Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation

Abstract: We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ~2.6e32 erg, about 50% of which is stored below 6 Mm. It decreases by ~0.3e32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field "implosion", and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more "compact" after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic.

• The paper presents rapid magnetic flux emergence in AR 11158 that causes significant free energy buildup and electric current injection.
• It employs high-resolution SDO/HMI vector magnetograms with NLFFF extrapolation to model coronal magnetic fields and quantify energy metrics.
• The findings document a 28% increase in the photospheric horizontal field and a swift release of free magnetic energy during an X-class flare, supporting tether-cutting reconnection.

Evolution of Magnetic Field and Energy in a Major Eruptive Active Region Based on SDO/HMI Observation

The study conducted by Sun et al. presents a detailed analysis of the evolution of the magnetic field and its associated energy in NOAA Active Region 11158 using comprehensive and continuous observations from the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO). Over a span of five days, complex magnetic activities, particularly during major solar eruptions, are scrutinized to enhance our understanding of the dynamic processes in solar active regions (ARs). This essay delineates the significant findings, numerical results, and theoretical implications presented in this research.

Overview and Methodology

NOAA AR 11158 serves as a prime testbed due to its high activity and occurrence of the first X-class flare of Solar Cycle 24. The research utilizes vector magnetograms from HMI with high spatial (360 km) and temporal (12 minutes) resolution. A non-linear force-free field (NLFFF) extrapolation is applied to these magnetograms to model the coronal magnetic field structure and calculate the free magnetic energy.

Key Findings

Magnetic Field Evolution

1. Fast Flux Emergence: Initially, AR 11158 exhibited rapid magnetic flux emergence, leading to a significant injection of electric currents. The shearing motions between oppositely polarized sunspots formed a quadrupolar sunspot configuration. A substantial filament developed along the polarity inversion line (PIL), characterized by a sheared kilogauss magnetic field.
2. Field and Current Distribution: The study reveals that a large portion (50%) of the magnetic free energy is concentrated below 6 Mm, indicative of a low-lying, non-potential field configuration. The distribution of vertical current density aligns with regions of strong horizontal fields, especially along the filament channel.

Magnetic Energy Evolution

1. Energy Build-Up and Release: The computed magnetic free energy in the AR reached a maximum of approximately $2.6 \times 10^{32}$ ergs. Significant energy release (around $0.3 \times 10^{32}$ ergs) occurred within one hour of the X-class flare, although this figure likely underestimates the total energy loss due to limitations in the model's force-free assumptions.
2. Photospheric and Coronal Field Changes: The photospheric horizontal magnetic field exhibited a 28% increase in strength during the flare, becoming more aligned with the PIL. This is consistent with the hypothesized coronal magnetic "implosion," where a reduction in coronal magnetic energy led to the contraction of coronal loops.

Implications and Future Directions

The findings underscore the critical role of magnetic reconfiguration in driving solar flares and coronal mass ejections (CMEs). The observed changes in the photospheric magnetic field and supporting coronal observations suggest that tether-cutting reconnection is a pivotal mechanism in explosive solar events. This study provides a nuanced view of the energy storage and release processes within ARs, offering predictive insights into solar flare activities.

Theoretically, this research advances our understanding of the "storage-release" model of solar eruptions, emphasizing the necessity of high-cadence, vector magnetic field data for capturing the rapid dynamics of ARs. In future analysis, implementing full-sphere NLFFF modeling and incorporating chromospheric observations may address some of the current model limitations and improve energy estimation accuracy. Additionally, continuous monitoring and statistical analysis across multiple ARs can generalize these findings, enhancing space weather predictive capabilities.

In conclusion, the paper by Sun et al. significantly contributes to the solar physics community by elucidating the intricate relationship between evolving magnetic fields and solar eruptive phenomena, paving the way for more refined models and improved understanding of solar magnetic activity.