Small-scale Heating Events in the Solar Atmosphere. I. Identification, Selection, and Implications for Coronal Heating

We present a comprehensive method to analyze small-scale heating events in detail in a 3D magnetohydrodynamics simulation for quiet-Sun conditions. The method determines the number, volume, and some general geometric properties of the small-scale heating events at different instants in a simulation with a volume of 16 x 8 x 16 Mm(3), spanning from the top of the convection zone to the corona. We found that there are about 10(4) small-scale heating events at any instant above the simulated area of 128 Mm(2). They occur mainly at heights between 1.5 and 3.0 Mm. We determine the average value of their projected vertical extent, which ranges from 375 to 519 km over time, and we show that height, volume, and energy distribution of the events at any instant resemble power laws. Finally, we demonstrate that larger heating structures are a combination of much smaller heating events and that small-scale heating events dissipate enough energy to maintain the coronal energetic balance at any instant.