The first end-to-end magnetohydrodynamic simulation of a solar coronal mass ejection powered solely by helicity condensation (Dahlin, Antiochos and DeVore 2019) demonstrated a single realization: small-scale photospheric vortical flows inject magnetic helicity that inverse-cascades to the polarity inversion line, builds a filament channel, and erupts via magnetic breakout when flare reconnection turns on. What the field still lacks is any general, quantified criterion — in measurable coronal or low-coronal quantities such as accumulated relative helicity, shear flux, free-energy fraction, or topological flux transfer — that predicts when such quasi-static buildup becomes explosively eruptive, together with a determination of the domain of validity of any such criterion (for example, how robust the condensation-to-eruption pathway is to the form of the photospheric driving, to numerical resolution, and to more complex multipolar topologies). No such general, quantified criterion has yet been established, while adjacent results (torus-instability decay-index criteria, flux-emergence angle thresholds, nested-topology failed eruptions) cover different onset channels and do not answer the question.

Background

Coronal mass ejections (CMEs) are explosive expulsions of magnetized plasma from the solar atmosphere, and the energy that powers them builds up slowly in filament channels: ribbons of highly sheared horizontal magnetic field straddling polarity inversion lines (PILs), the lines where the radial photospheric field reverses sign. Magnetic helicity is a topological measure of twist and linkage among magnetic flux systems; it is nearly conserved in the highly conducting corona, so helicity injected at the photosphere cannot be dissipated locally and must accumulate. The helicity-condensation theory (Antiochos 2013, ApJ 772, 72) posits that small-scale vortical convective motions continually inject twisted flux at small scales, and that pervasive reconnection transports this twist as an inverse cascade toward the large-scale PILs, 'condensing' shear there and forming filament channels. Confined-domain simulations (Knizhnik, Antiochos and DeVore 2015, ApJ 809, 137; 2017, ApJ 835, 85) verified channel formation by this process but could not address eruption, because their Cartesian upper boundaries artificially confined the field. Dahlin, Antiochos and DeVore (2019, ApJ 879, 96) performed the first end-to-end calculation in a fully 3D spherical domain extending to 30 solar radii: an embedded bipole (a compact active region inside a global dipole, whose separatrix dome — the surface separating the bipole's closed flux from the surrounding field — is bounded by a 3D magnetic null point where the field vanishes) was driven by 107 close-packed vortical flows on the minority-polarity photosphere. The resulting filament channel erupted as a fast CME via magnetic breakout, in which reconnection at the null removes restraining overlying flux, and the eruption trigger was shown to be the onset of flare reconnection in the current sheet above the PIL rather than an ideal instability. This contrasts with the main quantified onset criteria in the literature, which apply to pre-existing twisted flux ropes: the torus instability (Kliem and Török 2006), in which a rope erupts once the decay index of the ambient strapping field exceeds a critical value (a critical range of about 1.3 to 1.5 found by Zuccarello, Aulanier and Gilchrist 2015). In the condensation pathway the flux rope is created by onset-time reconnection itself, so those height-based criteria do not transfer, and the 2019 calculation offered one realization with no threshold or scaling law in measurable quantities. The authors noted that they assumed uniform rotational driving 'for simplicity', asserting without test that the driving form should not matter so long as net helicity is injected, and that the separatrix boundary fragments down to the grid scale, leaving resolution effects on the reconnection dynamics unquantified. Reviews through 2023-2024 (the NASA Living With a Star Focused Science Team report on CME/flare onset by Linton et al. 2023; Jiang 2024) confirm that how, when, and why CMEs erupt — the transition from slow buildup to explosive release — remains a central open question, complicated above all by the lack of direct measurements of the 3D coronal magnetic field, which is why any usable criterion must be cast in terms of quantities accessible from the photosphere or low corona.

Problem Statement

For a coronal magnetic field energized by helicity condensation — photospheric vortical (or otherwise complex) flows injecting magnetic helicity at small scales, which inverse-cascades via pervasive reconnection to concentrate shear at polarity inversion lines — determine whether there exists a general, quantified criterion, expressible in quantities measurable at the photosphere or in the low corona (for example accumulated relative helicity, shear-flux content, free-energy fraction, topological flux transfer, or current-sheet formation diagnostics), that predicts the transition from quasi-static filament-channel buildup to explosive eruption, including whether the outcome is a successful CME or a confined/failed eruption. The overarching objective is converting the demonstrated single-realization helicity-condensation eruption into predictive capability. A resolution requires both the criterion itself (or a demonstration that no such general criterion exists) and a determination of its domain of validity, at minimum for the embedded-bipole class; 'general' here means characterized over a class of configurations rather than confined to the single 2019 realization, so a criterion valid only within a stated sub-class still counts as a resolution provided its limits are stated. The axes enumerated here are illustrative aspects of that domain of validity rather than conjunctive requirements; they include the sensitivity of the condensation-to-eruption pathway to the form, spatial scale, and number of photospheric driving cells (the 2019 calculation assumed uniform rotational driving 'for simplicity' and asserted without test that the particular form of the driving should not matter so long as net helicity is injected), including non-vortical drivers and helicity injection by flux emergence and cancellation rather than rotational flows; the effect of numerical resolution on the reconnection dynamics, given the observed fragmentation of the separatrix boundary down to the grid scale; and the degree to which the pathway generalizes from the simple embedded-bipole topology to more complex multipolar and nested active-region configurations and to observationally realistic, spatially and temporally variable photospheric flows. A negative conclusion that no such general criterion exists cannot rest on the failure of any particular approach or of a small number of configurations.

References

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