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

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.