Strangeon-Star Model: Compact Star Physics

• Strangeon-Star Model is a framework where compact stars are self-bound dense objects composed of localized quark clusters (strangeons), distinct from neutron or deconfined quark stars.
• It utilizes phenomenological approaches like Lennard-Jones and linked bag models to derive a stiff EOS, predicting high maximum masses, unique mass-radius relations, and a finite surface density.
• The model explains observable phenomena such as glitches, magnetar QPOs, supernova neutrino cutoffs, and accretion effects in ULXPs, providing testable predictions across multi-messenger astronomy.

Searching arXiv for recent and foundational papers on strangeon stars to ground the article in the literature. Strangeon stars are a proposed class of pulsar-like compact stars in which the bulk matter is not ordinary nucleonic matter and not deconfined strange quark matter, but a self-bound condensed phase composed of localized multi-quark clusters called strangeons. In this framework, strangeons are “strange nucleons,” i.e. quark clusters with approximate three-light-flavor symmetry involving $u$, $d$, and $s$ quarks, and a strangeon star is treated as a 3-flavored gigantic nucleus rather than a gravity-bound neutron star (Lai et al., 2017, Lu et al., 2017). The model is motivated by the possibility that, at densities of a few times nuclear saturation density and energy scales of order $\sim 0.5\ \mathrm{GeV}$, QCD remains strongly coupled, so quarks may cluster rather than deconfine into a weakly interacting Fermi liquid (Lu et al., 2017). A central consequence is that strangeon stars are self-bound by the strong interaction, can have a sharp finite-density surface, may become globally solid at low temperature, and can therefore exhibit phenomenology that differs qualitatively from both conventional neutron stars and MIT-bag strange stars (Lai et al., 2017, Lu et al., 2017, Li et al., 17 Sep 2025).

1. Conceptual definition and microphysical basis

The strangeon-star model generalizes Witten’s strange-matter idea by allowing the stable bulk phase of dense matter to consist of localized quark clusters rather than free deconfined quarks (Lai et al., 2017). In this terminology, a strangeon is a cluster containing roughly equal numbers of $u$, $d$, and $s$ quarks; specific cluster sizes mentioned in the literature include $6, 9, 12, 18,$ or more quarks, although the precise number is not fixed (Lu et al., 2017, Lai et al., 2017). The intended distinction is threefold: nucleons are ordinary three-quark baryons without built-in strangeness, quark stars assume deconfined quarks, and strangeon stars assume confined but clustered quarks as the relevant effective degrees of freedom (Lu et al., 2017).

The microphysical motivation rests on the claim that matter in compact stars occupies a nonperturbative QCD regime. The model emphasizes that at compact-star densities the strong coupling can be large, making a weak-coupling quark description unreliable and suggesting that localization into clusters is plausible (Lai et al., 2017). In parallel, the model assumes approximate 3-flavor symmetry restoration: dense matter becomes energetically favorable to include strange quarks, but the energy scale is still insufficient for full quark deconfinement (Lu et al., 2017). This is the defining contrast with strange quark stars, where bulk stability is attributed to deconfined quark matter.

A complementary phenomenological construction appears in the liquid-drop treatment of strangeon matter, where strangeon matter is modeled as a 3-flavor analog of ordinary nuclei with energy per baryon

$$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$

In that formulation, stability improves with baryon number, and for $M\sim \text{GeV}$ and $d$0, the critical baryon number can be as low as $d$1 (Wang et al., 2017). This does not constitute a first-principles derivation, but it provides a phenomenological basis for the claim that bulk strangeon matter could be absolutely stable.

2. Self-bound structure, equation of state, and stellar properties

A defining structural assumption is that strangeon matter is self-bound, so the stellar surface has a finite density rather than the smooth density decline characteristic of neutron stars (Lu et al., 2017, Gao et al., 2021). In recent applications to accretion physics, this sharp interface is made explicit: the bulk strangeon matter at the surface is described as having density $d$2, while accreted normal matter above it in a polar mound can remain at only $d$3 (Li et al., 17 Sep 2025). This sharp surface density discontinuity is one of the key physical differences from a neutron star.

