Gravitational energy, solar radius and solar cycle

Physics

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Maunder Minimum, Sunspot Activity, Gravitational Energy, Luminosity

Scientific paper

A self-consistent approach is used. From the change (1.2 W/m2) in the solar constant (1367 W/m2) during a solar cycle we deduced a relation between the change in solar radius ΔR and the depth d = (1-α)R in the convection zone where the expansion starts. A second relation is obtained by equating the gravitational energy required for the expansion and the decrease in luminosity during half a solar cycle. This yields values for ΔR ≍ 8 km, d ≍ 0.96R (super-granular region) and for the change in gravitational energy ΔE ≍ 1032J. Similar considerations are made for the Maunder Minimum yielding ΔR ≍ 60 km, d ≍ 0.94R and ΔE ≍ 1033J. There is some change, say 40 per cent, if we use a quadratic expansion instead of a linear one. Moreover this theory suits a qualitative explanation why the Sun expands during a minimum of the magnetic activity.

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