On the Constraints and Observational Manifestations of Failed Solar Eruptions in Toroidal Magnetic Cage

Abstract

Observations show that many solar eruptions remain confined within strong overlying magnetic fields, forming a so-called magnetic cage. While confinement by poloidal overlying fields has been widely investigated, the role of strong external toroidal fields remains unclear. Using three-dimensional magnetohydrodynamic simulations, we study confined eruptions in a toroidal magnetic cage, focusing on the interplay between the Lorentz force and magnetic reconnection, and their observational signatures. We further employ a guiding-center test-particle approach to synthesize hard X-ray emission for comparison between thermal and nonthermal responses. We find that overlying toroidal fields play a crucial role in confinement by generating strong return currents that produce a significant downward Lorentz force, suppressing flux rope ascent. At the same time, they induce large-angle rotation of the flux rope, leading to reconnection with overlying fields and eventual break-up. Synthetic EUV emission reveals multi-ribbon flares with highly sheared, globally cowboy-hat-like loop structures. Hard X-ray diagnostics show that thermal and nonthermal emissions are not co-spatial, with return currents acting as an efficient accelerator of energetic electrons. These results demonstrate that toroidal-field-induced forces govern both the confinement and rotation of erupting flux ropes, providing an explanation for failed eruptions even under torus-unstable conditions. These results suggest that the morphology and shearing angle of flare loops are the useful diagnostics for distinguishing confined from eruptive events.

Figures (22)

• Figure 1: Visualisation of the initial magnetic fields viewed from the (a) side and (b) top. The yellow, cyan and magenta tubes represent the twisted flux rope, overlying poloidal and toroidal magnetic fields, respectively. $N_{\rm _{P}}$/$N_{\rm _{T}}$ and $P_{\rm _{P}}$/$P_{\rm _{T}}$ labels the negative and positive sub-photosphere magnetic charges to build the poloidal/toroidal magnetic fields, respectively.
• Figure 2: Height profiles of the decay index computed from external total horizontal magnetic fields ($B_{h}$, blue line), poloidal fields ($B_{\rm p}$, orange line) and toroidal fields ($B_{\rm T}$, green line). The orange and green bands indicate regions of the flux rope at initial and stopping moments, respectively.
• Figure 3: Temporal evolution of (a--d) the magnetic field and (e, f) the twist number $T_{w}$ distributions in the eruption process. The yellow, cyan and pink tubes are traced from the $N_{\rm _{FR}}$, $N_{\rm _{P}}$ and $N_{\rm _{T}}$ polarities, respectively. The colours in the bottom and vertical planes exhibit the distributions of the $B_{z}$ and $T_{e}$, respectively. Panels (e) and (f) display the $T_{w}$ distributions on the vertical and bottom planes, respectively.
• Figure 4: Temporal evolution of (a) the axial magnetic field component $B_{y}$, (b) the number density $n$ and (c) the temperature $T_{e}$ at $t=2, 6, 9, 15\tau$. The dashed line in the $t=9$ column outlines the border of the flux rope (with added reconnected flux).
• Figure 5: Kinematics of the eruptive flux rope. Panel (a) shows the time-distance diagram of the $B_{y}$ component along the $z$-axis. In panel (b) the blue dots and red crosses show the evolution of height and velocity during the eruption, which are measured with the positive $B_{y}$ front in panel (a).