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

Abstract Magnetic flux ropes 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 (AR) evolution, making their relative contributions challenging to quantify. Here, we analyze the formation of a flux rope in a MURaM radiative magnetohydrodynamic simulation, which formed and evolved for approximately 3 hr before an M-class flare. The formation process is quantified by the magnetic helicity flux, which drives the nonpotential evolution of the 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 the helicity flux, together with the 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 AR evolution: as the flux emergence transports the magnetic flux upward, photospheric shearing motions adjust the magnetic field and inject helicity into the solar atmosphere, and magnetic reconnection ultimately assembles the main body of flux ropes.