Figure 6: Physical ingredients leading to flare organization in time.

Different cases are compared to extract the crucial ingredients of the observed waiting time distribution. The system size is L=512 for all curves. (a) Waiting time distribution for simulations where a single flux tube (N=1) evolves in the turbulent flow and reconnects at the twisting threshold. The distribution exhibits an exponential decay (dashed blue line). Conversely, for different degrees of interaction (interacting tubes, λ_R<1 and λ_R>1) and non-interacting tubes (λ_R=1), one recovers the behaviour measured in Fig. 4. (b) Distributions evaluated for the evolution of N=400 tubes in the two cases: Interacting tubes (λ_R<1), whose footprints diffuse by random motion (denoted by ‘R.M.’) and evolution in the turbulent flow w/o twist. In both cases, deviations from the observational result are observed (the dash blue line denotes an exponential decay). The solid line in a and b represents the best fit for the largest system size, L=2,048. Results indicate that tube interactions rule the temporal organization of flares.