What heats the solar corona above $10^{6}\ \mathrm{K}$?
In plain words
Energy from churning gas below the surface must be carried up by magnetic fields and released in the corona; how it is released is unknown.
Precise statement
The quiet corona requires an energy flux of $\sim 3 \times 10^{5}\ \mathrm{erg}\ \mathrm{cm}^{-2}\ \mathrm{s}^{-1}$ and active regions $\sim 10^{7}\ \mathrm{erg}\ \mathrm{cm}^{-2}\ \mathrm{s}^{-1}$. Determine the dominant dissipation mechanism: Alfven-wave turbulence, resonant absorption and phase mixing of waves, or nanoflares (small reconnection events) in braided fields. Answer: mechanisms with energy fluxes matching these requirements, by region type.
What would settle it
Observations resolving the energy flux in waves and in small reconnection events at the base of the corona, matched to the required heating by region type.
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