Arcade-to-Rope Reconnection Geometry

• Arcade-to-rope reconnection geometry describes the process by which sheared coronal arcades are transformed into twisted flux ropes, ultimately leading to solar eruptions such as CMEs and flares.
• Three-dimensional MHD simulations and multi-wavelength observations reveal the roles of breakout, flare, and interchange reconnection in the evolution and disconnection of flux ropes.
• Quantitative metrics like twist parameters, decay index, and reconnected flux provide actionable insights into predicting CME morphology and eruption dynamics in various solar structures.

The arcade-to-rope reconnection geometry encompasses the processes by which sheared coronal arcade magnetic fields are transformed into a coherent, twisted flux rope, typically leading to solar eruptions such as coronal mass ejections (CMEs) and flares. This topology has been extensively characterized through three-dimensional magnetohydrodynamic (MHD) simulations and multi-wavelength observations, with recent interest focused on its role in eruption dynamics across solar structures ranging from active regions to pseudostreamers (Wyper et al., 12 Sep 2024).

1. Magnetic Topology and Pre-Eruption Configuration

Arcade-to-rope reconnection initiates within a closed-field arcade straddling the photospheric polarity inversion line (PIL). In the canonical setup, the arcade field is quasi-potential or weakly sheared, with its footpoints displaced along the PIL. This arcade lies below a coronal null point or, more generally, an overlying system of open or large-scale field that enables breakout reconnection through a fan/spine topology. Typically, the null’s fan surface defines a closed dome, with one or both spines connecting to either interior bipole or the ambient open corona (Wyper et al., 12 Sep 2024).

Shearing photospheric motions or imposed flows inject free magnetic energy into the system, driving the arcade toward the formation of a thin hyperbolic flux tube (HFT) at its core. The HFT is the preferred locale for tether-cutting reconnection, which initially proceeds slowly as short, low-lying flare loops are produced and flare ribbons begin to form.

2. Flare Current Sheet and Arcade-to-Rope Transformation

As the overlying strapping field is weakened—either by breakout/interchange reconnection at the null or continued evolution—the arcade rises, creating a vertically extended flare current sheet (FCS) beneath it. Fast reconnection at the FCS converts the sheared arcade loops into twisted flux-rope field lines and additional post-flare arcades. The reconnection proceeds via elementary pairings: each event transforms two arcade field lines into a short flare loop and a highly twisted rope line.

The twist imparted to these newly reconnected lines is quantified by the field-line turns parameter:

$$T_w = \int_L \frac{(\nabla \times B) \cdot B}{4\pi |B|^2} dl$$

A weighted twist, $\tau_w = T_w (L/L_{\mathrm{PIL}})$, is often used to select rope-constituting lines; for instance, $\tau_w \geq 6$ defines the rope in certain simulations. As reconnection proceeds, a coherent flux rope rapidly accumulates significant axial flux and twist—by $t \approx 8.6$ hr in some models, the rope may contain up to 30% of the former closed-arcade flux (Wyper et al., 12 Sep 2024).

Energetically, the onset of flare reconnection is marked by a drop in free magnetic energy and a sharp rise in kinetic energy, with reconnection rates matching the surface-swept flux by the ribbons.

3. Interchange Reconnection and Rope-Leg Disconnection

Following rope formation and continued rise, the system may transition into a phase where the rope interacts directly with the overlying null and breakout current sheet (BCS). The FCS and BCS merge into a long, curved current sheet that wraps obliquely around the rope’s flank. At select regions—specifically where a rope leg and adjacent open field become anti-parallel—interchange reconnection converts one closed leg of the rope into open flux, effectively severing it from the Sun.

This leg-severing reconnection induces a whip-like rotation of the flux rope and launches a burst of torsional Alfvén waves and dense plasmoids into the solar wind. The process is manifest in observations as a transient “V” shape in the rope and significant outflows, with the formerly closed flux eventually replaced by open lines (Wyper et al., 12 Sep 2024).

Secondary interchange events can result in footpoint migration, such as a shift of the remaining closed rope segment’s anchoring from one location to another around the circular PIL.

4. Current Sheet Orientations, Fan/Spine Structures, and Reconnection Metrics

Three principal current sheets mediate the arcade-to-rope geometry:

• Breakout Current Sheet (BCS): Horizontal, situated in the fan plane at the coronal null.
• Flare Current Sheet (FCS): Vertical, spans the PIL directly beneath the erupting rope.
• Merged Sheet: Oblique, encloses the rope’s flank post-merger.

The inner spine connects the null to the interior bipole; the outer spine projects into the open field above. Surface maps of the squashing factor $Q$ distinctly trace the interaction of flare ribbons and breakout circular ribbons at points of disconnection and footpoint migration.

Quantitative metrics include:

• Twist parameter: $T_w$ and $\tau_w$
• Decay index: $n = -d\ln{B_{\mathrm{ex}}}/d\ln{h}$, diagnosing torus instability regions
• Flux measures: Cumulative reconnected (flare and interchange) fluxes, $\Phi_{\mathrm{FR}}(t)$ and $\Phi_{\mathrm{int}}(t)$
• Reconnection rates: $d\Phi_{\mathrm{FR}}/dt$, $d\Phi_{\mathrm{int}}/dt$
• Magnetic field initialization and driving flows: Specified via analytic forms in simulations.

5. Implications for Pseudostreamer CMEs and Morphological Outcomes

The arcade-to-rope geometry underpins the eruptive evolution of CMEs from pseudostreamers, distinguishing them from helmet-streamer CMEs. The early breakout and interchange reconnection phases weaken strapping fields and enable the formation and eventual disconnection of the flux rope. The final CME ejected into the solar wind carries remnants of its flux tube structure—a partly open hose-spiral with embedded twist—and is accompanied by a sheath of kinked but untwisted field lines forged during the reconnection (Wyper et al., 12 Sep 2024).

Pseudostreamer CMEs follow the same overall magnetic progression as coronal jets in terms of breakout and flare reconnection, yet diverge morphologically due to the distinct geometry of the null and surrounding field. The simulations and observational data demonstrate that these events inject torsional waves and bursty flows into the solar wind, providing a robust framework for interpreting CME footpoint migration, ribbon formation, and the final CME topology.

6. Summary Table of Topological Phases and Key Processes

Phase	Dominant Topology	Key Process
I. Breakout	Arcade + coronal null	Interchange reconnection, fan dome
II. Flare (A→R)	Arcade + vertical CS	Fast tether-cutting reconnection, rope formation
III. Disconnection	Rope + open field	Leg-severing interchange, CME launch

In conclusion, the arcade-to-rope reconnection geometry provides a physically complete description of CME initiation via successive phases of breakout, flare reconnection, and interchange processes, with quantifiable metrics and well-defined topological domains that are applicable across solar structures exhibiting eruptive behavior (Wyper et al., 12 Sep 2024).