Several phenomenological EOS constructions are used in the literature. One widely used family adopts a Lennard-Jones model for the strangeon-strangeon interaction,

$d$4

or equivalently

$d$5

With a simple-cubic lattice, this yields energy density and pressure of the form

$d$6

$d$7

or equivalent expressions parameterized by $d$8, $d$9, and $s$0 (Yang et al., 2024, Gao et al., 2021). The physical rationale is that the repulsive core makes the EOS very stiff.

A second phenomenological route is the linked bag model, which extends bag-model ideas to condensed matter in both 2-flavor and 3-flavor sectors (Miao et al., 2020). In this model the maximum mass of strangeon stars can be as large as $s$1, while the tidal deformability of a $s$2 strangeon star lies in the range of $s$3 (Miao et al., 2020). The same work argues that increasing the number of valence quarks per strangeon lowers the energy per baryon and stiffens the EOS, thereby increasing the maximum mass.

The macroscopic consequences of self-binding and stiffness recur across the literature. Strangeon stars are predicted to support high masses, with early overview papers quoting

$s$4

(Lu et al., 2017), while specific Lennard-Jones calculations report maximum stable baryonic masses as large as

$s$5

for the chosen EOS in the nonrotating case (Yang et al., 2024). Because the stars are self-bound, the mass-radius behavior differs from neutron stars: the radius can increase with mass over much of the sequence, and the minimum mass can be very small, even down to planet-like masses $s$6 in the overview discussion (Lu et al., 2017). Low-mass realizations are used explicitly in the proposed interpretation of Calvera, where a strangeon-star atmosphere fit yields $s$7, $s$8, and $s$9 (Li et al., 2017).

3. Rotation, tidal deformability, and merger remnants

The rotating and tidally deformed strangeon-star problem has been studied in perturbative general relativity with particular attention to the role of the finite surface density (Gao et al., 2021). In the Hartle-Thorne slow-rotation treatment, the finite surface density introduces crucial surface corrections into the perturbation equations and matching conditions. This distinguishes self-bound strangeon stars from ordinary neutron stars and affects the inferred moment of inertia, quadrupole moment, and tidal Love number (Gao et al., 2021).

The same study concludes that strangeon stars satisfy quasi-universal I-Love-Q relations in terms of

$\sim 0.5\ \mathrm{GeV}$0

with relative deviations from standard fits generally below $\sim 0.5\ \mathrm{GeV}$1 (Gao et al., 2021). It also notes that the conservative constraint $\sim 0.5\ \mathrm{GeV}$2 implies $\sim 0.5\ \mathrm{GeV}$3 for the strangeon-star model within the scanned parameter space (Gao et al., 2021).

Merger-related calculations exploit the unusually large maximum masses implied by strangeon-matter EOSs. One merger study reports that the tidal deformability for a $\sim 0.5\ \mathrm{GeV}$4 strangeon star can be

$\sim 0.5\ \mathrm{GeV}$5

consistent with GW170817 bounds (Lai et al., 2017). In that picture, two $\sim 0.5\ \mathrm{GeV}$6 strangeon stars can merge to produce a hyper-massive strangeon star of mass around $\sim 0.5\ \mathrm{GeV}$7, with multimessenger signatures distinct from neutron-star mergers (Lai et al., 2017). The same work proposes a “strangeon kilonova” in which early blue emission is powered by decay of unstable strangeon nuggets and later red emission by remnant spin-down (Lai et al., 2017).

A complementary post-merger scenario focuses on slowly rotating massive strangeon stars as engines of short-GRB X-ray plateaus. Using the Lennard-Jones EOS parameter set LX3630 with

$\sim 0.5\ \mathrm{GeV}$8

the calculation finds that rigid rotation increases the maximum supported gravitational mass along constant-baryon-number sequences by about 9.3% over $\sim 0.5\ \mathrm{GeV}$9, compared with about 5.6% for the neutron-star comparison model (Yang et al., 2024). In that framework, spin-down-induced contraction releases gravitational energy,

$u$0

which is proposed as an alternative power source for short-GRB plateau emission (Yang et al., 2024). The fit results imply magnetic dipole fields in the range

$u$1

with efficiencies

$u$2

and initial periods from about $u$3 to $u$4 ms (Yang et al., 2024).

