors. In the dark compact planet framework, the existence of $y=m_f/m_I$7 pulsars implies $y=m_f/m_I$8 for weakly interacting dark matter, while in the strongly interacting benchmark $y=m_f/m_I$9 already drives the neutron-star maximum mass below $y=10^{-1}$0 (Tolos et al., 2015). In the broader admixed-star survey, strongly self-interacting dark matter with masses $y=10^{-1}$1–$y=10^{-1}$2 is argued to be excluded or disfavored in compact-star interiors because it drives the total mass above ordinary neutron-star and white-dwarf scales when enough dark matter is present (Deliyergiyev et al., 2019). In neutron-dark-decay models, a similar tension appears in a different form: if dark conversion remains active at all densities, the equation of state softens too much to retain the $y=10^{-1}$3 limit, so a suppression mechanism at a few times nuclear saturation density becomes essential (Vikiaris et al., 4 Feb 2026).

6. Conceptual issues, misconceptions, and open directions

One persistent misconception is that constraints derived for monochromatic compact-object populations can be read off directly for extended mass spectra. The explicit counterexample with a top-hat distribution in the EROS-2 band $y=10^{-1}$4 shows that normalizing to the weakest endpoint bound would permit $y=10^{-1}$5, yet the actual predicted count is $y=10^{-1}$6, above the exclusion threshold, whereas the true maximum allowed fraction is $y=10^{-1}$7 (Green, 2016). The broader methodological lesson is that EDCO observables must usually be recalculated, not translated by inspection.

A second conceptual issue is that not every extended dark object is lens-equivalent to a point mass. The supermagnified-star constraint extends to some extended lenses, but only if they are sufficiently centrally concentrated to generate microcritical perturbations near the cluster macro-critical line (Müller et al., 2024). Likewise, the Earth-gravimeter bound is exact only for objects that remain compact relative to the object–detector separation and experience negligible drag or disruption in terrestrial matter (Horowitz et al., 2019). This suggests that profile-dependent reinterpretation is unavoidable for genuinely diffuse EDCOs.

A third issue is that many of the strongest constraints are deliberately conservative and model-specific. The CMB analysis retains only spherical accretion and collisional ionization, while noting that disk accretion or photoionization would typically strengthen the exclusion (Croon et al., 2024). The dimming program for photon-coupled dark clumps is at the opposite end of the maturity spectrum: it establishes a new search channel and projected constraints using EROS-2 and OGLE windows, but does not yet perform a full light-curve reanalysis with realistic efficiencies and backgrounds (Bramante et al., 2024). The field therefore contains both highly exclusionary mature probes and exploratory phenomenological proposals.

Formation remains one of the main unresolved questions. Dark compact planets are structurally viable but not formed by ordinary late-time capture; primordial dark seeds are suggested instead (Tolos et al., 2015). Primordial horizonless ECO dark matter is phenomenologically allowed in some models, but the collapse mechanism into an ECO rather than a black hole is assumed rather than derived (Raidal et al., 2018). Two-dark-fluid compact stars reveal substantial structural richness, but the core radius is often treated as an external parameter and stability is inferred from turning-point arguments rather than full mode calculations (Cassing et al., 2022). A plausible implication is that the main bottleneck for EDCO theory is no longer only equilibrium structure, but the connection between microphysics, cosmological production, and astrophysical population statistics.

The same applies to gravitational-wave phenomenology. Dark boson star mergers, dark white dwarf inspirals, and slowly rotating pure-dark fermion stars all show that tides, spin-induced quadrupoles, contact dynamics, and post-merger remnants can differ substantially from black-hole and neutron-star expectations (Bezares et al., 2018, Ryan et al., 2022, Buras-Stubbs et al., 6 Feb 2026). Yet these results are still model-fragmented: bosonic and fermionic stars occupy different parameter spaces, initial data are sometimes approximate, and detector-level inference has not been unified across the EDCO landscape. This suggests that “EDCO” is presently best understood not as a single model class with universal predictions, but as a program for studying how dark-sector structure, finite size, and extended environments imprint themselves on lensing, transits, compact-star observables, and gravitational waves.