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Why do pre-main-sequence stars on the Hayashi track remain at a constant temperature while they contract?

I've read the Wikipedia article, so no need to repeat the derivation.

What I took away from that is that the extra heat generated by contraction is given off almost exactly because the whole star is convective and the atmosphere is very capable of radiating that heat away if the opacity is mainly caused by hydrogen ions, which is the case in the cooler of the pre-main-sequence stars.

Is that correct?

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    $\begingroup$ At least one statement here is incorrect. Only half the heat generated by contraction is radiated away. The rest makes the star hotter. $\endgroup$
    – ProfRob
    May 1, 2016 at 6:54

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The surface temperature of fully convective stars is set by their opacity mechanism, often emission when the H minus ion is created. The rate the star emits light is not set by the contraction rate, it is the other way around-- the star loses heat at a rate set by its structure, and that's what sets the contraction rate. (As said, the rate of gravitational energy release is always double the rate the star loses heat to starlight.) The reason the surface temperature always has to be something like 3000 K is pretty complicated, but it seems to be due to the fact that this temperature is a kind of peak in the surface's ability to emit light. Convection sets the temperature structure, but there are a range of possible solutions with different internal energy, so the history of heat loss picks out whichever solution has the right internal energy. But just why the surface is always about the same T is still the trickiest part to understand, I am hoping to get a better handle on that eventually. Ignore anything you see in introductory textbooks, they never get it right.

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