Why do old stars get so big?

[Yora]

When a star gets older and runs out of hydrogen it contracts and the increased pressure starts leads to the fusion of helium. And somehow this makes the star bloat massively in size. Why is that? As the volum expands pressure should decrease, which in turn should decrease the rate of fusion and the energy output that presses outward.
I would suspect that because of this the volume should remain stable and the star slowly shrink as it radiates mass and energy into space. But the opposite is happening. Why is that?

[Xuc Xac]

When a star gets older and runs out of hydrogen it contracts and the increased pressure starts leads to the fusion of helium.

Not exactly. Helium fusion starts before the hydrogen is gone. Hydrogen becomes helium. Helium falls to the core. When there's enough helium in the core, that starts to fuse too. Helium fusion releases more energy than the hydrogen fusion, so the star bloats up from the extra pressure. If the star is massive enough, it will continue fusing heavier and heavier elements in layers. When the star's gravity is no longer strong enough to keep the pressure on for more fusion, it collapses again into a dwarf. If it's massive enough, it will keep "igniting" fusion reactions with heavier and heavier elements until it gets to iron. Fusion generates energy until you get to iron. After that, it actually takes more energy to build heavier elements (the reaction consumes energy instead of produces it). If the star is really massive, it will supernova and the energy released will slam that iron together hard enough to make things heavier than iron. Those heavy elements will usually be radioactive elements that want to undergo fission (and release that extra energy) to get back to being iron.

Every element heavier than hydrogen and helium was formed inside a star. Every element heavier than iron was formed when a really big star exploded (or when we slammed stuff together in a particle accelerator).

[Yora]

But if the energy output of heavier elements fusing goes down, how does helium fusion produce more energy than hydrogen fusion? Shouldn't it be less?

[Ninja_Prawn]

But if the energy output of heavier elements fusing goes down, how does helium fusion produce more energy than hydrogen fusion? Shouldn't it be less?

It depends on which isotopes you're talking about. See this chart (http://physics.ucsd.edu/do-the-math/wp-content/uploads/2012/01/Binding_energy_curve_-_common_isotopes1.png) for more details.

Perhaps this (http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit2/mainseq.html) is also relevant? More helium atoms means lower density which necessitates faster movement to ensure enough atoms collide. More movement means more heat which produces the expansion?

[factotum]

I'm pretty sure fusing helium doesn't produce as much energy as fusing hydrogen does. The way it happens is like this, AFAIK: as the star fuses hydrogen, helium accumulates in the core, eventually forming a large dead space where fusion is no longer occurring surrounded by a "shell" of fusing hydrogen. In larger stars the dead helium collapses under its own weight until its temperature rises high enough for helium fusion to start (the so-called "helium flash" event), still surrounded by the shell where hydrogen fusion is still occurring. Because this outer shell is closer to the outer layers of the star, more heat makes its way into those layers and forces them to expand--so, while the core of a red giant star is just as dense as it was before and fusion can still occur, the outer layers are much more tenuous.

[Yora]

There seems to be a substential difference between low mass stars and high mass stars. Let's keep it to low mass stars like the sun for now.

I think I am understanding how a helium flash works. The helium core of the star becomes degenerate matter which does not expand when it gets hotter and so once helium starts fusing it can't reach hydrostatic equilibrium and just keeps getting hotter and fusing more helium until the whole core turns to carbon within a matter of minutes.
But after that the core undegenerates and becomes normal matter again and the whole star goes back to hydrostatic equilibrium. And in my mind a star in equilibrium should slowly shrink, not expand to thousand times its volume over a billion years.

For hydrogen fusion taking place in the shell instead of the core, the pressure in the shell would have to increase which would require a contraction instead of an expansion.

What about the energy released in the helium flash? The amount of power is absolutely massive but doesn't radiate into space but is fully absorbed by the hydrogen shell. Could it be the leftover heat generated by the helium flash that causes the hydrogen to bloat up? But I would expect that to happen much faster than a billion years.

[NichG]

It's been awhile since I took the class where we actually calculated this stuff. If I remember correctly, there are a few nontrivial bits having to do with things like the opacity of the star as a function of temperature (especially near the surface, there's a point that deeper and deeper electrons start getting stripped off of atoms, and that drastically changes the opacity and therefore the degree to which the radiation pressure couples to that layer of the star). The transition to convection is also a big factor. It's not necessarily as simple as 'it gets hotter, so it gets bigger'.

Anyhow, trying to dredge up my memories of this stuff... Both main sequence and red giants are burning hydrogen. I think the point is, however, that the hydrostatic equilibrium for a burning spherical core and the hydrostatic equilibrium for a burning shell surrounding an inert spherical core are different - essentially, the core has to suddenly get much hotter and denser so that the excluded shell can be hot enough to still burn. If you think of a fixed mass budget being responsible for the pressure at a point, in the main sequence you can still have a lot of mass outside of the core so the pressure is gradually changing as you move inwards. But if the core collapses and you start to get a burning shell, more of the mass budget (and therefore the pressure gradient) occurs in that central region, leaving the rest of the star at lower pressure. For that lower pressure to be balanced against gravity, that outer material has to be further away from the core than in the case of the more uniform star. As to the surface cooling down compared to the denser main sequence star, I can make some hand-waving arguments (bigger surface area, so radiation into space is more efficient, etc), but I feel like you have to be careful because both P and rho are changing compared to the main sequence case, so you need some additional argument other than just ideal gas law.

