Strange Quark Stars: Hypotheses, EOS, and Phenomenology

• Strange quark stars are self-bound compact objects made entirely of deconfined three-flavor quark matter, offering an alternative to gravity-bound neutron stars.
• Research utilizes various phenomenological EOS frameworks—such as the MIT bag model and NJL model—to characterize their self-binding, mass-radius relations, and tidal deformability.
• Observational signatures including fast rotation, unique surface electric fields, and merger dynamics provide actionable probes to distinguish strange quark stars from traditional neutron stars.

Strange quark stars (SQSs) are hypothetical compact stars entirely composed of deconfined quark matter, usually taken to be three-flavor strange quark matter (SQM) containing $u$, $d$, and $s$ quarks, together with electrons when needed for charge neutrality. In the strange-matter hypothesis, bulk three-flavor SQM can have an energy per baryon lower than that of the most stable atomic nucleus, so the star is self-bound by the strong interaction rather than only by gravity. SQSs have been theoretically proposed since the 1970s, can have masses and compactness similar to neutron stars (NSs), and remain observationally unconfirmed despite decades of multiwavelength data (Becerra et al., 29 Jul 2025, Weber et al., 2012, Zhang et al., 2024).

1. Strange-matter hypothesis and defining properties

The defining microscopic assumption is absolute stability of bulk three-flavor SQM. A commonly used criterion is that the zero-pressure energy per baryon,

$e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$

satisfies $e^0_{uds}<930\ \mathrm{MeV}$, while two-flavor matter remains unstable; this is the standard way to realize the Bodmer–Witten picture without destabilizing ordinary nuclei (Lugones et al., 14 Mar 2025, Weber et al., 2012). In this regime, the pressure vanishes at a finite, nonzero density rather than at zero density, so SQSs are self-bound objects with a sharp surface (Lugones et al., 14 Mar 2025, Zhu et al., 2021).

Self-boundness leads to several structural consequences repeatedly emphasized across the literature. Bare quark stars exhibit the approximate scaling $M\propto R^3$, may have no strict minimum mass in the slowly rotating case, and typically occupy radii of order $R\sim 10$–$12$ km with maximum masses around $\sim 2\,M_\odot$ in representative models (Weber et al., 2012). This differs qualitatively from hadronic NS sequences, which are gravitationally bound and organized essentially by a single parameter, the central density (Weber et al., 2012).

The same self-bound character underlies modern scaling analyses. In both the quark-mass density-dependent model with excluded-volume corrections and the vector MIT bag model, the maximum mass is controlled by the zero-pressure binding energy and by repulsive interactions. One explicit fit is

$$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$

accurate to better than $d$0 in the quoted model class; a related effective form is used in the vector MIT bag realization (Lugones et al., 14 Mar 2025). This suggests that observational upper limits on compact-star masses can directly constrain the depth of self-binding and the strength of repulsive quark interactions.

2. Equation-of-state frameworks

Because first-principles QCD at compact-star densities remains incomplete, SQS research is organized around phenomenological and QCD-inspired equations of state (EOSs). The literature represented here uses several distinct frameworks, all aiming to realize self-bound three-flavor matter while preserving thermodynamic consistency and stability constraints.

Framework	Key ingredients	Notable consequence
MIT bag model	bag pressure $d$1, sometimes density dependent	simple self-bound EOS; constant-$d$2 models are often too restrictive for the heaviest compact objects
NJL / MNJL	chiral dynamics; Fierz-weighted interaction via $d$3	increasing $d$4 stiffens the EOS and raises $d$5 and $d$6
QMDD / DDQM / CIDDM	density-dependent quark masses; sometimes excluded volume or isospin dependence	finite-density self-binding, simple scaling laws, and strong sensitivity to repulsion parameters
Dyson–Schwinger model	dressed propagators and quark–gluon vertex truncations	stable SQSs exist only in a narrow allowed parameter region
Perturbative QCD + bag term	running $d$7, running $d$8, effective bag constant	density-dependent $d$9 can satisfy both $s$0 and tidal constraints

