Formation of a Magnetic Flux Rope Prior to the Eruption: Insight from a Radiative MHD Simulation of Active Region Emergence

TL;DR

This study addresses how pre-eruptive magnetic flux ropes form in a realistic solar active region by analyzing a radiative RMHD simulation with self-consistent flux emergence. By quantifying magnetic helicity flux and its decomposition into advection ($\dot{H}_a$) and shear ($\dot{H}_s$) terms, the authors demonstrate that flux cancellation driven by photospheric shear plays the dominant role in flux rope formation, with reconnection above the photosphere enhancing helicity transport at higher altitudes. Height-dependent analysis shows a transition from shear-dominated to advection-driven helicity contributions, linked to magnetic reconnection processes. The work highlights flux cancellation as a robust mechanism for flux rope assembly in complex active regions and provides quantitative diagnostics relevant for predicting solar eruptions in more realistic solar atmospheres.

Abstract

Magnetic flux ropes (MFRs) are fundamental magnetic structures in solar eruptions, whose formation is generally attributed to (1) the emergence of subsurface flux tubes or (2) flux cancellation driven by photospheric horizontal flows and magnetic reconnection. Both mechanisms can operate simultaneously during active region evolution, making their relative contributions challenging to quantify. Here, we analyze the formation of a flux rope in a MURaM radiative magnetohydrodynamic (RMHD) simulation, which formed and evolved for approximately three hours before an M-class flare. The formation process is quantified by magnetic helicity flux, which drives the non-potential evolution of magnetic field, with its advection and shear terms on the photosphere corresponding to the emergence and photospheric horizontal flows, respectively. Examining the helicity injected into the flux rope through the photosphere, we find both terms increase significantly as the eruption approaches, with the shear term prevailing overall. Height-dependent analysis of helicity flux, together with magnetic field and velocity distributions, further reveals a gradual transition from the shear to the advection term with an increasing altitude, which is driven by magnetic reconnection above the photosphere. Our results provide quantitative evidence that flux cancellation governs flux rope formation, arising naturally from magnetic field reorganization during active region evolution: as flux emergence transports magnetic flux upward, photospheric shearing motions adjust magnetic field and inject helicity into solar atmosphere, and magnetic reconnection ultimately assembles the main body of flux ropes.

Figures (6)

