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 Quote by Ken G ...However, let's say you don't have a job, instead you have a diamond mine in your back yard...
I wish. But hey if I wish upon the right star....
 This is the better analogy for how main-sequence stars work-- they require a certain luminosity based on their basic structure, and they simply "mine" nuclear energy at whatever rate they require to maintain that structure. Thus we can say that the luminosity determines the burning rate, not the other way around, as is so often claimed.
I see your point here - luminosity is the driver in the feedback cycle. So if it drops a little, star contracts a little, driving up internal (especially core) pressure which in turn cranks up fusion rate, and vice versa if luminosity rises. That's about right? Does this imply all main sequence stars 'breathe' to a detectable degree, and if so is this more noticeable for more massive stars?