Global Energetics of Solar Flares. XII. Energy Scaling Laws

Abstract

In this study we test 30 variants of 5 physical scaling laws that describe different aspects of solar flares. We express scaling laws in terms of the magnetic potential field energy $E_p$, the mean potential field strength $B_p$, the free energy $E_{free}$, the dissipated magnetic flare energy $E_{diss}$, the mean loop length scale $L$, the mean helically twisted flux tube radius $R$, the sunspot radius $r$, the emission measure-weighted flare temperature $T_w$, the electron density $n_e$, and the total emission measure $EM$, measured from a data set of $\lapprox 400$ GOES M- and X-class flare events. The 5 categories of physical scaling laws include (i) a scaling law of the potential-field energy, (ii) a scaling law for helical twisting, (iii) a scaling law for Petschek-type magnetic reconnection, (iv) the Rosner-Tucker-Vaiana scaling law, and (v) the Shibata-Yokoyama scaling law. We test the self-consistency of these theoretical scaling laws with observed parameters by requiring two conditions: a cross-corrleation coefficient of CCC$>$0.5 between the observed and theoretically predicted scaling laws, and a linear regression fit with a slope of $\alpha \approx 1$. With these two criteria we find that 10 out of the 30 tested scaling law variants are consistent with the observed data, which strongly corroborates the existence and validity of the tested flare scaling laws.

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References in corpus (17)

• Preprocessing of vector magnetograph data for a non-linear force-free magnetic field reconstruction
• A HR-like Diagram for Solar/Stellar Flares and Corona -- Emission Measure vs Temperature Diagram
• Scaling laws of solar and stellar flares
• Global Energetics of Solar Flares: II. Thermal Energies
• Global Energetics of Solar Flares: I. Magnetic Energies
• Reconnection of a kinking flux rope triggering the ejection of a microwave and hard X-ray source. II. Numerical Modeling
• Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part III: Twist Number Method
• Benchmark Test of Differential Emission Measure Codes and Multi-Thermal Energies in Solar Active Regions
• A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory
• Bootstrapping the Coronal Magnetic Field with STEREO: I. Unipolar Potential Field Modeling
• Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: II. Hydrodynamic Scaling Laws and Thermal Energies
• Validation of a Scaling Law for the Coronal Magnetic Field Strengths and Loop Lengths of Solar and Stellar Flares
• Scaling laws of quasi-periodic pulsations in solar flares
• Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops
• Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: I. Universal Scaling Laws of Space and Time Parameters
• Global Energetics of Solar Flares. IX. Refined Magnetic Modeling
• Global Energetics of Solar Flares: X. Petschek Reconnection Rate and Alfven Mach Number of Magnetic Reconnection Outflows

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