Quark Magnetars: Deconfined Quark Matter Effects

• Quark magnetars are compact stars in which deconfined quark matter generates extreme magnetic fields, leading to magnetar-like burst activity.
• They encompass hybrid stars, strange quark stars, and quark-nova remnants, illustrating multiple formation channels and observational signatures.
• Modeling these objects requires detailed treatment of Landau quantization, phase transitions, and anisotropic equations of state that shape stellar structure.

Quark magnetars are compact-star configurations in which magnetar-like phenomenology is attributed to deconfined quark matter, either in the core of a hybrid star or throughout a quark star. In the literature, the term is used for several related classes: hybrid stars with quark cores and hadronic envelopes, strange quark stars modeled as self-bound quark matter, color-superconducting quark stars left by quark-novae, and rapidly rotating supramassive postmerger quark stars invoked in short gamma-ray burst afterglows. Across these usages, the central claim is that quark microphysics materially alters magnetic-field generation, the equation of state, polarization, burst phenomenology, and observational diagnostics relative to purely hadronic magnetar models (Dexheimer et al., 2012, Ouyed et al., 2016, Li et al., 2017).

1. Terminology and model classes

The literature does not use quark magnetar in a single narrow sense. In one line of work, magnetars are modeled as hybrid stars whose core consists of quark matter and whose outer layers remain hadronic. In this construction, deconfinement occurs dynamically as density or temperature increases, and a mixed phase can arise if global rather than local charge neutrality is imposed (Dexheimer et al., 2012). In another line, magnetars are treated as highly magnetized quark stars, often in MIT bag-model or NJL-type descriptions, with strange quark matter furnishing the bulk stellar medium (Orsaria et al., 2010, Chu et al., 2014).

A distinct usage appears in quark-nova scenarios. There, the compact remnant is a quark star in a color-superconducting phase, possessing an intrinsically high magnetic field and surrounded by metal-rich fallback debris in the form of a co-rotating shell or a Keplerian ring. These remnants are described as being frequently misconstrued as neutron-star magnetars, even though the model assigns their persistent and bursting activity to vortex expulsion and intermittent accretion from r-process-rich debris (Ouyed et al., 2016). Closely related proposals treat AXPs and SGRs as quark-star or fallback-disk systems, or as a “quarctar,” namely a crusted quark star in an accretion disk, rather than as canonical neutron-star magnetars (Tong et al., 2011, Qiao et al., 2012).

This diversity of usage is itself part of the subject. A quark magnetar may therefore denote a strongly magnetized strange star, a hybrid star whose magnetar behavior is shaped by quark deconfinement in the core, or a quark-nova remnant whose magnetic phenomenology is mediated by superconducting vortices and debris dynamics. This suggests that the term is best understood as a family resemblance concept rather than a single equilibrium model.

2. Deconfinement, mixed phases, and quark-matter interfaces

A central framework for hybrid-star magnetars is the extended SU(3) non-linear realization of the sigma model, in which the active degrees of freedom change naturally from hadrons to quarks as temperature and baryon chemical potential increase. The relevant order parameters are the chiral condensate $\sigma$, which signals chiral symmetry restoration, and the Polyakov-loop variable $\Phi$, which signals deconfinement. In this model, the Polyakov-loop potential depends on baryon chemical potential, enabling the same construction to address low-temperature, high-density regions relevant for compact stars (Dexheimer et al., 2012).

Within that framework, magnetars are modeled under $\beta$-equilibrium and charge neutrality, with a hadronic outer region, a quark core, and potentially a mixed phase between them. The mixed phase is a consequence of adopting global charge neutrality, motivated by the assumption of small interface surface tension. The transition is tracked by the evolution of $\sigma$ and $\Phi$ with baryon chemical potential, and the calculations show hadronic matter turning first into a mixed phase and then into pure quark matter. Hyperons are reported to be almost entirely suppressed by the early appearance of quarks at high density (Dexheimer et al., 2012).

