Non-Eruptive Sigmoid Structures

• Non-eruptive sigmoids are S-shaped coronal structures characterized by high-temperature, highly sheared magnetic loops that arise through localized reconnection without leading to eruptions.
• Their formation involves mechanisms such as double-J and slipping reconnection, which reconfigure sheared arcade loops into stable, low-lying flux bundles that do not meet eruption thresholds.
• Observations and simulations reveal distinct morphological, thermal, and magnetic signatures, challenging the assumption that sigmoidal formations necessarily signal imminent solar eruptions.

A non-eruptive sigmoid denotes an S-shaped coronal structure formed in a solar active region that does not lead to a coronal mass ejection (CME) or flare-driven eruption during its observable evolution. Such sigmoids manifest as high-temperature, highly sheared magnetic loops visible in extreme ultraviolet (EUV) and X-ray wavelengths, mainly tracing sites of magnetic non-potentiality and ongoing reconnection. Non-eruptive sigmoids are of broad scientific interest as they illustrate the decoupling between magnetic flux rope formation and dynamic eruption, challenging the view that all sigmoids necessarily precede or signal imminent eruptive activity. Observational, numerical, and theoretical analyses constrain their configurations, dynamics, and thermal budgets, providing benchmarks for coronal magnetic field diagnostics and reconnection models.

1. Morphological and Thermodynamic Characteristics

Non-eruptive sigmoids are observationally characterized by their S-shaped (sigmoidal) emission patterns across distinct coronal temperature diagnostics. Multi-instrument campaigns (Hinode/EIS, XRT, STEREO/EUVI, SDO/AIA) establish that these sigmoids typically exhibit a morphological composite:

• Double J-shaped hot arcs: In the hottest diagnostics (XRT Al_poly, EIS Fe XV λ284), T > 2 MK, the sigmoid appears as two distinct, highly sheared “J”-shaped loop systems.
• Cooler S-shaped core: At lower temperatures (T ≈ 1.3–1.6 MK, e.g., EUVI Fe XII 195 Å), a continuous S-shaped structure bridges the gap between the J-arcs, following the photospheric polarity inversion line (PIL) (0904.4782).
• Spatial relationship to PIL: The hot J-shaped arcs reside on either side of the PIL, while the S-shaped emission closely traces the PIL, reflecting the locus of ongoing or recent reconnection.
• Thermal evolution: Differential emission measure (DEM) studies of impulsively heated non-eruptive sigmoids show initial dominance at T ≳ 10 MK (DEM peak at log T ≈ 7.2), followed by sequential brightening in cooler bands as the structure cools conductively and radiatively (Wang et al., 9 Dec 2025).

Table: Summary of Non-Eruptive Sigmoid Structural Features

Diagnostic Passband	Observed Structure	Typical Temperature (MK)
XRT Al_poly, EIS Fe XV	Double J-shaped arcs	>2–16
EUV Fe XII 195 Å	Continuous S-shaped core	1–1.6
EUV 335 Å, 211 Å	Late-phase EUV brightening	2–4

These morphologies are invariant across both direct observations and radiative MHD simulations for non-eruptive scenarios (0904.4782, Wang et al., 9 Dec 2025, Rempel et al., 2023).

2. Formation Mechanisms and Magnetic Topology

Non-eruptive sigmoids result from distinct, yet interrelated, mechanisms of magnetic stress buildup, reconnection, and topological reconfiguration:

• Classical double-J reconnection: Two oppositely oriented J-shaped loops reconnect at a low-lying quasi-separatrix layer (QSL) above the PIL, converting sheared arcades into a single, helically twisted S-shaped flux bundle (0904.4782, Wang et al., 9 Dec 2025). The reconnection site coincides with zones of high squashing factor Q (Q ≳ 10³).
• Slipping reconnection of a single J-loop: Alternative scenarios document the formation of an S-shaped structure via the rapid, localized slippage of one footpoint of a single J-shaped loop through regions of enhanced current density, driven by significant non-ideal electric fields (R ≠ 0). Peak footpoint slippage speeds can exceed 1000 km s⁻¹, far above Alfvénic values (Pan et al., 2022).
• Absent eruption: Magnetic extrapolations and MHD models consistently show that non-eruptive sigmoids fail to satisfy ideal instability thresholds—specifically, the torus instability decay index $n < 1.3$ (critical $n_{\mathrm{c}} \sim 1.5$) and twist number $T_w < 1.0$ (well below the kink instability threshold) (Wang et al., 9 Dec 2025, Rempel et al., 2023).

Thus, non-eruptive sigmoids form in environments where reconnection reorganizes sheared arcades into low-lying flux bundles, but where overlying field strength or insufficient twist preclude destabilization and eruption.

