<p>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. </p>

<p>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.</p>

<p>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.</p>

CC BY-SA 3.0
2018-04-09T00:45:38.450Z
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
CC BY-SA 3.0
2018-04-09T17:55:50.100Z
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.
ProfRob
CC BY-SA 3.0
2018-04-09T18:50:27.837Z
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
CC BY-SA 4.0
2018-04-08T18:12:15.850Z
2018-06-09T00:56:21.463Z
2018-06-09T00:56:21.463Z
Ken G
<p>From blackbody radiation (<span class="math-container">$L = c r^2 T^4$</span>) the horizontal evolution implies increasing radius and decreasing temperature.</p>

<p>This happens because of the depletion of H at the core:</p>

<p>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) -> ...</p>

CC BY-SA 4.0
2018-08-08T14:51:58.970Z
Doesn't explain why the luminosity is almost constant.
ProfRob
CC BY-SA 4.0
2018-08-08T20:02:54.330Z
"increasing radius and decreasing temperature"
Kornpob Bhirombhakdi
CC BY-SA 4.0
2018-08-18T20:50:59.347Z
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
CC BY-SA 4.0
2018-10-07T12:26:24.777Z
Any references for M-L relationship for pre/post MS? I might not aware of something new.
Kornpob Bhirombhakdi
CC BY-SA 4.0
2018-11-07T01:45:09.080Z
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
CC BY-SA 4.0
2018-04-08T18:37:12.293Z
2019-08-01T11:06:59.990Z
2019-08-01T11:06:59.990Z
Kornpob Bhirombhakdi
<p><a href="https://i.sstatic.net/507OY.jpg" rel="noreferrer"><img src="https://i.sstatic.net/507OY.jpg" alt="enter image description here" /></a></p>
<p>It is stated that:</p>
<blockquote>
<p>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!</p>
<p>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.</p>
</blockquote>
<p>But I still can't understand.</p>

CC BY-SA 4.0
2021-04-28T14:37:53.543Z
If you quote, you should link to your source and give attribution
planetmaker
<star><red-giant><hr-diagram>
Why is the track of the subgiant stage almost horizontal on the HR diagram?
velut luna
# Why is the track of the subgiant stage almost horizontal on the HR diagram?

(Asked by: username_0 on 2018-04-08)

[![enter image description here](https://i.sstatic.net/507OY.jpg)](https://i.sstatic.net/507OY.jpg)

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.

**Tags:** star, red-giant, hr-diagram
> **Comments:**
> **username_1**: If you quote, you should link to your source and give attribution  

---

## 2 answers

### Answer by username_2 on 2018-04-08. Score: 3

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.

> **Comments:**
> **username_2**: 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.  
> **username_3**: 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.  
> **username_2**: 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.  

---

### Answer by username_4 on 2018-04-08. Score: -1

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

This happens because of 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) -> ...

> **Comments:**
> **username_3**: Doesn't explain why the luminosity is almost constant.  
> **username_4**: "increasing radius and decreasing temperature"  
> **username_2**: 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.  
> **username_4**: Any references for M-L relationship for pre/post MS? I might not aware of something new.  
> **username_2**: 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.  

---

