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Abstract Full-disk measurements of the solar magnetic field by the Helioseismic and Magnetic Imager (HMI) are often used for magnetic field extrapolations, but its limited spatial and spectral resolution can lead to significant errors. We compare HMI data with observations of NOAA 12104 by the Hinode Spectropolarimeter (SP) to derive a scaling curve for the magnetic field strength,B. The SP data in the Feilines at 630 nm were inverted with the SIR code. We find that the Milne–Eddington inversion of HMI underestimatesBand the line-of-sight flux, Φ, in all granulation surroundings by an average factor of 4.5 in plage and 9.2 in the quiet Sun in comparison to the SP. The deviation is inversely proportional to the magnetic fill factor,f, in the SP results. We derived a correction curve to match the HMIBwith the effective fluxBfin the SP data that scaled HMIBup by 1.3 on average. A comparison of non-force-free field extrapolations over a larger field of view without and with the correction revealed minor changes in connectivity and a proportional scaling of electric currents and Lorentz force (∝B∼ 1.3) and free energy (∝B² ∼ 2). Magnetic field extrapolations of HMI vector data with large areas of plage and quiet Sun will underestimate the photospheric magnetic field strength by a factor of 5–10 and the coronal magnetic flux by at least a factor of 2. An HMI inversion including a fill factor would mitigate the problem. 

Context.Erupting magnetic flux ropes (MFRs) are believed to play a crucial role in producing solar flares. However, the formation of erupting MFRs in complex coronal magnetic configurations and the role of their subsequent evolution in the flaring events are not fully understood. Aims.We perform a magnetohydrodynamic (MHD) simulation of active region NOAA 12241 to understand the formation of a rising magnetic flux rope during the onset of an M6.9 flare on 2014 December 18 around 21:41 UT (SOL2014-12- 18T21:41M6.9), which was followed by the appearance of parallel flare ribbons. Methods.The MHD simulation was initialised with an extrapolated non-force-free magnetic field generated from the photospheric vector magnetogram of the active region taken a few minutes before the flare. Results.The initial magnetic field topology displays a pre-existing sheared arcade enveloping the polarity inversion line. The simulated dynamics exhibit the movement of the oppositely directed legs of the sheared arcade field lines towards each other due to the converging Lorentz force, resulting in the onset of tether-cutting magnetic reconnection that produces an underlying flare arcade and flare ribbons. Concurrently, a magnetic flux rope above the flare arcade develops inside the sheared arcade and shows a rising motion. The flux rope is found to be formed in a torus-unstable region, thereby explaining its eruptive nature. Interestingly, the location and rise of the rope are in good agreement with the corresponding observations seen in extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Furthermore, the foot points of the simulation’s flare arcade match well with the location of the observed parallel ribbons of the flare. Conclusions.The presented simulation supports the development of the MFR by the tether-cutting magnetic reconnection inside the sheared coronal arcade during flare onset. The MFR is then found to extend along the polarity inversion line (PIL) through slip-running reconnection. The MFR’s eruptive nature is ascribed both to its formation in the torus-unstable region and also to the runaway tether-cutting reconnection.