Solar Flares as Cascades of Reconnecting Magnetic Loops

A model for the solar coronal magnetic field is proposed where multiple directed loops evolve in space and time. Loops injected at small scales are anchored by footpoints of opposite polarity moving randomly on a surface. Nearby footpoints of the same polarity aggregate, and loops can reconnect when they collide. This may trigger a cascade of further reconnection, representing a solar flare. Numerical simulations show that a power law distribution of flare energies emerges, associated with a scale-free network of loops, indicating self-organized criticality.

Figure 1

Snapshot of a configuration of loops in the steady state with $L=200$ and $m=1$ (see text).

Figure 2

Diagram showing the process of a reconnection event, from top to bottom. In frame 1 loop $a$ moves from its previous position (dashed line) and crosses loop $b$. In frame 2 the loops exchange footpoints and move to their rewired state. Frame 3 shows the final relaxed configuration.

Figure 3

Distribution of number of loops (links) per footpoint (node). The slope on the log-log scale is $-2$. Thus, $P_{\mathrm{f}\mathrm{o}\mathrm{o}\mathrm{t}}(k)\sim k^{-\gamma }$ with $\gamma =2$.

Figure 4

Distribution of flare energies in the multiloop reconnection model. The slope on the log-log scale is $-3$.