4. Surface physics, atmospheres, and the strangeness barrier

The strangeon-star model assigns central importance to the surface, because the transition from normal matter to strangeon matter is regulated not only by electromagnetic effects but also by flavor conversion. The relevant concept is the strangeness barrier: ordinary 2-flavor matter cannot simply become part of the 3-flavor strangeon phase without weak-interaction conversion (Lai et al., 2017, Lu et al., 2017). This barrier is repeatedly invoked to explain why a strangeon star can be bare, or instead be covered by a corona, atmosphere, or crust of normal matter (Lu et al., 2017).

In accretion settings, the barrier is more important than the Coulomb barrier. In the ULXP accretion-column calculation, the Coulomb penetration probability is written as

$u$5

with $u$6 and $u$7, and the conclusion is that the Coulomb barrier alone is not a strong obstacle (Li et al., 17 Sep 2025). Instead, because weak conversion is slow, most inflowing material is “bounced back” and accumulates above the surface, producing a thermal mound (Li et al., 17 Sep 2025).

The same surface physics underlies atmosphere models for X-ray dim isolated neutron stars (XDINSs). In the first bremsstrahlung-atmosphere model, a strangeon star is surrounded by a thin, two-temperature plasma atmosphere formed and maintained by ISM-accreted matter because the strangeness barrier inhibits direct incorporation into the star (Wang et al., 2016). The emergent flux is written as

$u$8

with optical depth

$u$9

The fitted radiation radii of XDINSs are from 7 to 13 km, while the modelled electron temperatures are between 50 and 250 eV, except RX J0806.4-4123 with a radiation radius $d$0 km (Wang et al., 2016).

The later nonuniform-atmosphere extension attributes the optical/UV excess and spectral deviation to bremsstrahlung emission from a nonuniform plasma atmosphere supplied by accretion that is funneled to the poles and then spreads over the surface (Wang et al., 2017). The model uses

$d$1

and reports electron temperatures $d$2 eV with radiation radii $d$3 km (Wang et al., 2017). For five XDINSs—RX J0720.4−3125, RX J0806.4−4123, RX J1308.6+2127, RX J1605.3+3249, and RX J1856.5−3754—the spectra from optical/UV to X-ray bands could be well fitted and exhibit gaussian absorption lines at $d$4 eV (Wang et al., 2017).

The same atmosphere framework is applied to Calvera. A joint fit to XMM-Newton and Chandra data with the strangeon-star atmosphere model yields $d$5, reduced chi-square values around $d$6, and supports the interpretation of Calvera as a low-mass strangeon star with inactive magnetosphere, small radius, and likely fallback-disk braking (Li et al., 2017).

5. Solid-state dynamics: glitches, oscillations, and free energy

A major claim of the strangeon-star framework is that the star can be globally solid, not merely crusted, and that this opens a unified class of starquake phenomena (Lai et al., 2017, Lu et al., 2017). Glitch modeling is a central application. In the original glitch formulation, the starquake is decomposed into plastic flow in a fractured outer layer and elastic motion in the inner region (Lai et al., 2017). The moment of inertia is parameterized as

$d$7

and the recovery coefficient is defined as

$d$8

The model proposes an empirical relation

$d$9

with observationally reasonable range $s$0 (Lai et al., 2017). It also derives the inter-glitch waiting time

$s$1

and argues that Crab- and Vela-like glitches can be explained in a unified bulk-invariable starquake picture with small radiative output (Lai et al., 2017).

The activity analysis extends this framework statistically. Using the observed relation

$s$2

the strangeon-star glitch-activity model infers that the shear modulus must be

$s$3

for a canonical star of mass $s$4 and radius $s$5 (Wang et al., 2020). It further argues that the observed glitch activity requires about ten times the oblateness shift accumulated during the glitch interval, i.e. $s$6, and estimates energy releases of

$s$7

for a Vela-like glitch with $s$8, and

$s$9

for a Crab-like glitch with $6, 9, 12, 18,$0 (Wang et al., 2020).

