Role of magnetic shear distribution on the formation of eruptive flux ropes

TL;DR

This study investigates how the spatial distribution of magnetic shear along coronal arcades governs eruptive flux rope formation. It employs a 2.5D resistive MHD framework with nonadiabatic terms—optically thin radiative losses, field-aligned thermal conduction, and steady background heating—in a stratified solar atmosphere, comparing two initial shear angles, $72.5^ ^\circ$ and $25.8^ ^\circ$. The results show that strong initial shear ($ ilde heta=72.5^ ^\circ$) drives spontaneous flux rope formation and dual eruptions via Lorentz-force–driven reconnection, while weaker shear ($ ilde heta=25.8^ ^\circ$) yields no flux rope formation; the evolution of mean shear and the evolving ratio between guide and reconnection fields explain heating and particle acceleration, including hot onset behavior. These findings highlight the need for coronal-scale diagnostics beyond footpoint shear to interpret eruptive onset and energy release in solar observations.

Abstract

Erupting flux ropes play crucial role in powering a wide range of solar transients, including flares, jets, and coronal mass ejections. These events are driven by the release of stored magnetic energy, facilitated by the shear in the complex magnetic topologies. However, the mechanisms governing the formation and eruption of flux ropes, particularly the role of magnetic shear distribution in coronal arcades are not fully understood. We employ magnetohydrodynamic simulations incorporating nonadiabatic effects of optically thin radiative losses, magnetic field-aligned thermal conduction, and spatially varying (steady) background heating, to realistically model the coronal environment. A stratified solar atmosphere under gravity is initialized with a non-force-free field comprising sheared arcades. We study two different cases by varying the initial shear to analyze their resulting dynamics, and the possibility of flux rope formation and eruptions. Our results show that strong initial magnetic shear leads to spontaneous flux rope formation and eruption via magnetic reconnection, driven by Lorentz force. The shear distribution infers the non-potentiality distributed along arcades and demonstrates its relevance in identifying sites prone to eruptive activity. The evolution of mean shear and the relative strength between guide to reconnection fields during the pre- and post-eruption phases are explored, with implications of bulk heating for the ``hot onset'' phenomena in flares, and particle acceleration. On the other hand, the weaker shear case does not lead to formation of any flux ropes. Our findings highlight the limitations of relying solely on foot point shear and underscore the need for coronal scale diagnostics. These results are relevant for understanding eruptive onset conditions and can promote a better interpretation of coronal observations from current and future missions.

Figures (8)

• Figure 1: Top row: Spatial distribution of $|\bf{J}|/|B|$ (in arbitrary units in log scale), and the projected magnetic field lines (in red) in the $x-y$ plane for (a) $t=5.44$, (b) $t=7.51$, and (c) $12.59$ s obtained from "simulation 1". The saturation level of the color bars are chosen appropriately as shown in the legends for a better visualization of the CS structures. Bottom row: (d), (e), and (f) are same as the corresponding top panels, for the $|B_z|$ in logarithm scale, where the saturation level of the color bars are chosen between as shown in the respective legends for a better visualization.
• Figure 2: Variation of the shear angle along the magnetic field lines from the central arcade region for $t=5.44$, 7.51 and 12.59 min going from left to right columns respectively, obtained from "simulation 1". The shear angle (in degree) are shown in the respective color bars. The top and bottom rows represent the side and top views of the field lines configuration respectively. The 2D slices show spatial variation of $B_y$ in the $x-z$ plane at the base of the simulation box, and values of $B_y$ is shown by the color bar common for all the panels. The orientation of the $x, y, z$ axes are shown in red, green and blue arrows respectively. The number of field lines at the bottom panels are chosen less compared to the corresponding top panels for a better visualization of the field lines.
• Figure 3: (a) Distribution of magnetic field lines (in gray) for the entire spatial domain of "simulation 1", at $t=7.51$ min, where the red curve represents the field line that is anchored at the seed point (foot point) location $(x, y)=(1.61, 0)$ Mm (FP1) as marked by the red circle. (b) Same as the top-left panel, but for $t=12.52$ min, where the blue field line is anchored at the seed point location $(x, y)=(2, 0)$ Mm (FP2). (c) The red and the blue curves represent the distribution of the shear, $\gamma$ along the red and blue field lines as shown in the top-left and top-right panels respectively, where the vertical dashed lines are the positions along the red field line marked by the gray dots ($s_1, .., s_4$) at the top-left panel. (d) Distribution of $\gamma$ along the field lines anchored at FP1 (red curve) and FP2 (blue curve) at the beginning of the semi-equilibrium phase at $t=5.44$ min.
• Figure 4: (a) Temporal variation of mean shear ($\bar{\gamma}$) of the field lines anchored at FP1 (red curve) and FP2 (blue curve) for the simulation with strong initial shear ("simulation 1"), which has multiple flux rope eruptions. The vertical dashed lines are the time markers at $t=7.51$ and 12.52 min, after which the reconnection occurs at those field lines. (b) Temporal variation of $\bar{\gamma}$ for the field lines anchored at different FPs as shown in the legend for the simulation with a weak initial shear ("simulation 2"), which do not have formation of any flux rope.
• Figure 5: Temporal variation of the total arcade length anchored at FP1 (red curve) and FP2 (blue curve) for "simulation 1". The left and right vertical dashed lines are the time markers for $t=7.51$ and 12.52 min respectively.