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It is stated that:

After the main sequence, as fusion weakens or stops in the core, outward radiation weakens. The helium core contracts and heats up. Gravitational energy is converted to thermal energy again!

The star will appear to cool slowly and will undergo a modest increase in luminosity. During this phase, the path the star will follow in the HR diagram is almost horizontal to the right of its position on the Main Sequence. Stars in this phase are usually referred to as subgiants.

But I still can't understand.

  • It's answered-- the luminosity stays constant because the star retraces its path on the pre-main-sequence "Henyey track" as it re-expands somewhat. The luminosity is constant on the Henyey track because it is set by radiative diffusion, not fusion or convection, and radiative diffusion tends to produce a luminosity that depends only on mass and opacity. Neither changes much into the subgiant phase, so luminosity stays nearly the same, rising only because helium involves fewer free electrons than hydrogen and that reduces the opacity. If people don't like the answer, that can't be helped. – Ken G Jul 9 at 8:05

From blackbody radiation -- L = c r^2 T^4 -- the horizontal evolution implies increasing radius and decreasing temperature.

This happens because the depletion of H at the core:

Depletion of H at core -> core contraction -> increasing core temperature + starting H fusion in the envelope (in HR diagram, the star goes up) -> to maintain the equilibrium from the injection of energy of H fusion in the envelope, envelope expands and cools (moving horizontally to the right in HR diagram) -> ...

  • Doesn't explain why the luminosity is almost constant. – Rob Jeffries Aug 8 at 14:51
  • "increasing radius and decreasing temperature" – Kornpob Bhirombhakdi Aug 8 at 20:02
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    The luminosity is almost constant because it is set by radiative diffusion, and the nature of radiative diffusion (for fixed opacity) is to produce a luminosity that depends only on mass, and not on radius. This is the "mass-luminosity relation." The question could be reframed, "why do people think the mass-luminosity relation only holds in the main sequence, when tracks show it also holds pre- and post- main sequence?" Answer: because they aren't paying attention. – Ken G Aug 18 at 20:50
  • Any references for M-L relationship for pre/post MS? I might not aware of something new. – Kornpob Bhirombhakdi Oct 7 at 12:26
  • Why would you need a reference for the M-L relationship post MS when the whole question here is why does the M-L relationship still hold for subgiants? That's the question being asked, the question was not does the M-L relationship still hold, it was why does it still hold. And that's what was answered. – Ken G Nov 7 at 1:45

I will replace the previous answer to focus on the "subgiant" branch prior to red giant, rather than the pre-main-sequence or the "horizontal branch" of core helium fusion. Those are other times that the luminosity is constant, but this question is about the subgiant branch, which I missed before.

The reason the luminosity is nearly constant on the subgiant branch is related to the "mass-luminosity relation" of pre- and main-sequence stars. It is due to radiative diffusion and how it leads to a luminosity that depends only on mass, for a given composition. If you compare to pre-main-sequence tracks, you should find that the subgiants more or less retrace that prior evolution, just with a somewhat higher luminosity because many of the electrons have been swallowed into neutrons, reducing the opacity and increasing the all-important rate of radiative diffusion. It's essentially just a helium-dominated mass-luminosity relation, instead of hydrogen-dominated, as the radius rises due to the details of how the interior is evolving.

The reason the luminosity eventually rises steeply on the red giant branch is that as the degenerate core starts to build in mass, it starts to control the temperature of the fusing region, and this significantly changes the internal structure in ways that get into explaining red giants.

  • Apparently someone who doesn't know much about stellar evolution put a -1, but you can be sure my answer is correct all the same. An interesting fact about the mass-luminosity relation is that it is independent of radius, which is a basic element of the combination of internal light content times the diffusion rate. So that's why the luminosity doesn't change as the radius changes, but the surface temperature does change. – Ken G Apr 9 at 0:45
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    Maybe they thought that you appear to be saying there is "no important shell fusion" during the subgiant phase? I would also think that many if not most subgiants have convective envelopes. – Rob Jeffries Apr 9 at 17:55
  • I am referring to the importance of shell fusion in setting the luminosity of the star. It's already obvious from the question that there is not important shell fusion in the setting of the luminosity of the star-- the luminosity does not change when fusion shifts from core fusion to shell fusion! What could make it more obvious than that? Hence the question. As for convective envelopes, that's covered in why the star's surface temperature drops, but clearly has little to do with the luminosity. Just look at the track. – Ken G Apr 9 at 18:50

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