MHD consistent cellular automata (CA) models

II. Applications to solar flares

¹ Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Thessaloniki, 54006 Thessaloniki, Greece e-mail: vlahos@helios.astro.auth.gr
² Institute for Space Applications and Remote Sensing, National Observatory of Athens, 15236 Penteli, Greece e-mail: anastasi@space.noa.gr

Corresponding author: H. Isliker, isliker@helios.astro.auth.gr

Received: 27 November 2000
Accepted: 30 July 2001

Abstract

In Isliker et al. ([CITE]), an extended cellular automaton (X-CA) model for solar flares was introduced. In this model, the interpretation of the model's grid-variable is specified, and the magnetic field, the current, and an approximation to the electric field are yielded, all in a way that is consistent with Maxwell's and the MHD equations. The model also reproduces the observed distributions of total energy, peak-flux, and durations. Here, we reveal which relevant plasma physical processes are implemented by the X-CA model and in what form, and what global physical set-up is assumed by this model when it is in its natural state (self-organized criticality, SOC). The basic results are: (1) On large-scales, all variables show characteristic quasi-symmetries: the current has everywhere a preferential direction, the magnetic field exhibits a quasi-cylindrical symmetry. (2) The global magnetic topology forms either (i) closed magnetic field lines around and along a more or less straight neutral line for the model in its standard form, or (ii) an arcade of field lines above the bottom plane and centered along a neutral line, if the model is slightly modified. (3) In case of the magnetic topology (ii), loading can be interpreted as if there were a plasma which flows predominantly upwards, whereas in case of the magnetic topology (i), as if there were a plasma flow expanding from the neutral line. (4) The small-scale physics in the bursting phase represent localized diffusive processes, which are triggered when a quantity which is an approximately linear function of the current exceeds a threshold. (5) The interplay of loading and bursting in the X-CA model can be interpreted as follows: the local diffusivity usually has a value which is effectively zero, and it turns locally to an anomalous value if the mentioned threshold is exceeded, whereby diffusion dominates the quiet evolution (loading), until the critical quantity falls below the threshold again. (6) Flares (avalanches) are accompanied by the appearance of localized, intense electric fields. A typical example of the spatio-temporal evolution of the electric field during a flare is presented. (7) In a variant on the X-CA model, the magnitude of the current is used directly in the instability criterion, instead of the approximately linear function of it. First results indicate that the SOC state persists and is only slightly modified: distributions of the released energy are still power-laws with slopes comparable to the ones of the non-modified X-CA model, and the large scale structures, a characteristic of the SOC state, remain unchanged. (8) The current-dissipation during flares is spatially fragmented into a large number of dissipative current-surfaces of varying sizes, which are spread over a considerably large volume, and which do not exhibit any kind of simple spatial organization as a whole. These current-surfaces do not grow in the course of time, they are very short-lived, but they multiply, giving rise to new dissipative current-surfaces which are spread further around. They show thus a highly dynamic temporal evolution. It follows that the X-CA model represents an implementation of the flare scenario of Parker ([CITE]) in a rather complete way, comprising aspects from small scale physics to the global physical set-up, making though some characteristic simplifications which are unavoidable in the frame-work of a CA.