The MIT bag model remains the canonical baseline. In its simplest form the EOS can be written linearly, but recent work increasingly replaces a fixed bag constant by a density-dependent one. A representative prescription is

$s$1

with $s$2, $s$3, $s$4, and $s$5 in one rotating-star study (Kayanikhoo et al., 14 Jan 2026). In perturbative-QCD-based models, a different density-dependent ansatz,

$s$6

is used to emulate nonperturbative vacuum physics, and the constant-$s$7 limit is recovered at $s$8 (Sedaghat et al., 2024).

NJL-like models incorporate chiral dynamics more explicitly. In the modified NJL construction,

$s$9

increasing $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$0 makes the EOS stiffer, increases $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$1, and also increases the tidal deformability $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$2; the SQM stability requirement restricts $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$3 in the quoted parameter set (Sedaghat et al., 2024). In QCD-motivated APT and BPT descriptions, the infrared running coupling remains finite, producing maximum rotating SQS masses of $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$4–$e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$5 depending on the onset density and coupling prescription (Sedaghat et al., 2021).

Density-dependent-mass models provide another major branch. The CIDDM model uses

$e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$6

which enforces confinement as $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$7 and asymptotic freedom as $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$8 for $e^0_{uds}\equiv \frac{\epsilon}{n_B}\bigg|_{p=0},$9 (Chu et al., 2014). The older quark mass-density-dependent model uses

$e^0_{uds}<930\ \mathrm{MeV}$0

and finds maximum masses in the range $e^0_{uds}<930\ \mathrm{MeV}$1 across $e^0_{uds}<930\ \mathrm{MeV}$2, with radii decreasing as $e^0_{uds}<930\ \mathrm{MeV}$3 increases (Li, 2010). More recent DDQM treatments add full thermodynamic self-consistency at finite temperature and lepton fraction, enabling proto-SQS evolution calculations (Issifu et al., 2023, Chen et al., 16 Jan 2026).

3. Surfaces, crusts, and equilibrium structure

A central distinction from NSs is the surface structure. A bare quark star has quark matter exposed at the surface, and the quark surface itself is very thin, of order $e^0_{uds}<930\ \mathrm{MeV}$4. Electrons extend above the positively charged quark surface in a layer of thickness of several hundred fermis, producing a dipole layer and ultra-high electric fields of order $e^0_{uds}<930\ \mathrm{MeV}$5, or $e^0_{uds}<930\ \mathrm{MeV}$6 if the matter is in a color-superconducting state (Weber et al., 2012). The field energy density can be comparable to the energy density of strange matter itself, changing the mass by about $e^0_{uds}<930\ \mathrm{MeV}$7 and the radius by about $e^0_{uds}<930\ \mathrm{MeV}$8 (Weber et al., 2012).

SQSs may also be crusted rather than bare. In a dressed star, the nuclear crust is electrostatically suspended above the quark surface and is not in direct contact with the quark core. The crust consists of heavy ions immersed in an electron gas, and the density at its base cannot exceed neutron drip,

$e^0_{uds}<930\ \mathrm{MeV}$9

so only the outer crust exists, not the inner crust familiar from NSs (Weber et al., 2012). This gives quark stars with crusts a genuine two-parameter equilibrium sequence, determined by the central density and the crust-base density (Weber et al., 2012).

These surface properties feed directly into observables. Because the surface constituents of a bare SQS are not gravitationally bound in the usual way, the standard Eddington luminosity limit does not apply. Photon luminosities can exceed $M\propto R^3$0, and pair-plasma luminosities can reach $M\propto R^3$1 for surface temperatures around $M\propto R^3$2 K (Weber et al., 2012). By contrast, crusted SQSs are Eddington-limited at the outer nuclear surface (Weber et al., 2012).

