Abstract
Solar flares are the most powerful events in the solar atmosphere, releasing a huge amount of energy in a few minutes. Any progress in predicting when a flare of a big magnitude will occur is extremely important to evaluate the risk related to space weather. The Lu and Hamilton (Astrophys. J. Lett. 380, L89, 1991) self-organized criticality (SOC) model for solar flares is the one most conspicuous amongst the several avalanche models for flares that have been developed in the last 30 years. It has been very successful in reproducing some of the characteristic features of observed flares (e.g. probability density function of flare energy) and in the last years has been explored as a way of predicting extreme flaring events.
In this work, we study the predicting capabilities of Lu and Hamilton model by assessing the proximity to stability of the 2D lattice and studying the influence of the lattice structure in the generation of large avalanches. We find that the mean value of the lattice nodes bears enough information to predict large avalanches in more than half of the cases, making it a reliable precursor for forecasting purposes.
Similar content being viewed by others
References
Aschwanden, M.: 2011, Self-Organized Criticality in Astrophysics, Springer Praxis Books, Springer, Berlin. http://libproxy.bus.umich.edu/login?url=https://link.springer.com/openurl?genre=book&isbn=978-3-642-15000-5.
Aschwanden, M.J.: 2019, Self-organized criticality in solar and stellar flares: Are extreme events scale-free? Astrophys. J. 880(2), 105. DOI. ADS.
Aschwanden, M.J., Parnell, C.E.: 2002, Nanoflare statistics from first principles: Fractal geometry and temperature synthesis. Astrophys. J. 572(2), 1048. DOI.
Bak, P., Tang, C., Wiesenfeld, K.: 1987, Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett. 59(4), 381. DOI. ADS.
Barnes, G., Leka, K.D., Schrijver, C.J., Colak, T., Qahwaji, R., Ashamari, O.W., Yuan, Y., Zhang, J., McAteer, R.T.J., Bloomfield, D.S., Higgins, P.A., Gallagher, P.T., Falconer, D.A., Georgoulis, M.K., Wheatland, M.S., Balch, C., Dunn, T., Wagner, E.L.: 2016, A comparison of flare forecasting methods. I. Results from the “all-clear” workshop. Astrophys. J. 829(2), 89. DOI. ADS.
Bélanger, E., Vincent, A., Charbonneau, P.: 2007, Predicting solar flares by data assimilation in avalanche models. I. Model design and validation. Solar Phys. 245(1), 141. DOI. ADS.
Bennet, A., Kaye, R.: 1792, A new suspension of the magnetic needle, intended for the discovery of minute quantities of magnetic attraction: Also an air vane of great sensibility; with new experiments on the magnetism of iron filings and brass. Phil. Trans. Roy. Soc. London 82, 81. ADS.
Brueckner, G.E., Delaboudiniere, J.-P., Howard, R.A., Paswaters, S.E., St. Cyr, O.C., Schwenn, R., Lamy, P., Simnett, G.M., Thompson, B., Wang, D.: 1998, Geomagnetic storms caused by coronal mass ejections (CMEs): March 1996 through June 1997. Geophys. Res. Lett. 25(15), 3019. DOI. ADS.
Charbonneau, P., McIntosh, S.W., Liu, H.-L., Bogdan, T.J.: 2001, Avalanche models for solar flares (Invited Review). Solar Phys. 203, 321. DOI.
Cliver, E.W.: 1994, Solar activity and geomagnetic storms: The first 40 years. Eos Trans. 75(49), 569. DOI. ADS.
Dennis, B.R.: 1985, Solar hard X-ray bursts. Solar Phys. 100, 465. DOI. ADS.
Dmitruk, P., Gómez, D.O.: 1997, Turbulent coronal heating and the distribution of nanoflares. Astrophys. J. 484(1), L83. DOI.
Fletcher, L., Dennis, B.R., Hudson, H.S., Krucker, S., Phillips, K., Veronig, A., Battaglia, M., Bone, L., Caspi, A., Chen, Q., Gallagher, P., Grigis, P.T., Ji, H., Liu, W., Milligan, R.O., Temmer, M.: 2011, An observational overview of solar flares. Space Sci. Rev. 159(1–4), 19. DOI. ADS.
Georgoulis, M.K.: 2012, Are solar active regions with major flares more fractal, multifractal, or turbulent than others? Solar Phys. 276(1–2), 161. DOI. ADS.
Giovanelli, R.G.: 1939, The relations between eruptions and sunspots. Astrophys. J. 89, 555. DOI. ADS.
Karakatsanis, L.P., Pavlos, G.P., Xenakis, M.N.: 2013, Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar flares dynamics. Physica A 392(18), 3920. DOI. ADS.
Lu, E.T.: 1995, The statistical physics of solar active regions and the fundamental nature of solar flares. Astrophys. J. Lett. 446, L109. DOI. ADS.
Lu, E.T., Hamilton, R.J.: 1991, Avalanches and the distribution of solar flares. Astrophys. J. Lett. 380, L89. DOI.
Mendoza, M., Kaydul, A., de Arcangelis, L., Andrade, J.J.S., Herrmann, H.J.: 2014, Modelling the influence of photospheric turbulence on solar flare statistics. Nat. Commun. 5, 5035. DOI. ADS.
Morales, L., Charbonneau, P.: 2008, Self-organized critical model of energy release in an idealized coronal loop. Astrophys. J. 682(1), 654. DOI. ADS.
Parker, E.N.: 1988, Nanoflares and the solar X-ray corona. Astrophys. J. 330, 474. DOI. ADS.
Ramos, O., Altshuler, E., Måløy, K.J.: 2009, Avalanche prediction in a self-organized pile of beads. Phys. Rev. Lett. 102(7), 078701. DOI. ADS.
Sammis, C.G., Smith, S.W.: 1999, Seismic cycles and the evolution of stress correlation in cellular automaton models of finite fault networks. Pure Appl. Geophys. 155(2–4), 307. DOI. ADS.
Sarlis, N.V., Christopoulos, S.-R.G.: 2012, Predictability of the coherent-noise model and its applications. Phys. Rev. E 85(5), 051136. DOI. ADS.
Shibata, K., Magara, T.: 2011, Solar flares: Magnetohydrodynamic processes. Living Rev. Solar Phys. 8(1), 6. DOI. ADS.
Strugarek, A., Charbonneau, P.: 2014, Predictive capabilities of avalanche models for solar flares. Solar Phys. 289(11), 4137. DOI. ADS.
Viitanen, L., Ovaska, M., Alava, M.J., Karppinen, P.: 2017, Predicting crackling noise in compressional deformation. J. Stat. Mech. Theory Exp. 5(5), 053401. DOI. ADS.
Wheatland, M.S.: 2005, A statistical solar flare forecast method. Adv. Space Res. 3(7), S07003. DOI. ADS.
Acknowledgements
Research reported in this publication was supported by Agencia Nacional de Promoción Científica y Tecnológica grant PICT-1707-2015 and Consejo Nacional de Investigaciones Científicas y Ténicas PIP 11220150100324CO.
Author information
Authors and Affiliations
Ethics declarations
Disclosure of potential conflict of interest
The authors declare there are no conflicts of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article belongs to the Topical Collection:
Towards Future Research on Space Weather Drivers
Guest Editors: Hebe Cremades and Teresa Nieves-Chinchilla
Rights and permissions
About this article
Cite this article
Morales, L.F., Santos, N.A. Predicting Extreme Solar Flare Events Using Lu and Hamilton Avalanche Model. Sol Phys 295, 155 (2020). https://doi.org/10.1007/s11207-020-01713-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11207-020-01713-0