On the post-main-sequence evolution

[Singlau]

The path on an HR diagram after a star leaves the main sequence stage is known as post-main sequence evolution. In the graph, it consists of 2 parts: sub-giant branch and red giant branch. The near-horizontal is the former one, and the near-vertical is the latter one.

Subgiants are near-horizontal because as it expands, it loses temperature so the luminosity remain approx. constant. However, in the red giant stage, it suddenly pops up growing extremely large with the temperature decreases only slightly.

I have two questions upon this:
1. What is the trigger event of a star changing from subgiant to red giant? (About electron Degeneracy?)
2. Why does red giants expand so much, but the temperature remains constant? (just as subgiants temperature should decrease along expansion)

Thank you!

 

[Drakkith]

1. What is the trigger event of a star changing from subgiant to red giant? (About electron Degeneracy?)

As I understand the process, it starts when the contraction of the star (after it has run out of hydrogen in the core) reaches a point where a large shell of hydrogen around the core ignites. The amount of fusion taking place in this shell is greater than what took place in the core, a result of the larger volume of the shell compared to the core. This greater energy output puffs up the outer layers of the star, turning it into a red giant.

2. Why does red giants expand so much, but the temperature remains constant? (just as subgiants temperature should decrease along expansion)

The temperature does decrease. That's why it turns red.

 

[Singlau]

Actually when I first learned stellar evolution two years ago, I directly skipped from main sequence to red giant, omitting subgiant, as most people regard it 'minor.

But I read some articles that says the ignition point of hydrogen shell is the turnoff point from the main sequence (i. e. Start of subgiant). Then my question is the difference between subgiant and red giants, as both of them fuse hydrogen shell.

For the second question, yes, it does decrease. But if you consider that it similarly burns hydrogen like subgiants, why does it have a near 90° turn off? If it can increase in radius so much without decreasing the temperature a lot (unlike subgiants), there must be vigorous heating event to do the effect?

I read wikipedia about 'dredging-up', where the fusion reach the very surface, and brings some metals up. But I don't know if it relates to my question.

Anyway, thanks for your reply!

 

[Drakkith]

But I read some articles that says the ignition point of hydrogen shell is the turnoff point from the main sequence (i. e. Start of subgiant). Then my question is the difference between subgiant and red giants, as both of them fuse hydrogen shell.

Not sure. Wiki's article on subgiants says the following:

Once a main sequence star ceases to fuse hydrogen in its core, the core begins to collapse under its own weight. This causes it to increase in temperature and hydrogen fuses in a shell outside the core, which provides more energy than core hydrogen burning. Low- and intermediate-mass stars expand and cool until at about 5,000 K they begin to increase in luminosity in a stage known as the red-giant branch. The transition from the main sequence to the red giant branch is known as the subgiant branch. The shape and duration of the subgiant branch varies for stars of different masses, due to differences in the internal configuration of the star.

It looks like subgiants may be on their way to the red giant phase?

 

[Singlau]

Yes indeed subgiants are going to be red giants eventually. The graph I showed is a model for a star slightly larger than sun. What I'm curious about is the quick turn off from subgiant branch to red giant branch.

For every other turn offs in the graph it has a trigger event: e. g.
Main sequnce-->subgiant: H shell ignition
Red giant-->horizontal branch: helium flash

I'm wondering what is the powerful event turning subgiant branch horizontal suddenly to a vertical red giant branch.

 

[Bandersnatch]

I've been trying to get a sensible answer out of Prialnik's book on stellar evolution, but I'm not sure I grok it.
What I think is happening during the subgiant phase, is the hydrogen depleted core contracts and heats up, which then expands the envelope without significant change in total energy production, or even with a decrease as fusion processes switch from core to shell burning, hence little to no luminosity change.
As the core (and by extension - shell) heats up, fusion in the shell becomes dominated by the CNO cycle, whose high temperature sensitivity means that any further temperature increase due to helium ash being deposited onto the core (i.e further collapse) leads to rapid increase in luminosity. The star expands to find new equilibrium. This would be the near vertical ascension on the H-R diagram.
That's the best I can make out of it. Furthermore, I'm not sure if this reasoning works for intermediate-mass stars, whose cores don't reach the Shonberg-Chandrasekhar instability. But then again, for those stars the subgiant phase is not such a horizontal line.

