Do Sandpile Models Explain Observations of Complex Dynamics in Solar Flares and Polar Aurora?

Many complex systems in nature are at present not accessible for description based on first physical principles, partly due to the complexity of the dynamics and partly due to lack of necessary observational data. For some phenomena, like solar flare activity or optical aurora, detailed spatiotemporal information is only available as fluctuations of a scalar 2D radiation field emitted from the system, while the internal 3D dynamics is not accessible to direct observation. Analysis of such fields presented to this date strongly indicates that some astro and geospace systems may exhibit simultaneous statistical signatures that are traditionally attributed to either intermittent turbulence or self-organized avalanche dynamics. A paradigm for the latter is the Bak-Tang-Wiesenfeld (BTW) sandpile model or related models, but it is not obvious, however, if and how it is possible to derive from this model a scalar field with the properties observed in these geospace phenomena. The problem is that the sandpile toppling activity field has only two states at every site (toppling or non-toppling), while the occupation number field looks basically like random noise in space, and hence neither have the properties of the observation data that are used to define patches that are interpreted as avalanches, and which allows computation of structure functions. In this work we consider an approach by which the binary toppling field can be transformed into a field with a continuous range. This feature is necessary for large patches to be defined by a threshold condition, and for generation of structure functions which are not flat and trivial. The method involves hypothesizing that a toppling site emits radiation which does not disappear at the next time step, but decays with a given time constant. This creates a field with continuous range and, if the time constant is long, a much smoother spatial structure. We analyze this field generated from numerical simulations of the BTW sandpile by the same methods which have been used for observational data, and compare the results with those from observations and with avalanche statistics obtained from the traditional treatment of the BTW sandpile.