The kinetics of forming quark matter in magnetars has also been studied through homogeneous nucleation of chirally symmetric droplets in a cold, dense magnetic environment, using the one-loop effective potential of the two-flavor quark-meson model within the thin-wall approximation. In this treatment, the magnetic field modifies the critical chemical potential, critical radius, correlation length, and surface tension in a non-monotonic way because of Landau-level structure. Moderate magnetic fields can lower the critical chemical potential by up to $15\%$, and the combined behavior of the nucleation parameters can allow nucleation of quark droplets in magnetar matter even when the surface tension is not especially small (Kroff et al., 2014).

A complementary finite-size analysis uses the MIT bag model with the multiple reflection expansion formalism for three-flavor quark matter in cold deleptonized magnetars, proto-magnetars, and hot postmerger magnetars. In that study, the total surface tension lies between $0.2$ MeV/fm$^2$ and $15$ MeV/fm$^2$, increases with baryon density, and becomes anisotropic under strong magnetic fields: $\Phi$0 grows while $\Phi$1 decreases. Since the calculated values remain below the quoted critical threshold $\Phi$2, mixed phases are favored, and strong fields imply elongated droplets aligned with the magnetic field rather than spherical ones (Grunfeld et al., 2020).

3. Magnetic-field microphysics in quark matter

Magnetic microphysics enters quark-magnetar models through Landau quantization, anomalous magnetic moments, chiral imbalance, electroweak parity violation, and color-superconducting flux organization. In the hybrid-star calculations, a variable magnetic field increasing from a surface value of order $\Phi$3 G toward central values up to $\Phi$4–$\Phi$5 G is introduced as a function of baryon chemical potential. This avoids discontinuities at the phase boundary and allows a detailed treatment of Landau quantization and anomalous magnetic moments in the particle population. Charged particles occupy discrete Landau levels, only one spin projection is allowed in the zeroth Landau level, and the resulting particle densities show “wiggles” as new Landau levels become kinematically accessible. The total spin polarization is defined by

$\Phi$6

with $\Phi$7 for baryons, $\Phi$8 for quarks, and $\Phi$9 for leptons. In this model, polarization increases with magnetic field and with baryon chemical potential, but drops when quark matter appears because quark anomalous magnetic moments are not included in the calculation (Dexheimer et al., 2012).

A different mechanism addresses the origin of magnetar-strength fields in quark or hybrid stars with chirally symmetric quark matter. There, the magnetic instability is driven by parity-violating electroweak interactions of quarks and produces an anomalous current along the magnetic field,

$\beta$0

with

$\beta$1

For typical quark-matter parameters, this mechanism amplifies a seed field of $\beta$2 to $\beta$3, with saturation reached within minutes to hours after the star reaches thermal equilibrium. The saturation field depends strongly on the initial temperature, with reported values $\beta$4 G for $\beta$5 K and $\beta$6 G for $\beta$7 K (Dvornikov, 2016).

When magnetohydrodynamic turbulence is added to the same chiral-magnetic framework, small-scale fields develop pulse profiles that resemble magnetar bursts. In that treatment, scales $\beta$8–$\beta$9 cm produce high-field episodes lasting $\sigma$0 s, $\sigma$1–$\sigma$2 cm yields durations of $\sigma$3 s, and $\sigma$4–$\sigma$5 cm gives $\sigma$6–$\sigma$7 s behavior akin to giant flares. The proposed interpretation is that fluctuations generated in the central quark matter initiate magnetar bursts, potentially by triggering a thermoplastic wave in the crust (Dvornikov, 2016).

In quark-nova remnant models, the magnetic structure is instead governed by color superconductivity. The Meissner effect forces the field into vortices forming an Abrikosov lattice and aligns the magnetic axis with the rotation axis. Spin-down then expels vortices and magnetic flux, with reconnection near the surface producing persistent X-ray emission and heating (Ouyed et al., 2016).

