Frequencies of Flare Occurrence: Interaction between Convection and Coronal Loops

Abstract

Abstract Observations of solar and stellar flares have revealed the presence of power-law dependences between the flare energy and the time interval between flares. Various models have been proposed to explain these dependences and the numerical value of the power-law indices. Here, we propose a model in which convective flows in granules force the footpoints of coronal magnetic loops, which are frozen-in to photospheric gas, to undergo a random walk. In certain conditions, this can lead to a twist in the loop, which drives the loop unstable if the twist exceeds a critical value. The possibility that a solar flare is caused by such a twist-induced instability in a loop has been in the literature for decades. Here, we quantify the process in an approximate way with a view to replicating the power-law index. We find that, for relatively small flares, the random walk twisting model leads to a rather steep power-law slope that agrees very well with the index derived from a sample of 56,000+ solar X-ray flares reported by the GOES satellites. For relatively large flares, we find that the slope of the power law is shallower. The empirical power-law slopes reported for flare stars also have a range that overlaps with the slopes obtained here. We suggest that in the coolest stars, a significant change in slope should occur when the frozen-flux assumption breaks down due to low electrical conductivity.