Fast radio bursts (FRBs) are millisecond coherent radio transients whose engine is broadly attributed to magnetized compact stars, but the central unsolved link in every proposed channel is how efficiently stored magnetic energy is converted into coherent GHz emission. A specific engine was proposed by Song (Phys. Rev. D 111, 063018 (2025)): during cooling, a compact star's interior transitions to the color-spin-locked (CSL) phase of dense quark matter, an electromagnetic superconductor, and a thin surface layer expels magnetic flux with energy EB,expE_{B,\mathrm{exp}} up to roughly 104410^{44} erg (for the expelled-layer field B′B' — the field enhanced just outside the CSL domain — near 101610^{16} G), which the paper compared directly to observed FRB isotropic-equivalent energies (the energy a burst would appear to carry if it radiated equally in all directions) of 103510^{35}–104210^{42} erg and concluded could act as an inducement mechanism to power typical FRBs. The paper models neither the interaction of the expelled flux with the external magnetosphere, nor particle acceleration, nor coherent emission, and gives no conversion efficiency, so the comparison is purely energetic. The open problem is to build the missing radiative link: a quantitative model of the magnetospheric energy release, particle acceleration, and coherent emission (including escape from the magnetosphere) for this flux-explosion channel that determines the efficiency η=Erad/EB,exp\eta = E_{\mathrm{rad}}/E_{B,\mathrm{exp}} (radiated electromagnetic energy divided by expelled magnetic energy), or a defensible bounded range, together with the predicted burst duration, spectrum, and energy scaling. Existing efficiency determinations for other magnetospheric reconnection geometries bracket η\eta over orders of magnitude (about 2×10−32\times10^{-3} in radiative particle-in-cell simulations of a flare-compressed magnetar-wind current sheet; less than about 10−610^{-6} under recent model-independent constraints on light-cylinder-scale forced reconnection), so the viability of the CSL channel remains unquantified.

Background

Fast radio bursts (FRBs) are extragalactic (one known Galactic) radio flashes of millisecond duration with luminosities up to about 104310^{43} erg/s; their radiation is so bright — brightness temperatures (the effective temperature a blackbody would need to match the observed intensity) up to ∼1036\sim10^{36} K, far above any incoherent thermal or synchrotron source — that the emission must be coherent, produced by organized charge bunches or a maser-like plasma instability, and the plasma physics that forms the emitting charges is not understood. The leading engines are magnetars — neutron stars with surface magnetic fields of 101410^{14}–101510^{15} G — after the Galactic magnetar SGR 1935+2154 produced the FRB-like burst FRB 200428 simultaneously with a hard X-ray burst whose energy exceeded the radio output by many orders of magnitude, showing that the magnetic-energy-to-radio conversion efficiency, not the total energy budget, is the crux. Two generic radiation sites are debated: emission inside the magnetosphere (the region of closed magnetic field lines around the star, where curvature radiation — emission from charges accelerated along curved magnetic field lines — from bunches or a maser could operate), and emission at relativistic shocks far outside the light cylinder (the radius where corotation with the star would reach light speed), as in the synchrotron-maser shock model of Lyubarsky (2014); in both, magnetic reconnection — the plasma process that changes field-line connectivity and releases stored magnetic energy, accelerating particles — is a natural dissipation channel, but its efficiency for producing coherent radio emission is uncomputed in general.

