The only viable mechanism to heat the outer solar atmosphere must involve the magnetic field. Two main approaches have been adopted. One is to model the heating along individual magnetic field lines and, by specifying the spatial and temporal form of the heating term in the thermal energy equation, try to compare predicted temperatures and densities with the observed values. In this way, constraints on the form of the heating are determined. However, the heating used is not determined from physical processes. The advantage of this approach is that the rapid spatial variations in the transition region can be adequately in 1D. The other approach is to solve the full MHD equations, without any assumptions on the form of the heating and see how heating occurs due to Ohmic and viscous effects. This second approach, while physically more realistic, requires the numerical resolution in 3D of large but narrow current sheets in which magnetic reconnection can occur. In the nanoflare heating model of Parker, a large number of intense current layers are required and this requires extremely large numerical grids to resolve the sharp current gradients. Hence, Dirac is the only UK computing facility that can cope with the computational requirements. However, it remains extremely difficult to resolve the transition region fully when the thermodynamics is included.
In a unique set of numerical experiments, the evolution of the solar coronal magnetic field is modelling by slowly stressing it, through slow photospheric motions. Once a significant amount of free magnetic energy has built up, and instability triggers a large release of energy. The important point is that the magnetic field does not release all the stored energy but tries to relax towards an non-potential state. After this large event, the imposed photospheric motions continue and the magnetic field releases more energy in the form of heat and kinetic energy in a series of smaller but more frequent events. The energy release is spread across the whole region covered by the magnetic field and this is known as an MHD avalanche process. For the first time, Reid et al, A&A 633, 2020, have used Dirac to investigate in detail how the heating process occurs and where the large number of heating are spatially located. Hence, the form of the coronal heating function is determined, without any prior assumptions, and can be used with the field aligned modelling to determine the plasma temperature and density for comparison with observations.
Figure 1 (left) shows a contour plot of the heating along one field line as a function of distances along the field and time. Red indicates strong heating events. They are localised in space and time. Figure 1 (middle) shows the time averaged heating along the same field line. There is one large heating event about 0.4 of the distance along the field line but this is due to the very first event. After that there is no preferred location for the heating. Figure 1 (right) shows the spatially averaged heating as a function of time. Again, there is one large event that start off the avalanche process and then the heating comes in regular bursts. For more details see Reid et al Astron. & Astrophys., 633, id.A158.