Simulating flaring events in complex active regions driven by observed magnetograms

Abstract

Context. We interpret solar flares as events originating in active regions that have reached the self organized critical state, by using a refined cellular automaton model with initial conditions derived from observations. Aims. We investigate whether the system, with its imposed physical elements, reaches a self organized critical state and whether well-known statistical properties of flares, such as scaling laws observed in the distribution functions of characteristic parameters, are reproduced after this state has been reached. Methods. To investigate whether the distribution functions of total energy, peak energy and event duration follow the expected scaling laws, we first applied a nonlinear force-free extrapolation that reconstructs the three-dimensional magnetic fields from twodimensional vector magnetograms. We then locate magnetic discontinuities exceeding a threshold in the Laplacian of the magnetic field. These discontinuities are relaxed in local diffusion events, implemented in the form of cellular automaton evolution rules. Subsequent loading and relaxation steps lead the system to self organized criticality, after which the statistical properties of the simulated events are examined. Physical requirements, such as the divergence-free condition for the magnetic field vector, are approximately imposed on all elements of the model. Results. Our results show that self organized criticality is indeed reached when applying specific loading and relaxation rules. Powerlaw indices obtained from the distribution functions of the modeled flaring events are in good agreement with observations. Single power laws (peak and total flare energy) are obtained, as are power laws with exponential cutoff and double power laws (flare duration). The results are also compared with observational X-ray data from the GOES satellite for our active-region sample. Conclusions. We conclude that well-known statistical properties of flares are reproduced after the system has reached self organized criticality. A significant enhancement of our refined cellular automaton model is that it commences the simulation from observed vector magnetograms, thus facilitating energy calculation in physical units. The model described in this study remains consistent with fundamental physical requirements, and imposes physically meaningful driving and redistribution rules.

Self-organized criticality in a spherically closed cellular automaton: Modeling soft gamma repeater bursts driven by magnetic reconnection

“…where V and η are the plasma velocity and the resistivity, respectively [18,20]. Note that the Laplacian of the magnetic field ∇ 2 B corresponds to the right hand side of equation (3) while the sign is opposite.…”

“…The site is unstable to reconnection when the absolute value of its magnetic stress exceeds some critical value B c [17,20],…”

“…This criterion is reasonable because a large magnetic stresses favors magnetic reconnection [20]. If a reconnection instability occurs, the magnetic field stress is canceled as follows:…”

Dynamic data-driven integrated flare model based on self-organized criticality

“…By design, such a model guarantees a zero magnetic field divergence and can be conceivably linked with actual coronal loop characteristics. Dimitropoulou et al (2011) constructed a static integrated flare model (S-IFM hereafter), using for the first time observed vector magnetograms as initial conditions, which allowed calculations in physical units and direct comparison with observations. This was not possible in a number of previous models, as explained by Georgoulis et al (2001).…”

“…6 discusses the strengths and weaknesses of the dynamic model, its relation with previous results and also suggests possible future enhancements. The Appendix provides a technical summary of the reused modules from the static model, as introduced by Dimitropoulou et al (2011).…”