Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 4 2010 10.5194/npg-17-339-2010 http://www.nonlin-processes-geophys.net/17/339/2010/ http://www.nonlin-processes-geophys.net/17/339/2010/npg-17-339-2010.html http://www.nonlin-processes-geophys.net/17/339/2010/npg-17-339-2010.pdf 339 344 2010-07-22 Self-organized criticality in solar flares: a cellular automata approach L. F. Morales laura@astro.umontreal.ca P. Charbonneau Canadian Space Agency, Saint-Hubert, Quebec, Canada Département de Physique, Université de Montréal, C.P. 6128 Succ. Centre-ville, Montréal, Quebec, H3C-3J7, Canada We give an overview of a novel lattice-based avalanche model that reproduces well a number of observed statistical properties of solar flares. The anisotropic lattice is defined as a network of vertically-connected nodes subjected to horizontal random displacements mimicking the kinks introduced by random motions of the photospheric footpoints of magnetic fieldlines forming a coronal loop. We focus here on asymmetrical driving displacements, which under our geometrical interpretation of the lattice correspond to a net direction of twist of the magnetic fieldlines about the loop axis. We show that a net vertical electrical current density does build up in our lattice, as one would expect from systematic twisting of a loop-like magnetic structure, and that the presence of this net current has a profound impact on avalanche dynamics. The presence of an additional energy reservoir tends to increase the mean energy released by avalanches, and yield a probability distribution of released energy in better agreement with observational inferences than in its absence. Symmetrical driving displacements are in better conceptual agreement with a random shuffling of photospheric footpoint, and yield a power-law distribution of energy release with exponent larger than 2, as required in Parker's nanoflare model of coronal heating. On the other hand, moderate asymmetrical driving generate energy distribution exponents that are similar to those obtained from SOHO EUV observations. Aschwanden, M J.: Physics of the solar corona, Springer-Praxis Books in Astronomy and Planetary Sciences, Chichester, UK, 2006. Aschwanden, M. J., Tarbell, T. D., Nightingale, R. W., Schrijver, C. J., Title, A., Kankelborg, C. C., Martens, P., and Warren, H. P.: Time Variability of the "Quiet" Sun Observed with TRACE. II. Physical Parameters, Temperature Evolution, and Energetics of Extreme-Ultraviolet Nanoflares, Astrophys. J., 535, 1047–1065,~2000. Charbonneau, P., McIntosh, S W., Liu, H.-L., and Bogdan, T J.: Avalanche models for solar flares (Invited Review), Sol. Phys., 203, 321–353,~2001. Dahlburg, R B., Klimchuk, J A., and Antiochos, S K.: An Explanation for the "Switch-On" Nature of Magnetic Energy Release and Its Application to Coronal Heating, Astrophs. J., 622, 1191–1201,~2005. De Moortel, I., Parnell, C E., and Hood, A W.: Determination of coronal loop properties from trace observations, Sol. Phys., 215, 69–86,~2003. Georgoulis, M K. and Vlahos, L.: Variability of the occurrence frequency of solar flares and the statistical flare, Astron. Astrophys., 336, 721–734,~1998. Gomez, D.: Heating of the Solar Corona, Fundamentals of Cosmic Physics, 14(2–3), 131–233,~1990. Isliker, H., Anastasiadis, A., and Vlahos, L.: MHD consistent cellular automata (CA) models. I Basic features, Astron. Astrophys., 363, 1134–1144,~2000. Klimchuk, J. A.: On Solving the Coronal Heating Problem, Sol. Phys., 234, 41–77,~2006. Lopez Fuentes, M C., Klimchuk, J A., and Démoulin, P.: The Magnetic Structure of Coronal Loops Observed by TRACE, Astrophys. J., 639, 459–474,~2006. Lu, E. T and Hamilton, R. J.: Avalanches and the distribution of solar flare, Astrophys. J., 380, L89–L92,~1991. Mandrini, C. H., Demoulin, P., and Klimchuk, J. A.: Magnetic Field and Plasma Scaling Laws: Their Implications for Coronal Heating Models, Astrophys. J., 530, 999–1015,~2000. Morales, L F. and Charbonneau, P.: Self-organized Critical Model of Energy Release in an Idealized Coronal Loop, Astrophys. J., 682(1), 654–666,~2008. Morales, L F. and Charbonneau, P.: Geometrical Properties of Avalanches in a Pseudo-3D Coronal Loop, Astrophys. J., 698(2), 1893–1902,~2009. Parker, E N.: Magnetic Neutral Sheets in Evolving Fields – Part Two – Formation of the Solar Corona, Astrophys. J., 264, 642–647,~1983. Parker, E. N.: Nanoflares and the solar X-ray corona, Astrophys. J., 330, 474–479,~1988. Podladchikova, O. and Lefebre, B.: Lattice models for solar flares and coronal heating (Invited Review), Solar Actvity and its Magnetic Origin, Proc IAU Symposium, 233, 481–488,~2006. Uritsky, V., Paczuki, M., Davila, J M., and Jones, S. I.: Coexistence of Self-Organized Criticality and Intermittent Turbulence in the Solar Corona, Phys. Rev. Lett., 99(2), 25001–25001-4,~2007.