Volume 553, May 2013
|Number of page(s)||11|
|Published online||06 May 2013|
Dynamic data-driven integrated flare model based on self-organized criticality
1 University of Athens, Department of Physics, 15483 Athens, Greece
2 University of Thessaloniki, Department of Physics, 54006 Thessaloniki, Greece
3 Research Center of Astronomy and Applied Mathematics, Academy of Athens, 11527 Athens, Greece
Received: 19 May 2012
Accepted: 20 March 2013
Context. We interpret solar flares as events originating in active regions that have reached the self-organized critical state. We describe them with a dynamic integrated flare model whose initial conditions and driving mechanism are derived from observations.
Aims. We investigate whether well-known scaling laws observed in the distribution functions of characteristic flare parameters are reproduced after the self-organized critical 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 the previously reported static cellular automaton model to a time series of seven solar vector magnetograms of the NOAA active region 8210 recorded by the Imaging Vector Magnetograph on May 1 1998 between 18:59 UT and 23:16 UT until the self-organized critical state was reached. We then evolved the magnetic field between these processed snapshots through spline interpolation, mimicking a natural driver in our dynamic model. We identified magnetic discontinuities that exceeded a threshold in the Laplacian of the magnetic field after each interpolation step. These discontinuities were relaxed in local diffusion events, implemented in the form of cellular automaton evolution rules. Subsequent interpolation and relaxation steps covered all transitions until the end of the processed magnetograms’ sequence. We additionally advanced each magnetic configuration that has reached the self-organized critical state (SOC configuration) by the static model until 50 more flares were triggered, applied the dynamic model again to the new sequence, and repeated the same process sufficiently often to generate adequate statistics. Physical requirements, such as the divergence-free condition for the magnetic field, were approximately imposed.
Results. We obtain robust power laws in the distribution functions of the modeled flaring events with scaling indices that agree well with observations. Peak and total flare energy obey single power laws with indices −1.65 ± 0.11 and −1.47 ± 0.13, while the flare duration is best fitted with a double power law (−2.15 ± 0.15 and −3.60 ± 0.09 for the flatter and steeper parts, respectively).
Conclusions. We conclude that well-known statistical properties of flares are reproduced after active regions reach the state of self-organized criticality. A significant enhancement of our refined cellular automaton model is that it initiates and further drives the simulation from observed evolving vector magnetograms, thus facilitating energy calculation in physical units, while a separation between MHD and kinetic timescales is possible by assigning distinct MHD timestamps to each interpolation step.
Key words: Sun: corona / Sun: flares / Sun: photosphere
© ESO, 2013
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