3. Energetics, Cooling, and Plasma Diagnostics

The energy release, heating, and subsequent cooling of non-eruptive sigmoids are governed by a balance between Ohmic dissipation, ongoing reconnection, and thermal conduction:

• Impulsive heating: Non-eruptive sigmoids can achieve core temperatures exceeding $10^7$ K in the absence of eruption, as demonstrated by DEM analysis and hard X-ray signatures (RHESSI sources at 3–12 keV) (Wang et al., 9 Dec 2025).
• Conductive and radiative cooling: The cooling phase is typically quantified through characteristic timescales:

$$\tau_{\text{cond}} = \frac{3 n_e k_B L^2}{\kappa_0 T_0^{5/2}}, \quad \tau_{\text{rad}} = \frac{3 k_B T_0^{3/2}}{\chi n_e}.$$

For sigmoid plasma at $T_0 \sim 16$ MK and $n_e \sim 4 \times 10^{10}$ cm⁻³, conductive cooling dominates ($\tau_{\text{cond}} \sim 200$ s) in the initial phase, with radiative loss timescales ($\tau_{\text{rad}} \sim 570$ s) becoming comparable as the structure cools (Wang et al., 9 Dec 2025).

• Distributed heating: In simulations, free magnetic energy builds up to $\sim 2 \times 10^{31}$ erg, but is dissipated gently (total quiescent energy over ~10 h $\sim 5 \times 10^{30}$ erg) rather than through flare-like impulsive release (Rempel et al., 2023).
• DEM and EM mapping: DEM analysis in these structures reveals the transition of EM peaks from high (>10 MK) to intermediate (5–8 MK), and finally to lower (2–4 MK) temperatures as the sigmoid cools and radiates in EUV channels (Wang et al., 9 Dec 2025, Pan et al., 2022).

The thermal and energetic evolution is thus diagnostic of ongoing reconnection and topological rearrangement, in the absence of catastrophic instability.

4. Observational Signatures and Distinct Diagnostics

Non-eruptive sigmoids present unique multi-wavelength, temporal, and spatial emission characteristics:

• Persistence and decay: Sigmoids can persist for ~10 hours in the gradual decay phase of active regions without flaring or CME onset, eventually fragmenting and dissipating (0904.4782).
• Absence of flare ribbons or post-flare loops: Synthetic and observed EUV/X-ray imagery consistently lack the sharp, compact ribbons or post-eruption loop arcades characteristic of eruptive flares (Rempel et al., 2023).
• EUV late phases: In events such as NOAA AR 11504, non-eruptive sigmoids can yield "extremely energetic" EUV late-phase peaks, with the 335 Å radiated energy exceeding the main flare phase by factors >4 (Wang et al., 9 Dec 2025).
• Magnetogram and Doppler signatures: Magnetograms register converging and canceling flux motions at the PIL concurrent with sigmoid formation, while Doppler patterns display weak counter-streaming flows (±5 km s⁻¹) along the sigmoidal barbs (Rempel et al., 2023, 0904.4782).

Advanced inversion and modeling techniques (e.g., multi-channel DEM analysis, QSL mapping, non-linear force-free extrapolations) are critical for accurate diagnosis and classification.

5. Theoretical Context and Implications

Non-eruptive sigmoids provide constraints and testbeds for coronal magnetic topology, reconnection physics, and eruptive flare/CME models:

• Flux rope stability: The existence of stable, low-lying flux ropes challenges the presumption that the presence of a sigmoid alone is a reliable flare/CME precursor. Critical conditions—torus decay index, coherent twist, overlying flux removal—are required to breach equilibrium (0904.4782, Wang et al., 9 Dec 2025, Rempel et al., 2023).
• Non-classical formation pathways: Scenarios involving slip-running reconnection of single J-loops, as opposed to classical double-J tether-cutting, emphasize the three-dimensionality and diversity of reconnection and flux rope assembly in the corona (Pan et al., 2022).
• Continued energy release: Prolonged reconnection in multipolar topologies can maintain non-eruptive sigmoids in an energetically active state, producing dominant EUV emission phases absent in impulsive, eruptive analogues (Wang et al., 9 Dec 2025).

A plausible implication is that not all coronal flux ropes or sigmoids are precursors to solar eruptions; instead, their stability and eventual fate are regulated by global and local boundary conditions, including overlying field geometry and history of flux cancellation.

6. Summary Table: Distinctions Between Eruptive and Non-Eruptive Sigmoids

Property	Non-Eruptive Sigmoid	Eruptive Sigmoid
Instability thresholds	Not met (decay index, twist low)	Met (torus, kink)
Typical outcome	Stable, long-lived structure	Flare, CME, post-flare arcade
Energy release mode	Distributed, gradual	Impulsive, flare-like
EUV/X-ray morphology	S-shaped, lacks flare ribbons	S-shaped, subsequent loop arcade/ribbons
Photospheric signature	Mild flux cancellation, no δ-spot	Extended cPIL, δ-spot, rapid evolution
Example studies	(0904.4782, Wang et al., 9 Dec 2025, Rempel et al., 2023, Pan et al., 2022)	(Rempel et al., 2023) (eruptive runs)

Non-eruptive sigmoids are thus essential markers of pre-eruptive magnetic stress, reconnection physics, and coronal energy storage, but their evolution diverges fundamentally from scenarios leading to energetic solar eruptions.