The recovery model further interprets post-glitch relaxation as a pressure-restoring viscous inflow of fragments into pressure-deficient equatorial cracks (Lai et al., 2023). The outflow velocity is assumed to decay as

$6, 9, 12, 18,$1

leading to the usual exponential frequency recovery

$6, 9, 12, 18,$2

Fits to five glitches give representative cracking depths and viscous timescales such as $6, 9, 12, 18,$3 d for B1838-04 and $6, 9, 12, 18,$4 d for B1800-21 (Lai et al., 2023). The reported trend is that $6, 9, 12, 18,$5 increases with glitch size $6, 9, 12, 18,$6 (Lai et al., 2023).

The solid-state interpretation is also applied to magnetar giant-flare quasi-periodic oscillations. In the strangeon-star torsional-mode study, the large shear modulus

$6, 9, 12, 18,$7

pushes the fundamental $6, 9, 12, 18,$8 torsional mode to roughly

$6, 9, 12, 18,$9

while first overtones are roughly

$$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$0

(Li et al., 2023). This enables identifications such as $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$1 Hz with $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$2, $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$3 Hz with $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$4, and $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$5 Hz with $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$6 (Li et al., 2023). Low-frequency QPOs are then attributed to ocean-crust interface modes with ocean densities $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$7–$$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$8, temperatures $$E/A = M + b_\mathrm{vol,\,s} + b_\mathrm{surf,\,s} A^{-1/3}.$$9–$M\sim \text{GeV}$0 K, and thickness $M\sim \text{GeV}$1–$M\sim \text{GeV}$2 m (Li et al., 2023).

A related line of work studies stored elastic/gravitational free energy through pressure anisotropy in general relativity. Using the anisotropy ratio

$M\sim \text{GeV}$3

the calculation finds that values of order

$M\sim \text{GeV}$4

are already sufficient for

$M\sim \text{GeV}$5

with the broader range $M\sim \text{GeV}$6 for $M\sim \text{GeV}$7 (Chen et al., 2023). This is presented as an alternative energy reservoir for SGR giant flares, FRBs, and related transients without requiring extremely strong magnetic fields (Chen et al., 2023).

6. Thermal evolution, neutrinos, and accretion-powered high-energy phenomena

The strangeon-star model has also been developed as a thermal-evolution framework. In the supernova context, a newborn strangeon star is assumed to be born as a hot liquid with internal energy of order

$M\sim \text{GeV}$8

and to cool through neutrino and photon emission until it reaches a melting temperature

$M\sim \text{GeV}$9

(Yuan et al., 2017). The total internal energy is split into

$d$00

with pion excitation emphasized as a major high-temperature contribution (Yuan et al., 2017). Because the neutrino mean free path is estimated as

$d$01

the star is opaque and cooling is diffusive (Yuan et al., 2017). The model identifies the sharp drop in SN1987A neutrino emission with the liquid-solid transition of strangeon matter (Yuan et al., 2017). This suggests that a future core-collapse supernova neutrino burst showing a cut-off or sharp drop would be a characteristic test of the model.

A much more recent extension applies the strangeon-star surface physics to ultraluminous X-ray pulsars. There the accretion column is solved in a one-dimensional steady model, and the weak-conversion probability is taken as $d$02 with $d$03, yielding a mound-base density $d$04 and $d$05 (Li et al., 17 Sep 2025). The resulting thermal mound can reach

$d$06

with base temperature

$d$07

and efficient neutrino cooling via electron–positron pair annihilation (Li et al., 17 Sep 2025).

