Formation and rising phase of a flux rope through data-constrained simulations

Abstract

Context. Data-constrained models incorporate observed photospheric magnetic fields. However, due to the lack of magnetic field information in the rest of the solar atmosphere, models rely on extrapolations that, in most cases, neglect the Lorentz force. Nevertheless, this force is present in the lower atmosphere and may play a key role in destabilising the equilibrium configuration and triggering eruptions. Aims. This study seeks to understand and reproduce a solar eruption SOL2014-12-18T21:41 that occurred in active region NOAA 12241, preceded by an M6.9 flare, and to investigate the impact of relaxing the initial force-free assumption. Methods. The resistive and compressible magnetohydrodynamic simulation is initiated using a non-force-free magnetic field extrapolated from a photospheric vector magnetogram taken minutes before the flare. The simulation includes a stratified atmosphere and non-ideal effects such as thermal conduction and radiative cooling. Results. A flux rope forms and rises in the simulation, carrying away dense material from the lower solar atmosphere. Its formation results from the non-zero Lorentz force acting on the initial sheared arcade, without assuming pre-existing flux ropes or photospheric driving motions. The flux rope is then deflected toward regions of low magnetic pressure, escaping the domain at 350 km/s with approximately constant acceleration. Conclusions. A robust numerical framework for modelling flaring active regions was applied to the eruption of NOAA AR12241 as a case study, assuming a realistic non-force-free magnetic field near the flare onset. It exemplifies how an initial Lorentz force imbalance can successfully trigger a flux rope formation that later escapes the simulation domain. It also enables comparison with real observations through the addition of a stratified atmosphere spanning from the photosphere to the corona.

Figures (14)

• Figure 1: Active region NOAA 12241. a) Full-disk image in 171 Å observed by SDO/AIA on December 18, 2014 at 21:24 UT. The blue rectangle indicates the active region under study. b) Zoom-in of the active region in 171 Å. c) Line-of-sight (LOS) magnetogram taken by SDO/HMI. The red rectangle indicates the horizontal domain for the numerical simulation.
• Figure 2: Initialization and evolution of the eruption at glance. In all the panels, a magnetogram, with white to black levels, is present in the background to make the link with observations in Fig. \ref{['fig:obs']}. The colour map is saturated, between -400 and 400 G for visualization purposes. a) Initial magnetic configuration and Lorentz force at $t=0$ s. The pink lines represent the magnetic arcade which later on is transformed in the erupting flux rope. The green to yellow colour map indicate a volumetric representation of the magnitude of the Lorentz force, being yellow (green) more (less) intense. b) A zoom-in at $t=0.23$ s within the region defined by the grey rectangle of panel a). The horizontal components of the Lorentz force are shown with arrows in blue (negative) and red (positive) drawn at height $z=2.2$ Mm. Temperature iso-surfaces of $2 \times 10^6$ K (red) to $4 \times 10^6$ (yellow) are also displayed. c) Rising phase is depicted for $t=6.87$ min, $t=9.92$ min and $12.59$ min. The coloured lines represent the magnetic field lines corresponding to the flux rope. The colour of the field lines represents the vertical speed $v_z$ in pink. The two lines on the $xy$-plane indicate the cuts where the tracking (T line in light turquoise) of the flux rope and the compression (C line in dark turquoise) analysis are performed, respectively.
• Figure 3: Thermodynamical variables in the rising phase. a) Density and b) temperature at $x=5$ Mm (corresponding to line T in Fig. \ref{['fig:3D']} c)) for $t=12.59$ min. Yellow denotes higher density and temperature and blue lower values. White solid lines represent the streamlines of the projected magnetic field vector on the plane. A movie showing the temperature in this cutting plane together with 3D visualization of the flux rope field lines is available in the online version.
• Figure 4: Kinematic properties of the flux rope apex. Vertical coordinate of the flux rope apex at $x=5$ Mm (blue dots) and quadratic fit (solid orange line). Values of the vertical velocity are added to different times. Before $t=4$ min the flux rope is not sufficiently well formed to infer the apex height.
• Figure 5: Evolution of energies averaged in the entire computational domain. Total energy is in solid black line, total magnetic energy in solid blue line, free magnetic energy in dashed blue, kinetic and internal in orange and green solid lines, respectively. Vertical dotted lines indicate different stages.