The same sharp surface complicates numerical relativity. Fully general-relativistic merger simulations therefore introduced a very thin crust via a polytrope,

$M\propto R^3$3

together with an enthalpy-continuity condition and a baryon-mass rescaling $M\propto R^3$4. In the MIT2cfl EOS, the physical zero-pressure baryon mass is $M\propto R^3$5, and the crust added for numerical regularization is only about two grid cells wide, with spatial width $M\propto R^3$6 m, mass $M\propto R^3$7, and tidal deformability changed by only about $M\propto R^3$8 (Zhu et al., 2021).

4. Formation channels and thermal evolution

A specific late-stage binary-supernova channel for SQS formation has recently been explored in detail. In this scenario, an evolved carbon-oxygen or Wolf-Rayet star collapses in a compact binary with an already existing NS companion. The pre-supernova orbital period is only a few minutes. Core collapse produces a newborn NS and a supernova, while fallback onto the newborn object and ejecta capture by the companion drive hypercritical, highly super-Eddington accretion onto both compact stars (Becerra et al., 29 Jul 2025).

The accreted material circularizes into disks around both stars within about one orbital period. The compact-star evolution is then followed by imposing

$M\propto R^3$9

with

$R\sim 10$0

where $R\sim 10$1 is the angular-momentum transfer efficiency and $R\sim 10$2 is the specific angular momentum at the disk inner radius (Becerra et al., 29 Jul 2025). In the two-family scenario adopted there, quark deconfinement is tied to the strangeness fraction rather than an arbitrary mass limit; the qualitative nucleation threshold is

$R\sim 10$3

Once a seed appears, the hadronic star rapidly converts into an SQS if absolutely stable SQM exists in bulk (Becerra et al., 29 Jul 2025).

The outcome depends strongly on progenitor mass, explosion energy, and spin. For the hadronic EOSs used in that study, the static maximum masses are only about $R\sim 10$4, rotation raises the supportable mass to $R\sim 10$5, and the critical mass for deconfinement is around $R\sim 10$6. A $R\sim 10$7 progenitor does not push the companion to $R\sim 10$8, but $R\sim 10$9 and $12$0 progenitors can do so for the weakest explosion energies. For the newborn NS, rapid initial rotation with $12$1 tends to lead to the Keplerian mass-shedding limit before deconfinement, whereas slower spins favor compression and conversion (Becerra et al., 29 Jul 2025).

When conversion occurs in that channel, the star is re-evaluated at the same baryon number and angular momentum with a quark EOS. The resulting SQS has a smaller gravitational mass and a larger equatorial radius than the progenitor hadronic star. The gravitational-mass change is about $12$2 for the unpaired bag model and about $12$3 for the CFL bag model, corresponding to conversion energies of roughly $12$4 and $12$5, respectively (Becerra et al., 29 Jul 2025). Bound remnants can emerge as NS-NS, NS-SQS, or SQS-SQS binaries and may merge on timescales of order $12$6 (Becerra et al., 29 Jul 2025).

Separate proto-SQS studies track stars assumed to be quark stars from birth. In one DDQM sequence, the star evolves through neutrino-trapped and neutrino-transparent stages into a cold $12$7 object, with maximum masses decreasing from $12$8 to $12$9; higher neutrino concentration makes the star slightly more massive because trapped neutrinos suppress strange-quark production and stiffen the EOS (Issifu et al., 2023). A closely related self-consistent thermodynamic treatment gives a similar decrease, from $\sim 2\,M_\odot$0 and $\sim 2\,M_\odot$1 in the earliest neutrino-trapped stage to $\sim 2\,M_\odot$2 and $\sim 2\,M_\odot$3 in the final cold star, along a fixed baryon-mass evolutionary picture (Chen et al., 16 Jan 2026).

5. Rotation, magnetic fields, and oscillation spectra

Rapid rotation is particularly natural for self-bound stars. For a typical pulsar-mass strange star ($\sim 2\,M_\odot$4), the Kepler period may be as short as $\sim 2\,M_\odot$5, compared with about $\sim 2\,M_\odot$6 ms for an NS of the same mass (Weber et al., 2012). More recent fully relativistic rotating models with a density-dependent bag constant find that the static maximum mass is $\sim 2\,M_\odot$7, while rotating sequences in the range $\sim 2\,M_\odot$8–$\sim 2\,M_\odot$9 Hz reach $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$0; in the summary of that study the explored interval is quoted as $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$1–$$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$2 (Kayanikhoo et al., 14 Jan 2026).

