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How can anyone be wrong if there is no present answer to start off with?
It seems to me that you are suggesting that because the rate of fusion is determined by the pressure (and temperature) of the plasma, any region of the sun that expands would see a reduction in fusion, causing it to cool and compress back to equilibrium, and any part of the sun would also resist compression by heating up and expanding due to increased fusion rate.If this is a misinterpretation of your theory, please correct me so we are discussing the same thing. If it sounds right, please keep reading...This equilibrium sounds reasonable to me, but I think it only ensures predictable density, and doesn't have a tremendous influence on the shape (symmetry) of the sun. Including gravity and the fusion equilibrium without any other forces around would certainly have a spherical optimum geometry. But I don't think that it will compensate other factors such as net rotation or magnetic field oscialtions to maintain the spherical shape. I am either misunderstanding something, or some other explanation is needed.