Coronal Heating

9.9 Summary

The coronal heating problem has been narrowed down by substantial progress in theoretical modeling with MHD codes, new high-resolution imaging with the SXT, EIT and TRACE telescopes, and with more sophisticated data analysis using automated pattern recognition codes. The total energy losses in the solar corona range from F=3 × 105 erg cm⁻² s⁻¹ in quiet Sun regions to F ≈ 107 erg cm⁻² s⁻¹ in active regions (§ 9.1). Theoretical models of coronal heating mechanisms include the two main groups of DC (§ 9.3) and AC models (§ 9.4), which involve as a primary energy source chromospheric footpoint motion or upward leaking Alfvén waves, which are dissipated in the corona by magnetic reconnection, current cascades, MHD turbulence, Alfvén resonance, resonant absorption, or phase mixing. There is also strong observational evidence for solar wind heating by cyclotron resonance, while velocity filtration seems not to be consistent with EUV data (§ 9.5). Progress in theoretical models has mainly been made by abandoning homogeneous fluxtubes, but instead including gravitational scale heights and more realistic models of the transition region, and taking advantage of numerical simulations with 3D MHD codes. From the observational side we can now unify many coronal small-scale phenomena with flare-like characteristics, subdivided into microflares (in soft X-rays) and nanoflares (in EUV) solely by their energy content (§ 9.6). Scaling laws of the physical parameters corroborate the unification of nanoflares, microflares, and flares; they provide a physical basis to understand the frequency distributions of their parameters and allow estimation of their energy budget for coronal heating (§ 9.8). Synthesized data sets of microflares and nanoflares in EUV and soft X-rays have established that these impulsive small-scale phenomena match the radiative loss of the average quiet Sun corona, which points to small-scale magnetic reconnection processes in the transition region and lower corona as primary heating sources of the corona.