Swift J1749.4-2807, the only known eclipsing accreting millisecond X-ray pulsar (spin 517.92 Hz, orbital period 8.82 h), was proposed by Yu & Xu (2010) as a possible quark (strange) star. Assuming its low-mass companion fills its Roche lobe, they derived a compact-object mass near 1 M⊙1\,M_\odot and argued that the observed spin is compatible with a quark star only if the critical frequency Ωc(T)\Omega_{\rm c}(T) for the rotational r-mode instability exceeds roughly 0.3 ΩK0.3\,\Omega_{\rm K} (the Keplerian limit) at accreting-binary temperatures — a condition that hinges on unsettled quark-matter viscosities and the equation of state. Fifteen years of follow-up have fixed the orbital geometry, measured an orbital-period derivative, and, in the 2021 outburst, revealed thermonuclear Type-I X-ray bursts and burst oscillations; yet no dynamical mass exists (the companion has never been spectroscopically identified), and no calculation of Ωc(T)\Omega_{\rm c}(T) for this source has been published. The problem is to determine whether the compact object in Swift J1749.4-2807 is a neutron star or a quark star; the source's decisive test is the r-mode stability of quark-star models, while the still-unmeasured dynamical mass and the surface-burning phenomenology provide further relevant evidence.

Background

An accreting millisecond X-ray pulsar (AMXP) is a transiently accreting neutron star in a low-mass X-ray binary (LMXB, a binary in which a compact object accretes from a low-mass companion) whose coherent X-ray pulsations at a few hundred Hz reveal the stellar spin; AMXPs are regarded as the evolutionary link between accreting binaries and recycled radio millisecond pulsars. Swift J1749.4-2807, recognized as a 517.9 Hz pulsar in 2010, is the only AMXP known to show X-ray eclipses: once per 8.82-hour orbit the compact object passes behind its companion, with eclipses lasting 2172±13 s, i.e. 6.85% of the orbit (Markwardt & Strohmayer 2010). The eclipse geometry, together with the pulsar's projected orbital semi-major axis of about 1.90 light-seconds and the binary mass function (the minimum companion mass implied by the pulsar's orbit alone), constrains the inclination to 74°–77° and the companion mass to roughly 0.5–0.8 M⊙M_\odot (Altamirano et al. 2010), making this system, in principle, the most precise future mass measurement of any AMXP once the companion star is identified (Markwardt & Strohmayer 2010; Jonker et al. 2012).

Yu & Xu (2010) asked whether the compact object in this system might be a quark star rather than a neutron star. By the Bodmer–Witten 'strange matter' hypothesis, strange quark matter — a deconfined mixture of up, down, and strange quarks — could be the true ground state of strongly interacting matter at zero pressure; compact stars made of it ('strange quark stars') would be self-bound rather than gravity-bound and could exist with small masses and radii. Xu (2003) further proposed that cold quark matter crystallizes into a 'solid quark star'. Assuming the companion fills its Roche lobe (the teardrop-shaped region around a star beyond which matter flows freely onto the compact object), or 90% of it, Yu & Xu combined the mass function, the eclipse geometry, and main-sequence/white-dwarf mass–radius relations to infer a companion of roughly 0.5 M⊙0.5\,M_\odot, an inclination near 76°, and a compact-object mass of only about 1.0 M⊙1.0\,M_\odot (0.7 M⊙0.7\,M_\odot in the 90% case) — unusually low for a recycled millisecond pulsar, and low enough to be accommodated naturally by self-bound quark-matter equations of state.

Their decisive test involved r-modes: rotational (Rossby) modes of a spinning star that are driven unstable by gravitational-radiation reaction (the Chandrasekhar–Friedman–Schutz mechanism) and damped by viscosity, so that a star is unstable above a critical angular frequency Ωc(T)\Omega_{\rm c}(T) that depends on temperature through the microphysical viscosities and on the equation of state; how this instability window limits spins of both neutron stars and compact stars in LMXBs remains an active research topic (Andersson et al. 2011). Madsen (2000) showed for strange stars that the window depends qualitatively on the quark-matter phase: a star of normal (ungapped) quark matter with a thin nuclear crust can hold millisecond spins over much of parameter space, while a star of color-flavor-locked (CFL) superconducting quark matter — a phase in which quark pairing removes much of the viscosity that damps r-modes — is r-mode unstable and spins down rapidly. Yu & Xu computed that the observed spin of J1749 (Ω≈3254 s−1\Omega\approx 3254\,{\rm s^{-1}}) is about 0.210.21–0.28 ΩK0.28\,\Omega_{\rm K} for quark-matter equations of state (where ΩK=GM/R3\Omega_{\rm K}=\sqrt{GM/R^3} is the Keplerian, or mass-shedding, frequency) but 0.340.34–0.59 ΩK0.59\,\Omega_{\rm K} for neutron-star equations of state, and concluded that the quark-star reading survives only if Ωc(T)≳0.3 ΩK\Omega_{\rm c}(T)\gtrsim 0.3\,\Omega_{\rm K} at the temperatures of an accreting binary; they argued that neutron stars could hardly sustain such spin, favoring a solid quark star. That last step is in tension with the observed pulsar population, since radio pulsars spinning at up to 716 Hz are known (Hessels et al. 2006), so the discriminating content of the question rests on Ωc(T)\Omega_{\rm c}(T) for quark matter, on the still-unmeasured dynamical mass, and on the surface phenomenology.

The surface phenomenology now includes thermonuclear (Type-I) X-ray bursts — flashes powered by unstable hydrogen/helium burning in accreted material on the star's surface — and burst oscillations, coherent intensity modulations during bursts at (or near) the spin frequency. Both were detected from J1749 in its 2021 outburst (Albayati et al. 2023). Such burning is standard physics for a nuclear stellar surface; whether a bare or solid quark-star surface can accumulate and ignite nuclear fuel in the same way has not been worked out for this source.

Problem Statement

Determine whether the compact object in the eclipsing accreting millisecond X-ray pulsar Swift J1749.4-2807 is a neutron star or a quark (strange) star, as posed by Yu & Xu (2010). In the source's framing, the discriminating test is the r-mode criterion: whether the critical frequency Ωc(T)\Omega_{\rm c}(T) for quark-star models (bare, crusted, or solid; normal or color-superconducting quark matter) exceeds roughly 0.3 ΩK0.3\,\Omega_{\rm K} at the thermal states the source traverses between outburst and quiescence, which would decide whether the observed 517.92 Hz spin — about 0.210.21–0.28 ΩK0.28\,\Omega_{\rm K} under quark-matter equations of state — can be stably sustained by a quark star. Other quantities bear on the identification as evidence rather than as separately mandated deliverables: a dynamical measurement of the compact object's mass and radius, replacing the untested assumption that the companion fills its Roche lobe, would test the ~1 M⊙1\,M_\odot estimate; and the observed surface phenomenology — coherent pulsations, thermonuclear Type-I bursts, and burst oscillations — bears on whether the two hypotheses can be distinguished through surface nuclear burning. The answer is a definite identification ('neutron star' or 'quark star') together with the evidence chain that discriminates the two hypotheses; if the evidence instead shows that the discrimination is impossible in principle for any viable model class and foreseeable observation, that conclusion, with the specific obstruction, also answers the question.

References

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