Mass and energy flow near sunspots

Sunspots block the flow of energy to the solar surface. The blocked energy heats the volume beneath the spot, producing a pressure excess which drives an outflow of mass. Linear numerical models of the mass and energy flow around spots were constructed to estimate the predictions of this physical picture against the observed properties of sunspot bright rings and moat flows. The width of the bright ring and moat are predicted to be proportional to the depth of the spot penumbra, in conflict with the observed proportionality of the moat width to the spot diameter. Postulating that spot depths are proportional to spot diameters would bury the moat flow too deeply to be observed, because the radial velocity at the surface is found to be inversely proportional to the depth of the spot penumbra. The radial velocity at the surface is of order a few hundred meters per second after 1 day, in agreement with the observed excess of moat velocities over supergranule velocities.