4. Equation of state, anisotropy, and stellar structure

Quark-magnetar structure is highly sensitive to the quark-matter model and to how magnetic stresses are incorporated. A comparative analysis of magnetized quark matter in the MIT and NJL models distinguishes three formalisms: isotropic equations of state, anisotropic equations of state with separate parallel and perpendicular pressures, and the chaotic field approximation. In the MIT model, magnetization is well-behaved and always positive at large fields; in the NJL model it is oscillatory, can be negative, and exhibits spikes associated with Landau-level crossings. This difference strongly affects anisotropic treatments: the NJL anisotropic EOS becomes unsuitable for stable stellar calculations, while the chaotic field approximation yields more modest structural changes, with maximum masses never varying more than $\sigma$8 (Menezes et al., 2015).

An extreme stiffening mechanism appears when quark matter is pushed into the lowest-Landau-level regime at a threshold field $\sigma$9 G. In that limit, only the lowest Landau level is occupied, the quark system becomes quasi-one-dimensional, and the EOS approaches

$\Phi$0

which saturates the causality bound with $\Phi$1. This construction yields high-mass stars beyond two solar masses and can generate a third family of compact stars if the adiabatic index increases discontinuously at the hadron–quark transition (Tatsumi et al., 2017).

Anisotropy is also central in the confined isospin- and density-dependent mass model. There the pressure perpendicular to the magnetic field exceeds the parallel pressure, so the stellar response depends on the internal field orientation. For a radial field orientation, the relevant supporting pressure is the longitudinal component and the maximum mass decreases; for a transverse orientation, the transverse pressure supports the star and the maximum mass increases. At central fields near $\Phi$2 G, the quoted maximum masses span roughly $\Phi$3–$\Phi$4 for radial orientation and $\Phi$5–$\Phi$6 for transverse orientation, demonstrating that field geometry is not a secondary detail (Chu et al., 2014).

Within a three-flavor SU(3) NJL model with vector interactions, the EOS of strange quark matter is found to be insensitive to vector-isovector interaction but strongly stiffened by repulsive vector-isoscalar interaction. A positive pressure contribution from magnetized gluons further increases the stiffness and can drive the sound speed squared toward unity. With a gentle density-dependent magnetic-field profile, the pressure anisotropy stays moderate enough that isotropic TOV calculations remain a reasonable approximation, and suitable combinations of vector-isoscalar interaction and magnetized gluon pressure can support $\Phi$7 quark magnetars (Chu et al., 2014).

Analytical MIT-bag calculations provide a complementary limit. For magnetic fields $\Phi$8 G, Landau quantization modifies the quark thermodynamic potential and yields analytic mass–radius relations from the energy variational principle in general relativity. These calculations also imply an upper bound on the magnetic field compatible with stable quark stars, with $\Phi$9 of order a few $15\%$0 G for the tabulated bag constants; above that range, the energy per baryon can violate the “iron condition” and destabilize the configuration (Orsaria et al., 2010).

5. Thermal evolution, bursts, and source diagnostics

In color-superconducting quark-star models, vortex dynamics provides a direct link between magnetic evolution, spin-down, and thermal observables. Rotational vortex lines confine interior magnetic flux, and as the star spins down, vortices are expelled and reconnection near the surface releases thermal energy. One implementation gives the persistent X-ray luminosity as

$15\%$1

and yields coupled evolution laws for $15\%$2 and $15\%$3 that have been used to argue for an ancestral link among SGRs, AXPs, and XDINs. In the same framework, a delay between supernova birth and entry into the color-superconducting phase can be used to estimate the deconfinement density, reported as five times nuclear saturation (Niebergal et al., 2010).

Quark-nova remnant models add fallback debris as an active component of the emission phenomenology. Persistent X-rays arise from vortex expulsion, while bursts are triggered by intermittent accretion from a co-rotating shell or a Keplerian ring. In the ring case, magnetic penetration of the degenerate disk triggers accretion and heating of both the quark star and the ring, producing two hot-blackbody components and hot spots. The same framework interprets recurrent $15\%$4 keV lines as atomic transitions of r-process elements such as strontium or rubidium rather than proton cyclotron lines, and explains anti-glitches as negative angular-momentum transfer from retrograde disk material (Ouyed et al., 2016).