Maybe we can get @Ken G or @e.bar.goum to comment?

I read wikipedia about 'dredging-up', where the fusion reach the very surface, and brings some metals up.

I don't think that's relevant. In any case, the first dredge-up in the red giant phase is not when fusion reaches the stellar surface, but when convection developing in the envelope due to its lower temperature reaches the fusing shell and starts bringing up fusion products to the surface.

 

[Singlau]

Do you mean the shell is doing CNO cycle in red giant stage? Then is it using PP chain or CNO cylcle in subgiant stage(i. e. First ignition)?

 

[Ken G]

The shell burning would be CNO cycle even in the subgiant phase for most stars, because remember, the solar core is already almost hot enough for CNO cycle fusion to dominate, so it wouldn't take much contraction and heating to get CNO to take over. But the basic story given above is correct-- as the core contracts, the shell gets hotter, fusion in the shell goes berserk, and heat is deposited in the envelope, expanding it. The expansion serves to take weight off the fusing shell, lowering the amount of mass in the shell and turning down the amount of fusion, thus maintaining equilibrium with what light can diffuse out through the shell. (Note that the luminosity ends up rising even as the shell gets less and less mass in it, because its temperature is going up, and the rate that light can diffuse out also goes up as the amount of mass in the shell drops, so it is always in equilibrium as the helium ash builds up in the core).

On the matter of the transition from sub-giant to giant, I would say that's the transition from an ideal-gas core to a degenerate core. This comes with a very significant shrinking of the core, such that at first the core and the fusing shell above it constitute a significant contribution to the radius of the star, so a significant part of the star is transporting heat by radiative diffusion. However, as the core and shell shrink and the envelope expands, most of the star is transporting heat by convection. The difference between a primarily radiatively diffusing star, and a primarily convecting star, is that the former evolves at nearly constant luminosity (i.e., horizontal), and the latter evolves at nearly constant surface temperature (i.e., vertical). These phases are also seen in pre-main-sequence evolution, in the reverse order. The fully convective interior is called the "Hayashi track," and the more radiatively diffusing interior is called the "Henyey track."

A small correction on the Schonberg-Chandrasekhar limit-- intermediate mass stars (say 2-10 solar masses) are the ones that encounter this limit, they are not the ones that don't encounter it. It happens whenever the inert (i.e., non-fusing) core is still an ideal gas, so has not yet become degenerate, and also acquires more than 10% of the star's mass. For the Sun, the post-main-sequence helium core is degenerate by the time it has 10% of the mass, so there's not the rapid core contraction that typifies this limit. That basically means the Sun stays a subgiant for a little while as its core contracts only slowly, allowing the star to remain mostly radiatively diffusing, before puffing out a huge fully convective envelope. But higher mass stars have convective cores, so the hydrogen runs out over the whole core at once, allowing them to still be ideal gases when they have more than 10% of the star's mass. That causes the rapid core contraction, so they essentially have their subgiant phase "skipped over", creating something known as the "Hertsprung gap" in the H-R diagram.

 

[Bandersnatch]

intermediate mass stars (say 2-10 solar masses)

Cheers. I actually thought <2 solar masses counts as intermediate and above that as massive. Gotta recheck my nomenclature.

 

[Ken G]

No worries, I don't think there's a hard-and-true boundary between high mass and intermediate mass. A typical thing is to say high mass stars are the ones that go supernova, intermediate are the ones that experience the Schonberg-Chandrasekhar limit, and low-mass have degenerate cores right after leaving the main sequence. But you could also make the boundary between intermediate and low-mass the boundary from CNO cycle core fusion to p-p fusion. Or, as you have done, you could hold that high-mass extends down to include all the Schonberg-Chandrasekhar limit stars, intermediate is the CNO cycle fusing non-Schonberg-limit stars, and low mass is the p-p chain fellows. There should probably also be an ultra-low mass category, for stars whose cores are feeling some degeneracy effects even on the main sequence, and whose entire envelopes are convective. The terms are kind of subjective, though I think there is a kind of standard that has the "intermediate" regime the Schonberg-Chandra regime.