It is well-known that magnetic fields dominate the dynamics in the solar corona, and new generation of numerical modeling of the evolution of coronal magnetic fields, as featured with boundary conditions driven directly by observation data, are being developed. This paper describes a new approach of data-driven magnetohydrodynamic (MHD) simulation of solar active region (AR) magnetic field evolution, which is for the first time that a data-driven full-MHD model utilizes directly the photospheric velocity field from DAVE4VM. We constructed a well-established MHD equilibrium based on a single vector magnetogram by employing an MHD-relaxation approach with sufficiently small kinetic viscosity, and used this MHD equilibrium as the initial conditions for subsequent data-driven evolution. Then we derived the photospheric surface flows from a time series of observed magentograms based on the DAVE4VM method. The surface flows are finally inputted in time sequence to the bottom boundary of the MHD model to self-consistently update the magnetic field at every time step by solving directly the magnetic induction equation at the bottom boundary. We applied this data-driven model to study the magnetic field evolution of AR 12158 with SDO/HMI vector magnetograms. Our model reproduced a quasi-static stress of the field lines through mainly the rotational flow of the AR's leading sunspot, which makes the core field lines to form a coherent S shape consistent with the sigmoid structure as seen in the SDO/AIA images. The total magnetic energy obtained in the simulation matches closely the accumulated magnetic energy as calculated directly from the original vector magnetogram with the DAVE4VM derived flow field. Such a data-driven model will be used to study how the coronal field, as driven by the slow photospheric motions, reaches a unstable state and runs into eruptions.
Magnetic flux ropes (MFRs) constitute the core structure of coronal mass ejections (CMEs), but hot debates remain on whether the MFR forms before or during solar eruptions. Furthermore, how flare reconnection shapes the erupting MFR is still elusive in three dimensions. Here we studied a new MHD simulation of CME initiation by tether-cutting magnetic reconnection in a single magnetic arcade. The simulation follows the whole life, including the birth and subsequent evolution, of an MFR during eruption. In the early phase, the MFR is partially separated from its ambient field by a magnetic quasi-separatrix layer (QSL) that has a double-J shaped footprint on the bottom surface. With the ongoing of the reconnection, the arms of the two J-shaped footprints continually separate from each other, and the hooks of the J shaped footprints expand and eventually become closed almost at the eruption peak time, and thereafter the MFR is fully separated from the un-reconnected field by the QSL. We further studied the evolution of the toroidal flux in the MFR and compared it with that of the reconnected flux. Our simulation reproduced an evolution pattern of increase-to-decrease of the toroidal flux, which is reported recently in observations of variations in flare ribbons and transient coronal dimming. The increase of toroidal flux is owing to the flare reconnection in the early phase that transforms the sheared arcade to twisted field lines, while its decrease is a result of reconnection between field lines in the interior of the MFR in the later phase.
Solar eruptions are an explosive release of coronal magnetic field energy manifested as solar flares and coronal mass ejections. Observations have shown that the core of eruption-productive regions are often a sheared magnetic arcade, namely, a single bipolar configuration, and, in particular, the corresponding magnetic polarities at the photosphere are elongated along a strong-gradient polarity inversion line (PIL). It remains unclear what mechanism triggers the eruption in a single bipolar field and why the one with a strong PIL is favorable for producing eruption. Recently, using highly accurate simulations, we established the fundamental mechanism behind solar eruption initiation by which a bipolar field driven by quasi-static shearing motion at the photosphere can form an internal current sheet, followed by fast magnetic reconnection that triggers and drives the eruption. Here, we investigate the behavior of the fundamental mechanism with different photospheric magnetic flux distributions, namely, magnetograms, by combining a theoretical analysis and a numerical simulation. Our study shows that the bipolar fields of different magnetograms, sheared continuously, all exhibit similar evolutions – from slow storage to the fast release of magnetic energy – that are in accordance with the fundamental mechanism and demonstrate the robustness of the proposed mechanism. Furthermore we found that the magnetograms with a stronger PIL produce larger eruptions and the key reason is that the sheared bipolar fields with a stronger PIL can achieve more non-potentiality and their internal current sheet can form at a lower height and with a higher current density, by which the reconnection can be more efficient. This also provides a viable trigger mechanism for the observed eruptions in active regions with a strong PIL.
The Sun often produces coronal mass ejections with similar structure repeatedly from the same source region, and how these homologous eruptions are initiated remains an open question. Here, by using a new magnetohydrodynamic simulation, we show that homologous solar eruptions can be efficiently produced by recurring formation and disruption of a coronal current sheet as driven by the continuous shearing of the same polarity inversion line within a single bipolar configuration. These eruptions are initiated by the same mechanism, in which an internal current sheet forms slowly in a gradually sheared bipolar field and reconnection of the current sheet triggers and drives the eruption. Each of the eruptions does not release all of the free energy, leaving a large amount in the post-flare arcade below the erupting flux rope. Thus, a new current sheet can be more easily formed by further shearing of the post-flare arcade than by shearing a potential field arcade, and this is favorable for producing the next eruption. Furthermore, it is found that the new eruption is stronger since the newly formed current sheet has a larger current density and a lower height. In addition, our results also indicate the existence of a magnetic energy threshold for a given flux distribution, and eruption occurs once this threshold is approached.
The relationship between solar eruption and sunspot rotation has been widely reported, and the underlying mechanism needs to be studied. Here we performed a full 3D MHD simulation using a data-constrained approach to study the mechanism of flare eruptions in active region (AR) NOAA 10930, which is characterized by continuous sunspot rotation and homologous eruptions. We reconstructed the potential magnetic field from the magnetogram of Hinode/SOT as the initial condition and drove the MHD system by applying continuous sunspot rotation at the bottom boundary. The key magnetic structure before the major eruptions and the preformed current sheet were derived, which is responsible for the complex MHD evolution with multiple stages. The major eruptions were triggered directly by fast reconnection in the preformed current sheet above the main polarity inversion line between the two major magnetic polarities of the AR. Furthermore, our simulation shows the homologous eruption successfully. It has reasonable consistency with observations in relative strength, energy release, X-ray and Hα features, and time interval of eruptions. In addition, the rotation angle of the sunspot before the first eruption in the simulation is also close to the observed value. Our simulation offers a scenario different from many previous studies based on ideal instabilities of a twisted magnetic flux rope and shows the importance of sunspot rotation and magnetic reconnection in efficiently producing homologous eruptions by continuous energy injection and impulsive energy release in a recurrent way.
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