Models for Short-Term Forecast of Maximum X-Ray Class of Solar Flares Based on Magnetic Energy of Active Regions

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Abstract

The accuracy of the M. Aschwanden’s (2020) model for short-term (24 h) prediction of the maximum X-ray class of solar flares based on the power-law dependence on the energy of potential magnetic field of active regions is checked and assessed. For this purpose, a sample of 275 flares (253 M-class and 22 X-class) in isolated active regions on the solar disk in 2010−2023 is analyzed. Magnetic field extrapolations are made in the nonlinear force-free and potential approximations using the GX Simulator based on photospheric vector magnetograms from the Helioseismic Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). It is found that in 6% of cases Aschwanden’s model underestimates the predicted maximum flare class relative to the observed one (maximal underestimation by 4.4 times). The accuracy of this model (the average ratio of the observed to predicted maximum flare class) is 0.31 ± 0.47. Four other statistical models are proposed, two of which, like Aschwanden’s model, are based on the power-law dependence of the maximum flare class on the energy of potential magnetic field, and the other two are based on the power-law dependence on the free magnetic energy of active regions. These models give fewer (or no) underestimations of the maximum flare class, but two to three times lower forecast accuracy, ranging from 0.11 to 0.17. Additionally, based on the obtained statistical sample, estimates of the limiting X-ray class of solar flares are made. The five models give different limits ranging from ~X14 to ~X250. The realism of these values and the possibility of refining the models by expanding the sample of events is briefly discussed.

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About the authors

I. V. Zimovets

Space Research Institute of the Russian Academy of Sciences

Author for correspondence.
Email: ivanzim@cosmos.ru
Russian Federation, Moscow

I. N. Sharykin

Space Research Institute of the Russian Academy of Sciences

Email: ivan.sharykin@phystech.edu
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Dependence of the observed daily maximum X-ray class of a solar flare on the potential magnetic field energy in the parent active region and short-term flare prediction models: A (dashed line), Z1 (dotted line), Z2 (dashed line). Small black asterisks are flares in 2010-2017 (cycle 24) and gray asterisks are flares in 2021-2023 (cycle 25). NOAA active area number and McIntosh class are indicated. Marginal flare class estimates are shown with a large triangle, diamond, and cross as the intersection of models A, Z1, Z2, respectively, with a vertical dashed line on the right.

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3. Fig. 2. Dependence of the ratio of the observed to predicted maximum solar flare class on the observed maximum class for models A (asterisks), Z1 (rhombuses), and Z2 (triangles). The mean values of the ratios (plus and minus standard deviations) for models A, Z1, and Z2 are shown by horizontal dashed, dashed, and dashed lines, respectively.

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4. Fig. 3. Dependence of the observed daily maximum X-ray class of a solar flare on the free magnetic energy in the parent active region and short-term flare prediction models: Z3 (dashed line), Z4 (dashed line). Black small stars are flares in 2010-2017 (cycle 24), gray small stars are flares in 2021-2023 (cycle 25). NOAA active area number and McIntosh class are indicated. Marginal flare class estimates are shown in large rhombuses as the intersection of models Z3, Z4 with a vertical dashed line on the right.

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5. Fig. 4. Dependence of the ratio of the observed to predicted maximum solar flare class on the observed maximum class for models A (asterisks), Z3 (rhombuses), and Z4 (triangles). The mean values of the ratios (plus and minus standard deviations) for models A, Z3, and Z4 are shown by horizontal dashed, dashed, and dashed lines, respectively.

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6. Fig. 5. Dependences of the magnetic energy of the nonlinear force-free field on the potential magnetic field energy (a), the free magnetic energy on the potential field energy (b), and on the nonlinear force-free field energy (c) in the active regions for the considered sample of flares. The dashed straight line is the y = x line. The small squares in (a) are cases with negative magnetic free energy (about 8.7%). On (d) and (e) are the dependences of the ratio of the free magnetic energy to the potential and nonlinear force-free field energy, respectively.

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7. Fig. 6. Dependences of the observed daily maximum class of the solar flare in the active region on its characteristics: (a) - the number of sunspots, (b) - the area of sunspots, (c) - the angular longitude size of a group of sunspots, (d) - the unsigned flux of the vertical component of the magnetic field vector on the photosphere, (e) - the unsigned “flux” of the horizontal field on the photosphere, (e) - unsigned vertical current on the photosphere, (f) - energy of the nonlinear force-free magnetic field, (g, h) - ratios of the free magnetic energy to the energy of the potential and nonlinear force-free magnetic field, respectively.

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