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Erupting magnetic flux ropes (MFRs) play a crucial role in producing solarflares. However, the formation of erupting MFRs in complex coronal magneticconfigurations and their subsequent evolution in the flaring events are notfully understood. We performed an MHD simulation of active region NOAA 12241 tounderstand the formation of a rising MFR during the onset of an M6.9 flare on2014 December 18, around 21:41 UT. The MHD simulation was initialised with anextrapolated non-force-free magnetic field generated from the photosphericvector magnetogram of the active region taken a few minutes before the flare.The initial magnetic field topology displays a pre-existing sheared arcadeenveloping the polarity inversion line. The simulated dynamics exhibit themovement of the oppositely directed legs of the sheared arcade field linestowards each other due to the converging Lorentz force, resulting in the onsetof tether-cutting magnetic reconnection that produces an underlying flarearcade and flare ribbons. Concurrently, an MFR above the flare arcade developsinside the sheared arcade and shows a rising motion. The MFR is found to beformed in a torus-unstable region, thereby explaining its eruptive nature.Interestingly, the location and rise of the rope are in good agreement with thecorresponding observations seen in EUV channels. Furthermore, the foot pointsof the simulation's flare arcade match well with the location of the observedparallel ribbons of the flare. The presented simulation supports thedevelopment of the MFR by the tether-cutting magnetic reconnection inside thesheared coronal arcade during flare onset. The MFR is then found to extendalong the polarity inversion line (PIL) through slip-running reconnection. TheMFR's eruptive nature is ascribed both to its formation in the torus-unstableregion and also to the runaway tether-cutting reconnection.

Formation of an observed eruptive flux rope above the torus instability threshold through tether-cutting magnetic reconnection