Frequencies of flare occurrence: Interaction Between convection and coronal loops

TL;DR

This paper presents a model linking convective flows to magnetic loop instabilities, explaining the power-law distribution of solar flare energies and their occurrence intervals, aligning well with observed data from solar and stellar flares.

Contribution

It introduces a convective flow-driven random walk model for magnetic loop twisting that reproduces observed flare energy distribution slopes.

Findings

The model matches the steep power-law slope for small solar flares.

It predicts a shallower slope for larger flares, consistent with observations.

The model's applicability extends to flare stars, with a predicted change in slope for cool stars.

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 to explain the numerical value of the power law indices. Here, we propose a model in which convective flows in granules force the foot-points 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 which 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 which 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.