Identification of coronal heating events in 3D simulations

Context. The solar coronal heating problem has been an open question in the science community since 1939. One of the proposed models for the transport and release of mechanical energy generated in the sub-photospheric layers and photosphere is the magnetic reconnection model that incorporates Ohmic heating, which releases a part of the energy stored in the magnetic field. In this model many unresolved flaring events occur in the solar corona, releasing enough energy to heat the corona.
Aims: The problem with the verification and quantification of this model is that we cannot resolve small scale events due to limitations of the current observational instrumentation. Flaring events have scaling behavior extending from large X-class flares down to the so far unobserved nanoflares. Histograms of observable characteristics of flares show powerlaw behavior for energy release rate, size, and total energy. Depending on the powerlaw index of the energy release, nanoflares might be an important candidate for coronal heating; we seek to find that index.
Methods: In this paper we employ a numerical three-dimensional (3D)-magnetohydrodynamic (MHD) simulation produced by the numerical code Bifrost, which enables us to look into smaller structures, and a new technique to identify the 3D heating events at a specific instant. The quantity we explore is the Joule heating, a term calculated directly by the code, which is explicitly correlated with the magnetic reconnection because it depends on the curl of the magnetic field.
Results: We are able to identify 4136 events in a volume 24 × 24 × 9.5 Mm³ (I.e., 768 × 786 × 331 grid cells) of a specific snapshot. We find a powerlaw slope of the released energy per second equal to α_P = 1.5 ± 0.02, and two powerlaw slopes of the identified volume equal to α_V = 1.53 ± 0.03 and α_V = 2.53 ± 0.22. The identified energy events do not represent all the released energy, but of the identified events, the total energy of the largest events dominate the energy release. Most of the energy release happens in the lower corona, while heating drops with height. We find that with a specific identification method large events can be resolved into smaller ones, but at the expense of the total identified energy releases. The energy release that cannot be identified as an event favors a low energy release mechanism.
Conclusions: This is the first step to quantitatively identify magnetic reconnection sites and measure the energy released by current sheet formation.