• Figure 1: Overview of the magnetic configuration. (a) Synthetic GOES light curve of the simulation. The eruption associated with the flux rope analyzed in this study is characterized by an impulsive enhancement of synthetic GOES flux. We define the time when the GOES flux reaches its maximum during the eruption as $t_0$ = 0 s and mark it with vertical dotted line. The gray-shaded region denotes the time interval considered in the subsequent analysis, covering the period from the initial stage of flux rope formation to the onset of its eruption. Other representative snapshots of the evolution ($t_1$, $t_2$, and $t_3$) are indicated by vertical dashed lines. (b) Photospheric magnetogram of the full simulation domain, with the core region of the eruption highlighted by a red box. (c) Zoom-in view of the core region, where P and N denote the main positive and negative sunspots, respectively. (d)-(f) Temporal evolution of the pre-eruptive magnetic structure. The yellow solid tubes illustrate selected magnetic field lines. The 3D visualization is produced using VAPOR VAPOR.
• Figure 2: An example of flux rope identification. (a)(b) Distributions of $\mathcal{T}_w$ and $\rm{log_{10}}$$\ Q$, respectively, at $t_3 = -$79.9 min on a horizontal plane at $z =$ 0.83 Mm, where the averaged plasma $\beta$ is approximately unity. (c) Smoothed $\mathcal{T}_w$ map overlaid with the cross section of flux rope (pink shading) on this layer identified by the region growing method. The white solid and dashed contours in (a)-(c) outline the regions with $B_z = \pm$1000 Gauss on the $\beta$ unity layer. (d) Photospheric cross section of the flux rope (pink shading) overlaid on the magnetogram. An animation showing the evolution of $\mathcal{T}_w$, $\rm{log_{10}}$$\ Q$, and the cross sections of the flux rope during flux rope formation is available, which spans the simulated time period from $t$ = -186.3 min to $t$ = - 21.0 min, aligning with the interval marked by the gray shaded in Figure \ref{['fig1']}(a).
• Figure 3: Distribution of helicity flux and its components on photosphere where $z = 0$ Mm. (a)-(c) Distributions of helicity flux $\dot{h}$, its shear term $\dot{h}_\mathrm{s}$, and its advection term $\dot{h}_\mathrm{a}$, respectively. White solid and dashed contours indicate regions with photospheric $B_z = \pm$1500 Gauss. The pink-shaded area in (a) marks the cross section of the flux rope on the photosphere. (d) Temporal evolution of the shear term $\dot{H}_\mathrm{s,AR}(t,0 \ \mathrm{Mm})$ and the advection term $\dot{H}_\mathrm{a,AR}(t,0 \ \mathrm{Mm})$ of the helicity flux in the AR, shown as green and orange solid curves, respectively. Dashed curves indicate the corresponding smoothed profiles. Horizontal dotted line marks the zero level, and vertical dotted line denotes the time corresponding to (a)-(c). The red curve represents the synthetic GOES flux. (e) Temporal evolution of the shear term $\dot{H}_\mathrm{s,MFR}(t,0 \ \mathrm{Mm})$ and the advection term $\dot{H}_\mathrm{a,MFR}(t,0 \ \mathrm{Mm})$ of helicity flux in the MFR cross section.Curve styles and symbols are the same as in (d). An animation showing the evolution of helicity flux density on photosphere is available, which spans the simulated time period from $t$ = -186.3 min to $t$ = - 21.0 min.
• Figure 4: Time–height diagrams of helicity flux injected into the flux rope. Panel (a) shows the evolution of shear term $\dot{H}_\mathrm{s,MFR}(t,z)$, while panel (b) shows the evolution of the advection term $\dot{H}_\mathrm{a,MFR}(t,z)$. The red curves represent the synthetic GOES flux.
• Figure 5: Parameters related to the evolution of helicity flux. (a)(b) Photospheric shearing velocity $v_{\rm sh}$, where a mask based on magnetic field strength is applied to highlight the velocity distribution only within regions of strong magnetic field. The contours of $B_z = \pm$ 1500 Gauss on the photosphere are overplotted in white solid and dashed lines, respectively. The gray contours marks the cross sections of the flux rope on photosphere where $z = 0$ Mm. The orange arrows mark the reference direction for velocity decomposition. The magenta (indigo) arrows denote shearing flows parallel (anti-parallel) to the reference direction. (c) Distribution of $(\nabla \times\bm{B}) \cdot \bm{B}/B^2$ on a $yz$-plane located at $x =$ 19.20 Mm, which is proportional to the field-aligned current density. The dashed and dotted horizontal lines mark the position of $z =$ 0 Mm (photosphere) and $z = 0.83$ Mm, respectively; the height range between them corresponds to that shown in Figure \ref{['fig4']}. The green dashed contour outlines the approximate location of the flux rope on this plane. The green box encloses the core region of the current sheet, which is selected for a detailed view in (d)-(h). (d)-(h) Zoom-in view of the selected region showing the distribution of $(\nabla \times\bm{B}) \cdot \bm{B}/B^2$, vertical velocity $v_z$, the ratio of $v_z$ to the local Alfven speed $v_{\rm a}$, the ratio of $v_y$ to $v_{\rm a}$, and the density of advection term, respectively. The gray streamlines in (f) depict the orientation of the magnetic field ($B_y$–$B_z$) on this plane, while the green arrows in (g) represent the direction of the in-plane components ($v_y$, $v_z$) of the conductive velocity.