Avalanches and the Distribution of Reconnection Events in Magnetized Circumstellar Disks

Cosmic rays produced by young stellar objects can potentially alter the ionization structure, heating budget, chemical composition, and accretion activity in circumstellar disks. The inner edges of these disks are truncated by strong magnetic fields, which can reconnect and produce flaring activity that accelerates cosmic radiation. The resulting cosmic rays can provide a source of ionization and produce spallation reactions that alter the composition of planetesimals. This reconnection and particle acceleration are analogous to the physical processes that produce flaring in and heating of stellar coronae. Flaring events on the surface of the Sun exhibit a power-law distribution of energy, reminiscent of those measured for Earthquakes and avalanches. Numerical lattice-reconnection models are capable of reproducing the observed power-law behavior of solar flares under the paradigm of self-organized criticality. One interpretation of these experiments is that the solar corona maintains a nonlinear attractor -- or ``critical'' -- state by balancing energy input via braided magnetic fields and output via reconnection events. Motivated by these results, we generalize the lattice-reconnection formalism for applications in the truncation region of magnetized disks. Our numerical experiments demonstrate that these nonlinear dynamical systems are capable of both attaining and maintaining criticality in the presence of Keplerian shear and other complications. The resulting power-law spectrum of flare energies in the equilibrium attractor state is found to be nearly universal in magnetized disks. This finding indicates that magnetic reconnection and flaring in the inner regions of circumstellar disks occur in a manner similar to activity on stellar surfaces.