Calculating Separate Magnetic Free Energy Estimates for Active Regions Producing Multiple Flares: NOAA AR11158

Abstract

It is well known that photospheric flux emergence is an important process for stressing coronal fields and storing magnetic free energy, which may then be released during a flare. The \emph{Helioseismic and Magnetic Imager} (HMI) onboard the \emph{Solar Dynamics Observatory} (SDO) captured the entire emergence of NOAA AR 11158. This region emerged as two distinct bipoles, possibly connected underneath the photosphere, yet characterized by different photospheric field evolutions and fluxes. The combined active region complex produced 15 GOES C--class, 2 M--class, and the X2.2 Valentine's Day Flare during the four days after initial emergence on February 12th, 2011. The M and X class flares are of particular interest because they are nonhomologous, involving different subregions of the active region. We use a Magnetic Charge Topology together with the Minimum Current Corona model of the coronal field to model field evolution of the complex. Combining this with observations of flare ribbons in the 1600Å channel of the \emph{Atmospheric Imaging Assembly} (AIA) onboard SDO, we propose a minimization algorithm for estimating the amount of reconnected flux and resulting drop in magnetic free energy during a flare. For the M6.6, M2.2, and X2.2 flares, we find a flux exchange of $4.2\times 10^{20}\unit{Mx},\ 2.0 \times 10^{20}\unit{Mx}, \hbox{and} 21.0 \times 10^{20}\unit{Mx}$, respectively, resulting in free energy drops of $3.89\times 10^{30}\unit{ergs}, 2.62\times 10^{30}\unit{ergs}, \hbox{and} 1.68\times 10^{32}\unit{ergs}$.

24 pages, 9 figures, submitted to ApJ, movies available at http://solar.physics.montana.edu/tarrl/ar11158.html

References in corpus (6)

• Impulsive phase flare energy transport by large-scale Alfven waves and the electron acceleration problem
• Modeling the Dispersal of an Active Region: Quantifying Energy Input into the Corona
• Free Magnetic Energy in Solar Active Regions above the Minimum-Energy Relaxed State
• A self-consistent nonlinear force-free solution for a solar active region magnetic field
• Gas-dynamic shock heating of post-flare loops due to retraction following localized, impulsive reconnection
• Charge-exchange limits on low-energy alpha-particle fluxes in solar flares

Cited by in corpus (10)

• The Origin of Major Solar Activity - Collisional Shearing Between Nonconjugated Polarities of Multiple Bipoles Emerging Within Active Regions
• Using Coronal Loops to Reconstruct the Magnetic Field of an Active Region Before and After a Major Flare
• Photospheric Electric Fields and Energy Fluxes in the Eruptive Active Region NOAA 11158
• The Magnetic Field of Active Region 11158 During the 2011 February 12-17 Flares : Differences between Photospheric Extrapolation and Coronal Forward-Fitting Methods
• The Vertical Current Approximation Nonlinear Force-Free Field Code - Description, Performance Tests, and Measurements of Magnetic Energies Dissipated in Solar Flares
• Quiescent Reconnection Rate Between Emerging Active Regions and Preexisting Field, with Associated Heating: NOAA AR11112
• Leveraging the Mathematics of Shape for Solar Magnetic Eruption Prediction
• Electric current evolution at the footpoints of solar eruptions
• Relationship between Successive Flares in the Same Active Region and Space-Weather HMI Active Region Patch (SHARP) Parameters
• Photospheric Magnetic Free Energy Density of Solar Active Regions