A detailed realization of this picture was proposed for SGR 0418+5729. The source is modeled as a $15\%$5 Myr old quark star surrounded by a $15\%$6 degenerate iron-rich Keplerian ring extending from $15\%$7 km to $15\%$8 km. Magnetar-like bursts are then attributed to magnetic penetration of the inner ring and subsequent accretion, while radiation feedback drives months-long atmospheric accretion matching the decay phase. The model makes specific predictions, including an accretion glitch of $15\%$9 during burst and a sub-keV proton cyclotron line from the ring (Ouyed et al., 2010).

Recent work has extended the diagnostic space to beyond-standard-model signatures. A study of SGR 0501+4516 as a strange quark magnetar uses a three-flavor NJL model with axion-induced charge-parity violation and predicts axion decay to gamma rays in a very strong magnetic field. The proposed observational channels are Fermi-LAT, IXPE, and XMM-Newton, with the signature arising from axion effects on quark matter and quark-matter cores in strange quark magnetars (Das, 2 Jul 2025).

6. Formation channels, energetic conversion, and contested interpretations

Several formation channels have been proposed for quark magnetars. One is gradual deconfinement in a magnetized hybrid star, producing a quark core and mixed phase as density rises (Dexheimer et al., 2012). Another is abrupt conversion: phase transitions from normal hadronic stars to strange or hybrid stars can release very large amounts of energy. In one analysis, the energy released during NS $0.2$0 SS conversion is always of the order of $0.2$1 ergs, whereas conversion from neutron magnetar to strange or hybrid magnetar releases less energy because magnetic fields soften the EOS. The same study concludes that magnetar conversions are more naturally associated with giant flares than with cosmological GRBs, especially when the transition is to a hybrid magnetar (Mallick et al., 2012).

Binary neutron-star merger remnants provide a separate context. Three postmerger quark-star EOSs, PMQS1–3, were constructed to match the posterior mass distribution inferred from short gamma-ray bursts with internal X-ray plateaus and from Galactic NS–NS binaries. Their static maximum masses are $0.2$2, $0.2$3, and $0.2$4, and the rotating maximum mass is parameterized as

$0.2$5

In this program, the key quantity selecting whether an EOS is compatible with the observed postmerger mass distribution is the static maximum mass $0.2$6 rather than rotational support alone. These models are used to estimate the fractions of stable stars, supramassive stars, and prompt black holes, and to assess the viability of quark-magnetar-powered internal plateaus and kilonovae (Li et al., 2017).

The subject remains controversial because quark magnetars are often advanced as alternatives to the standard neutron-star magnetar interpretation of AXPs and SGRs. One review emphasizes several tensions for the standard model, including the existence of SGR 0418+5729 with $0.2$7, the absence of the expected high-energy gamma-ray emission in Fermi-LAT observations, and the lack of unusually energetic supernova remnants or large kick velocities. In that perspective, if AXPs and SGRs are not magnetar candidates, then they must be “quark star/fallback disk” systems; quark magnetars remain possible, but observational discrimination is acknowledged to be subtle (Tong et al., 2011).

A more explicit alternative is the “quarctar” model, where AXPs and SGRs are crusted quark stars in accretion disks. That proposal argues that the standard dipole-braking magnetic-field estimate is invalid when $0.2$8 because wind braking is neglected, and that persistent emission, burst energetics, spectral properties, and transient radio activity can be reproduced without requiring magnetar-strength dipole fields. In that account, radio-emitting AXPs arise when superflares burn holes through the crust at the poles, temporarily exposing a bare quark surface (Qiao et al., 2012).

Taken together, these studies do not establish a unique quark-magnetar paradigm. They instead define a research program in which quark deconfinement, color superconductivity, chiral-magnetic instabilities, interface physics, and fallback debris are all treated as potentially observable ingredients of magnetar phenomenology. A plausible implication is that future discrimination will depend less on any single observable than on combined constraints from mass and radius measurements, burst timing and spectroscopy, X-ray polarimetry, gamma-ray non-detections or detections, and postmerger multi-messenger inference.