Rotation also introduces a minimum mass at sufficiently high frequency. While slowly rotating self-bound stars have no minimum mass, the same study finds that above about $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$3 Hz the sequence develops a minimum-mass configuration, with $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$4 over $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$5–$$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$6 Hz. Both the minimum-mass sequence and the mass-shedding sequence obey an approximately linear relation $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$7, with slopes $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$8 and $$M_{\mathrm{max}} = \frac{1}{\sqrt{q}\, \Bigl[5.1098 - 3.5154 \Bigl(\frac{e^0_{uds}}{930\,\mathrm{MeV}}\Bigr)\Bigr]}\, M_\odot,$$9 and $d$00, motivating the statement that the Keplerian frequency depends almost linearly on mass with slope about $d$01 (Kayanikhoo et al., 14 Jan 2026).

Strong magnetic fields make the pressure anisotropic. In the CIDDM model,

$d$02

so $d$03 decreases and $d$04 increases with field strength (Chu et al., 2014). The orientation of the internal field then becomes decisive: radial orientation reduces the maximum mass, while transverse orientation increases it. For the fast $d$05-profile, the largest masses are $d$06 in the transverse case and $d$07 in the radial case; for the slow profile they become $d$08 and $d$09, respectively (Chu et al., 2014).

Axisymmetric magnetized rotating equilibria using the density-dependent MIT bag model and fields up to $d$10 reach even larger masses when rapid spin is included. In the strongest-field, $d$11 configuration, the maximum mass is $d$12, the circumferential radius is $d$13, and the deformation parameter $d$14 reaches $d$15. The binding energy per baryon lies between $d$16 and $d$17, and the compactness is quoted as roughly $d$18 (Kayanikhoo et al., 14 Jan 2026).

Oscillation spectra provide a complementary diagnostic. For newly born SQSs, the quadrupolar $d$19-mode eigenfrequencies are about one order of magnitude lower than in newborn NSs, independent of whether the quark matter is described by the MIT bag model or the NJL model. In the MIT calculation, the $d$20 $d$21-mode is $d$22 at $d$23, whereas the corresponding NS values are $d$24. By contrast, SQS $d$25- and $d$26-modes are much higher, with $d$27-mode frequencies around $d$28–$d$29 and $d$30-mode frequencies around $d$31–$d$32 in the same study (Fu et al., 2017).

6. Binary dynamics, gravitational waves, and electromagnetic transients

Fully general-relativistic simulations of equal-mass $d$33 strange-star binaries show both similarities to and differences from hadronic mergers. For the MIT2cfl quark EOS, the stellar radius is $d$34 km and the tidal deformability is $d$35, while the comparison DD2 hadronic stars have $d$36 km and $d$37 (Zhu et al., 2021). Despite similar inspiral phasing when expressed through $d$38, dynamical mass loss is reduced: $d$39 for quark stars versus $d$40 for hadronic stars, and the quark-star ejecta exhibit much smaller high-velocity and very-high-entropy tails (Zhu et al., 2021).

The same simulations show that merger and post-merger frequencies obey the same quasi-universal relations derived from hadronic binaries when written in terms of tidal deformability, but not when written in terms of average compactness. This is important because it implies that gravitational-wave frequency information alone may not cleanly distinguish SQSs from NSs unless independent radius information is available (Zhu et al., 2021). Low-frequency newborn-star $d$41-modes add another potential discriminator because they are tied directly to the relativistic composition of quark matter (Fu et al., 2017).

