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 Helioseismic and Magnetic Imager (HMI) onboard the 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 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 × 10 20 Mx, 2.0 × 10 20 Mx, and 21.0 × 10 20 Mx, respectively, resulting in free energy drops of 3.89 × 10 30 ergs, 2.62 × 10 30 ergs, and 1.68 × 10 32 ergs.

Quiescent Reconnection Rate Between Emerging Active Regions and Preexisting Field, with Associated Heating: NOAA AR 11112

“…Direct comparison of reconnection rates and total flux transfers between these cases is thus problematic. Tarr, Longcope, and Millhouse (2013) used the conceptually unrelated free energy minimization scheme to estimate flux transferred during the M6.6, M2.2 and X2.2 flares of February 2011 in AR11158. They found the flux involved in each flare to be 4.2 × 10 20 Mx, 2.0 × 10 20 Mx, and 21.0 × 10 20 Mx, respectively, 1--2 orders of magnitude less than that for the Bastille Day and Halloween flares.…”

“…We repeat the flux-tracking analysis of Tarr and Longcope (2012). That analysis used the 45-second cadence line-of-sight (LOS) magnetograms from HMI available at the time.…”

“…We therefore use a simplified mask array, and correspondingly different region labels. With our slightly different analysis goal in the present work, we use slightly different algorithm parameters compared to Tarr and Longcope (2012). For this study, we use a lower threshold of 50 G average field strength over each pixel, and create a smoother mask structure using a potential field extrapolation from the lower (photospheric) boundary to a height h = 3.0 Mm.…”

“…We are therefore very confident that the mask region N2 contains only flux that predates emergence, and that any coronal loops we observe connecting N2 to the emerging positive flux P1 are due solely to reconnection between the two flux domains. The topology of the region is described in detail in Tarr and Longcope (2012). Those authors use a Magnetic Charge Topology (MCT) to describe the field at each time, together with a MCC constraint to model time evolution.…”

“…We focus on the slow, quiescent response prior to a GOES M2.9 class flare on 16 October 2010 19:00UT. Interested readers may refer to Tarr and Longcope (2012) for an analysis of magnetic field topology and energetics pertaining to the flare itself.…”