On the dense-matter side, quantum chromodynamics predicts that deconfined quark matter at high density may enter color-superconducting phases, in which quarks of different colors and flavors pair. Spin-one pairing includes the color-spin-locked (CSL) phase, which locks color and spin rotations and, uniquely among spin-one phases, behaves as an electromagnetic superconductor (an ordinary Meissner effect expels magnetic fields, of type I, with a critical field BcB_c). Song (Phys. Rev. D 111, 063018 (2025)) analyzed CSL quark matter in an NJL (Nambu-Jona-Lasinio, an effective model of dense quark matter with four-quark interactions) model and in the MIT bag model (a phenomenological model treating quark matter as free quarks confined by a vacuum pressure), and proposed that if a compact star's quark core cools through the CSL transition while carrying a magnetic field, the expanding superconducting region expels flux from a thin surface layer on a short timescale; in fast-cooling special cases the expelled magnetic energy EB,expE_{B,\mathrm{exp}} can reach an upper limit near 104410^{44} erg for the expelled-layer field B′B' near 101610^{16} G — the magnetic field enhanced just outside the superconducting domain, which grows to the critical field Bc≃1016B_c \simeq 10^{16} G — with an expulsion timescale that can match millisecond burst durations. The paper compares EB,expE_{B,\mathrm{exp}} directly with observed FRB isotropic-equivalent energies (103510^{35}–104210^{42} erg, with the maximum 2×10422\times10^{42} erg reached by FRB 20220610A) and concludes that CSL formation could act as an inducement mechanism to power typical FRBs — while explicitly noting that the surface could be heated via magnetic reconnection if the expelled field lines cross external ones, but without computing any of this physics. The gap is thus the same one that confronts the whole FRB field, specialized to a new engine: a released magnetic-energy reservoir is not a radio burst until the energy transfer to the magnetospheric plasma, particle acceleration, coherent emission, and escape from the surrounding plasma are all modeled. The only first-principles efficiency number for a reconnection-driven coherent-emission scenario is from two-dimensional radiative relativistic particle-in-cell (PIC, a kinetic simulation method resolving the plasma distribution function) simulations of a magnetar-flare pulse compressing the wind current sheet, which found a fraction f∼0.002f \sim 0.002 of the reconnected magnetic energy converted to escaping GHz fast-magnetosonic waves (compressive plasma waves) (Mahlmann et al. 2022); a 2026 model-independent analysis of kinetic-luminosity and brightness-temperature constraints (Beniamini and Kumar 2026) argues that light-cylinder-scale forced reconnection emits a radio energy typically below 10−610^{-6} of the injected energy and favors near-surface magnetospheric models with continuous in-situ particle acceleration. These values differ by more than three orders of magnitude, so even the best-studied reconnection geometry has no settled efficiency — and no analysis exists at all for the setting posed here, the conversion into coherent radio emission of magnetic flux expelled from a superconducting quark core.

Problem Statement

Determine the conversion efficiency η\eta from magnetic energy expelled by a color-spin-locked (CSL) phase transition in a compact star to radiated electromagnetic emission — specifically, build the predictive emission model that Song (Phys. Rev. D 111, 063018 (2025)) explicitly leaves uncomputed for the CSL-quark-star fast-radio-burst channel proposed there on energetics and timescale grounds. Starting from the source scenario (a quark core cooling through the CSL transition, expelling magnetic energy EB,expE_{B,\mathrm{exp}} of up to roughly 104410^{44} erg for the expelled-layer field B′B' near 101610^{16} G from a thin surface layer on a potentially millisecond timescale), the required work is: (i) model the interaction of the expelled flux with the pre-existing magnetosphere and any nuclear crust, and the physical channel through which the expelled energy is transferred to the magnetospheric plasma and its real-time evolution — the source mentions, without computing either, reconnection of expelled field lines with external ones and an intense evolution of magnetospheric magnetic fields converting EB,expE_{B,\mathrm{exp}} into kinetic energy of plasma in the magnetosphere and crust (potentially triggering starquakes); (ii) model the resulting particle acceleration; (iii) model the coherent emission — within an emission mechanism explicitly stated and justified for this channel, which may be an adopted candidate given that the mechanism is unsettled in the FRB field generally — together with its escape from the surrounding plasma (including absorption and induced-Compton constraints, i.e. stimulated Compton scattering by dense surrounding plasma, which can suppress an escaping coherent radio wave); and (iv) compute the efficiency η=Erad/EB,exp\eta = E_{\mathrm{rad}}/E_{B,\mathrm{exp}} (radiated electromagnetic energy divided by expelled magnetic energy), or a defensible bounded range of η\eta derived from the modeled chain (i)–(iii) for this channel rather than adopted from other reconnection geometries, together with its dependence on the expelled-layer field strength B′B', cooling history, and expelled-layer depth, and the predicted observable burst properties (duration, spectrum, luminosity). Because observed FRB energies are quoted as isotropic-equivalent values while EradE_{\mathrm{rad}} is the true radiated energy, the beaming convention relating the two must be stated wherever η\eta is compared with the observed range (an assumed isotropic emitter, or an explicit beaming factor fbf_b, e.g. of order θ2/2\theta^2/2 as in the source's own GRB comparison; the source's FRB comparison applies no beaming correction). The resulting efficiency, or bounded range, then yields a quantitative assessment — in place of the source's order-of-magnitude energy comparison — of whether flux expulsion during CSL formation can power typical observed FRBs (isotropic-equivalent energies 103510^{35}–104210^{42} erg, millisecond durations), and under which field strengths and cooling histories. The target is this CSL flux-expulsion channel specifically; a general-geometry efficiency result is not a substitute for it, although the same computation would inform the general unsettled question of how efficiently magnetospheric reconnection in compact stars converts magnetic energy into coherent radio emission, for which existing determinations in other geometries conflict by more than three orders of magnitude.

References

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