Global Energetics of Solar Flares. I. Magnetic Energies

Abstract

We present the first part of a project on the global energetics of solar flares and coronal mass ejections (CMEs) that includes about 400 M-and X-class flares observed with AIA and HMI onboard SDO. We calculate the potential (E p ), the nonpotential (E np ) or free energies (E f ree = E np − E p ), and the flare-dissipated magnetic energies (E diss ). We calculate these magnetic parameters using two different NLFFF codes: The COR-NLFFF code uses the line-of-sight magnetic field component B z from HMI to define the potential field, and the 2D coordinates of automatically detected coronal loops in 6 coronal wavelengths from AIA to measure the helical twist of coronal loops caused by vertical currents, while the PHOT-NLFFF code extrapolates the photospheric 3D vector fields. We find agreement between the two codes in the measurement of free energies and dissipated energies within a factor of < ∼ 3. The size distributions of magnetic parameters exhibit powerlaw slopes that are approximately consistent with the fractaldiffusive self-organized criticality model. The magnetic parameters exhibit scaling laws for the nonpotential energy, E np ∝ E 1.02 p , for the free energy, E f ree ∝ E 1.7p and E f ree ∝ B 1.0 ϕ L 1.5 , for the dissipated energy, E diss ∝ E 1.6 p and E diss ∝ E 0.9 f ree , and the energy dissipation volume, V ∝ E 1.2 diss . The potential energies vary in the range of E p = 1 × 10 31 − 4 × 10 33 erg, while the free energy has a ratio of E f ree /E p ≈ 1% − 25%. The Poynting flux amounts to F f lare ≈ 5 × 10 8 − 10 10 erg cm −2 s −1 during flares, which averages to F AR ≈ 6 × 10 6 erg cm −2 s −1 during the entire observation period and is comparable with the coronal heating rate requirement in active regions.Subject headings: Sun: Flares -Magnetic fields -Sun: UV radiation 1.Thus we expect that the corrected free energy is about a factor of q iso = (π/2) 2 ≈ 2.5 higher than the best-fit values of the vertical-current free energies E f ree ⊥ . 3.OBSERVATIONS AND RESULTS AIA and HMI ObservationsThe dataset we are analyzing for this project on the global energetics of flares includes all M-and X-class flares observed with the Solar Dynamics Observatory (SDO) (Pesnell et al. 2011) during the first 3.5 years of the mission (2010 June 1 to 2014 Jan 31), which amounts to 399 flare events. The catalog of these flare events is available online, see http://www.lmsal.com/∼aschwand/RHESSI/flare energetics.html. Magnetic energies are determined for events that have a heliographic longitude of < ∼ 45 • (177 events), of which 5 events contained incomplete or corrupted AIA data, so that we are left with 172 events suitable for magnetic data analysis. Using the COR-NLFFF code we calculate the evolution of free (magnetic) energies for all of these 172 events, while a subset of 57 events is subjected to the (computationally more expensive) PHOT-NLFFF code also. The analyzed SDO data set includes EUV images observed with the Atmospheric Imaging Assembly (AIA) (Lemen et al. 2012; Boerner et al. 2012), as well as magnetograms ...

Self-organized Criticality in Solar and Stellar Flares: Are Extreme Events Scale-free?

“…The original discoverers of self-organized criticality (SOC) models noted power law-like size distributions with power law slopes of α x ≈ 2 of the sizes x of SOC avalanches, as well as power law slopes of α T ≈ 2 for the durations T of SOC avalanches, obtained in cellular automaton simulations (e.g., Pruessner 2012). A more physical approach of modeling and predicting power law slopes of size distributions observed from astrophysical SOC systems has been put forward in terms of the so-called Fractal-Diffusive (FD-SOC) model (Aschwanden 2013(Aschwanden , 2014. We juxtapose theoretical predictions of this model and mean observational values in Table 2.…”

Global Energetics of Solar Flares. IX. Refined Magnetic Modeling

“…Previously we developed the original vertical-current approximation nonlinear force-free field code (VCA-NLFFF) code that has been described and continuously improved over a decade (Aschwanden and Sandman 2010;Sandman and Aschwanden 2011;Aschwanden et al 2012Aschwanden et al , 2014aAschwanden et al , 2016aAschwanden 2013aAschwanden , 2013bAschwanden , 2013cAschwanden , 2015Aschwanden , 2016bAschwanden , 2019Aschwanden and Malanushenko 2013;Warren et al 2018). In the following we mention the most significant changes in the data analysis method of the new VCA3-NLFFF code only.…”

“…One of the most important tasks in our study is the energy partition and energy closure in flares. Quantitative information on different forms of energies and their partition in flares and CMEs became more available lately (Emslie et al 2012;Mann 2016a, 2016b;Aschwanden et al 2014aAschwanden et al , 2015aAschwanden et al , 2016a2017;Aschwanden 2016aAschwanden , 2017Aschwanden and Gopalswamy 2019). Virtually no statistical study on flare energies existed 5 years ago (Aschwanden 2004(Aschwanden , 2019a.…”

Global Energetics of Solar Flares. V. Energy Closure in Flares and Coronal Mass Ejections

“…Energy closure is studied in many dynamical processes, such as in meteorology and atmospheric physics (e.g., the turbulent kinetic and potential energies, TKE and TPE, make up the turbulent total energy, TTE=TKE + TPE; Zilitinkevich et al 2007), in magnetospheric and ionospheric physics (e.g., where the solar wind transfers energy into the magnetosphere in the form of electric currents; Atkinson 1978), or in astrophysics (e.g., in the energetics of Xray afterglows from Swift gamma-ray bursts; Racusin et al 2009). The most famous example is probably the missing mass needed to close our universe (e.g., White et al 1993).…”