The heating rate entering the neutrino luminosity is written as

$d$08

The luminosity decomposition is

$d$09

with a surface heat-transport contribution

$d$10

emphasized to be essentially independent of the accretion rate (Li et al., 17 Sep 2025). Two regimes are distinguished: $d$11 where photons dominate, and

$d$12

where photon trapping makes neutrinos the main cooling channel and the photon luminosity saturates near

$d$13

For detectability, only Swift J0243.6$d$146124 is estimated to reach a marginally interesting Earth flux,

$d$15

while extragalactic ULXPs remain far below current backgrounds (Li et al., 17 Sep 2025).

7. Observational status, comparisons, and open issues

The strangeon-star model is presented throughout the literature as a third alternative to conventional neutron stars and strange quark stars (Lu et al., 2017). Compared with neutron stars, it posits self-bound matter, a finite surface density, stronger surface binding, a potentially globally solid interior, and a typically stiffer EOS (Lu et al., 2017, Lai et al., 2017). Compared with quark stars, it replaces deconfined quarks with localized quark clusters and often emphasizes solid-state behavior (Lu et al., 2017, Li et al., 17 Sep 2025).

This distinction matters because several observational signatures invoked in the model depend specifically on clustering and solidity rather than on generic self-binding. Examples include: starquake-driven glitches and their recovery (Lai et al., 2017, Lai et al., 2023), high-frequency magnetar QPOs from torsional oscillations (Li et al., 2023), phase-transition cutoffs in supernova neutrino bursts (Yuan et al., 2017), and accretion thermodynamics shaped by the strangeness barrier (Li et al., 17 Sep 2025). By contrast, properties such as high compactness, large surface redshift, or self-bound mass-radius behavior are shared more broadly with MIT-bag strange-star models (Rahaman et al., 2014, Deb et al., 2015). This suggests that some observables constrain self-binding in general, whereas others are intended to probe specifically strangeon clustering or solid-state physics.

Several studies explicitly state that the model remains phenomenological. The liquid-drop and linked-bag papers stress that the detailed microscopic dynamics are uncertain and not derived from first-principles QCD (Wang et al., 2017, Miao et al., 2020). The rotational and tidal calculations likewise note that perfect-fluid perturbation theory neglects the true shear modulus of a solid strangeon star, which may matter quantitatively for deformations and oscillations (Gao et al., 2021). The QPO analysis adopts a phenomenological Lennard-Jones EOS rather than deriving the interaction from QCD (Li et al., 2023). The accretion-column work in ULXPs makes specific choices for weak-conversion efficiency and timescale, which control the mound structure and neutrino luminosity (Li et al., 17 Sep 2025). These are not contradictions within the framework, but they delimit the current status of the model.

The observational program proposed in the literature is correspondingly broad. FAST and SKA are cited as probes of drifting subpulses, glitches, precession, and other timing phenomena (Lai et al., 2017, Lu et al., 2017). eXTP, NICER-like pulse-profile modeling, and future X-ray polarimetry are invoked as tests of surface composition, atmosphere geometry, and compactness (Lai et al., 2017, Gao et al., 2021, Wang et al., 2017). Gravitational-wave measurements of $d$16, $d$17, and post-merger dynamics are expected to constrain or falsify regions of the strangeon-matter parameter space (Lai et al., 2017, Gao et al., 2021, Yang et al., 2024). Future supernova neutrino observations could test the predicted liquid-solid transition cutoff (Yuan et al., 2017), and ULXP neutrino searches, although presently unfavorable for all but the nearest Galactic case, provide a further possible diagnostic of strangeon-star surface physics (Li et al., 17 Sep 2025).

Taken together, the strangeon-star model constitutes a coherent but still conjectural program: dense matter is assumed to form a self-bound, clustered 3-flavor phase; compact stars built from this matter acquire a sharp surface, very stiff EOS, and often a globally solid interior; and these properties are then used to reinterpret a wide range of compact-star phenomena—from glitches and magnetar QPOs to XDINS spectra, short-GRB plateaus, merger remnants, supernova neutrino bursts, and ULXP accretion columns (Lai et al., 2017, Lu et al., 2017, Li et al., 17 Sep 2025). A plausible implication is that the most discriminating tests will be those that directly probe the conjunction of self-binding, surface conversion barriers, and solid-state response, rather than compactness alone.