Several recent compact-binary observations have been interpreted in this context. Using infrared-finite QCD couplings in APT and BPT, one study infers rotating SQS maximum masses of $d$42–$d$43 and compares them with a GW190425 remnant estimate of $d$44–$d$45, concluding that the remnant might be a strange quark star (Sedaghat et al., 2021). In the two-families picture of the binary-supernova formation channel, mixed NS-SQS systems are explicitly mentioned as relevant to events like GW170817 (Becerra et al., 29 Jul 2025).

Electromagnetic transients have long been linked to SQS physics. A recent review emphasizes that strong gravitational-wave emission may arise from mergers, mode excitation, continuous-wave instabilities, or even close-in strange quark planets, while fierce electromagnetic bursts may be powered by neutron-star to strange-star conversion, binary strange-star mergers, or crust collapse (Zhang et al., 2024). The same review notes that such mechanisms have been discussed in connection with short gamma-ray bursts and fast radio bursts (Zhang et al., 2024). In the supernova-binary conversion channel, the quoted conversion energies up to $d$46 further reinforce this possibility, although detailed radiation-hydrodynamic modeling is left open (Becerra et al., 29 Jul 2025).

7. Constraints, extensions, and unresolved issues

No unambiguous SQS identification has yet emerged, and much of current work focuses on discriminants that differ from hadronic-star systematics. One robust line of attack is the existence of SQS-specific universal relations. Across both the QMDD and vector MIT bag models, the moment of inertia, tidal deformability, and compactness obey relations distinct from hadronic stars. Examples include

$d$47

and

$d$48

with quoted coefficients that differ from the usual hadronic fits (Lugones et al., 14 Mar 2025). This suggests that combined measurements of $d$49, $d$50, $d$51, and $d$52 could separate self-bound from gravity-bound stars without detailed EOS reconstruction.

Another active issue is how to reconcile heavy compact objects with tidal constraints. In perturbative QCD plus an effective bag term, constant-$d$53 models cannot comfortably exceed about $d$54 while satisfying $d$55, whereas a density-dependent $d$56 can raise $d$57 to $d$58, $d$59, $d$60, and $d$61 for $d$62, respectively (Sedaghat et al., 2024). The same framework is used to argue that PSR J0952-0607, PSR J2215+5135, PSR J0740+6620, and even the GW190814 secondary object can be interpreted as SQSs (Sedaghat et al., 2024).

More speculative extensions push SQSs into the mass-gap regime. In dRGT-like massive gravity with an MNJL EOS, increasing the bag constant softens the EOS and lowers $d$63, while modified hydrostatic balance allows self-bound SQSs in the interval $d$64 that still satisfy $d$65. The analysis further requires $d$66, sub-horizon compactness, and nonzero $d$67 to exclude black-hole behavior (Sedaghat et al., 2024). A different extension, involving fermionic dark matter admixed through a vector dark boson, finds that dark matter lowers mass and radius relative to the no-DM case, but can still yield configurations consistent with GW190814 (Sen et al., 2022).

SQSs have also been proposed as dark-matter detectors. By scanning 1403 solitary pulsar-like compact stars, one study identifies PSR J1801-0857D as the strongest source of limits on scalar-DM scattering, with age $d$68 Gyr and Galactic-center distance $d$69 kpc. If that object is assumed to be an SQS rather than an NS, the inferred DM–proton cross-section limits become much weaker and can be comparable to direct-detection bounds; this leads to the stated implication that if scalar dark matter were observed in future terrestrial experiments, old pulsars would be favored to be SQSs rather than NSs (Zheng et al., 2016).

The central controversy remains unchanged: SQSs are theoretically consistent in many EOS frameworks and now embedded in detailed calculations of formation, evolution, oscillations, magnetized rotation, merger dynamics, and multimessenger phenomenology, yet no single observational signature has isolated them beyond ambiguity. The literature therefore increasingly treats SQS identification as a problem of joint inference across mass, radius, spin, $d$70, mode spectroscopy, ejecta properties, and transient energetics rather than as a one-observable classification problem (Becerra et al., 29 Jul 2025, Zhang et al., 2024).