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Context. For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional (3D) models of the solar atmosphere, e. g., in coronal fields reconstructions or numerical simulations.
Aims. The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration.
Methods. We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used.
Results. The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component of the field. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence.
Conclusions. We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources. We also compare the efficiency of two divergence-cleaning techniques. These results are applicable to a broad range of numerical realizations of magnetic fields.
Coronal mass ejections (CMEs) erupt and expand in a magnetically structured solar corona. Various indirect observational pieces of evidence have shown that the magnetic field of CMEs reconnects with surrounding magnetic fields, forming, e.g., dimming regions distant from the CME source regions. Analyzing Solar Dynamics Observatory (SDO) observations of the eruption from AR 11226 on 2011 June 7, we present the first direct evidence of coronal magnetic reconnection between the fields of two adjacent active regions during a CME. The observations are presented jointly with a data-constrained numerical simulation, demonstrating the formation/intensification of current sheets along a hyperbolic flux tube at the interface between the CME and the neighboring AR 11227. Reconnection resulted in the formation of new magnetic connections between the erupting magnetic structure from AR 11226 and the neighboring active region AR 11227 about 200 Mm from the eruption site. The onset of reconnection first becomes apparent in the SDO/AIA images when filament plasma, originally contained within the erupting flux rope, is redirected toward remote areas in AR 11227, tracing the change of large-scale magnetic connectivity. The location of the coronal reconnection region becomes bright and directly observable at SDO/AIA wavelengths, owing to the presence of down-flowing cool, dense (1010 cm(-3)) filament plasma in its vicinity. The high-density plasma around the reconnection region is heated to coronal temperatures, presumably by slow-mode shocks and Coulomb collisions. These results provide the first direct observational evidence that CMEs reconnect with surrounding magnetic structures, leading to a large-scale reconfiguration of the coronal magnetic field.
The X8.2 event of 2017 September 10 provides unique observations to study the genesis, magnetic morphology, and impulsive dynamics of a very fast coronal mass ejection (CME). Combining GOES-16/SUVI and SDO/AIA EUV imagery, we identify a hot (T approximate to 10-15 MK) bright rim around a quickly expanding cavity, embedded inside a much larger CME shell (T approximate to 1-2 MK). The CME shell develops from a dense set of large AR loops ( greater than or similar to 0.5R(s)) and seamlessly evolves into the CME front observed in LASCO C2. The strong lateral overexpansion of the CME shell acts as a piston initiating the fast EUV wave. The hot cavity rim is demonstrated to be a manifestation of the dominantly poloidal flux and frozen-in plasma added to the rising flux rope by magnetic reconnection in the current sheet beneath. The same structure is later observed as the core of the white-light CME, challenging the traditional interpretation of the CME three-part morphology. The large amount of added magnetic flux suggested by these observations explains the extreme accelerations of the radial and lateral expansion of the CME shell and cavity, all reaching values of 5-10 km s(-2). The acceleration peaks occur simultaneously with the first RHESSI 100-300 keV hard X-ray burst of the associated flare, further underlining the importance of the reconnection process for the impulsive CME evolution. Finally, the much higher radial propagation speed of the flux rope in relation to the CME shell causes a distinct deformation of the white-light CME front and shock.