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Estimating the Maximum Intensities of Soft X-Ray Flares Using Extreme Value Theory

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Abstract

Solar flares are one of the most energetic events in the solar system, their impact on Earth at ground level and its atmosphere remains under study. The repercussions of this phenomenon in our technological infrastructure includes radio blackouts and errors in geopositional and navigation systems that are considered natural hazards in ever more countries. Occurrence frequency and intensity of the most energetic solar flares are being taken into account in national programs for civil protection in order to reduce the risk and increase the resilience from space weather events. In this work we use the statistical theory of extreme values as well as other statistical methods in order to assess the magnitudes of the most extreme solar-flare events expected to occur in a given period of time. We found that the data set under study presents a dual tail behavior. Our results show that on average we can expect one solar flare greater than X23 each 25 years, that is to say, one such event each two solar cycles.

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Notes

  1. The data can be found in https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/ .

  2. See DiCiccio and Efron (1996) and Diaconis and Efron (1983) for a description of the bootstrap method.

  3. In terms of Figure 4, the set \(S_{59}\) would be a combination of data points on the left and on the right of the dashed vertical line in the figure.

  4. For the generation of these synthetic samples, we used both, \(G_{1}\) and \(G_{2}\) as the parent distribution.

  5. www.swpc.noaa.gov/noaa-scales-explanation .

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Acknowledgements

The authors thank projects for Catedras Conacyt (Conacyt Fellow), Repositorios Institucionales (268273) and Ciencia Basica (254497).

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Authors and Affiliations

  1. Conacyt – SCiESMEX – LANCE, Instituto de Geofísica, Unidad Michoacán, Universidad Nacional Autónoma de México, Morelia, Michoacán, 58190, Mexico

    V. De la Luz

  2. Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Apartado Postal 61-3 (Xangari), Morelia, Michoacán, Mexico

    E. P. Balanzario & T. Tsiftsi

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  1. V. De la Luz
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Correspondence to V. De la Luz.

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De la Luz, V., Balanzario, E.P. & Tsiftsi, T. Estimating the Maximum Intensities of Soft X-Ray Flares Using Extreme Value Theory. Sol Phys 293, 119 (2018). https://doi.org/10.1007/s11207-018-1342-1

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