[shawnhcorey]

The confusion is the result of thinking that only one type of fusion happens at a time. Inside a star, fusion happens in layers. In the outer layer, hydrogen is being fused into helium. Inside that, helium is being fused into heavier elements. And if the star is old enough, the heavier elements are being fused into iron. All this fusion can happen at the same time.

When helium fusion becomes the dominate type, gravity compresses the helium layer making it smaller. This increases the pressure inside the star and causes fusion to happen more rapidly. The time of dominate helium fusion is much shorter than that of dominate hydrogen fusion (but not rapid enough to cause an explosion).

Because more fusion is taking place, more energy is released. This energy causes the outer layer of hydrogen to expand. This expansion can be so great that another layer is formed above the hydrogen fusion one where fusion shuts down. All that remains is a hot plasma of protons, electrons, and photons.

[Yora]

Turns out the helium flash only happens once the star is already a red giant. So it doesn't really matter for the main question here.

Something I've read now says that the non-fusing helium in the core contracts under gravity and while this happens potential gravitational energy is transformed into thermal energy. Which I get, the potential energy has to go somewhere.

And if I get this right this thermal energy is too low to get the hydrogen core into hydrostatic equilibrium, but still higher than the energy produced by the original hydrogen core fusion.
This energy from the contraction goes into the hydrogen shell and heats it up high enough to maintain hydrogen shell fusion. And once the hydrogen fusing shell gets close enough to the surface that the heat can convect upward (don't knw why the center parts of the star don't convect, but whatever) the whole outer layers heat up.And that leads to the extreme bloating.

So it's really the core contraction that causes the growth in size, not fusion?

[factotum]

And once the hydrogen fusing shell gets close enough to the surface that the heat can convect upward (don't knw why the center parts of the star don't convect, but whatever)

The centre of the star is under enormous pressures and thus acts more like a solid than a liquid, thus, no convection. Even in our own Sun it takes thousands of years for photons to battle their way out of the super-hot, super-dense core to a point where they can start moving more or less freely.

[Yora]

So convection is the actual physical movement of hot and colder atoms and molecules, not simply a redistribution of energy? Makes sense, a simple diffusion wouldn't lead to heat rising.

The Random Walk of photons inside a star is more complicated, though. It's not actually a single photon that moves from the core to the surface. What actually happens is that a fusion event of two atoms releases energy in form of a photon which then travels only an average distance of 1 cm before it hits another atom and gets absorbed. This atom goes into a higher energy state and the photon ceases to exist, a while later returns back to its previous lower energy state, with the excess energy being expelled as a new photon. This new photon will be emitted in a completely random direction which will be completely independent from the direction from which the previous photon came. So even if the previous photon was headed towards the surface the new photon might be heading towards the core. Or any imaginable direction really.
The photon released by the original fusion event starts a chain reaction of repeated absorption and emission. And with the average distance of each jump being only 1 cm and the diameter of the sun being 1.4x1011 cm it takes a really, really long time until the chain reaction leads to a photon being emitted at the surface and flying off into space. It's estimated to actually be hundreds of thousands of years on average.

[Tirunedeth]

Alright, my textbook doesn't seem to go into the exact details of this situation, but here's what I'm pretty sure is happening. First, the bit I'm fairly confident of: red giants expand because they have a greater luminosity. A star is basically a cloud of plasma held up against its own gravity by radiation pressure. A red giant has somewhat less mass than it had as a main sequence star, but a much greater luminosity. Thus, with greater radiation pressure and lesser gravity, the star expands.

Of course, the question remains of why red giants are more luminous. I think the answer is once again related to the balance between gravity and radiation pressure. Because helium fusion requires much higher temperature and pressure than hydrogen fusion, the star's core must be compressed a great deal more as a red giant than as a main sequence star. Thus, a greater luminosity is required to support the core against gravity.


The centre of the star is under enormous pressures and thus acts more like a solid than a liquid, thus, no convection. Even in our own Sun it takes thousands of years for photons to battle their way out of the super-hot, super-dense core to a point where they can start moving more or less freely.

Near as I can tell, this isn't true. While the Sun doesn't have a convective core, larger stars do; it has more to do with the size of the temperature gradient, with larger temperature gradients favoring convection over radiation.


...What actually happens is that a fusion event of two atoms releases energy in form of a photon which then travels only an average distance of 1 cm before it hits another atom and gets absorbed...

One thing my textbook did mention is that the mean free path in a stellar core is actually about on the order of 10-2 cm, so you're actually underestimating the time it takes for photons to escape the star.

[LokeyITP]

A few important things don't seem emphasized enough but most of the explanation at https://en.wikipedia.org/wiki/Stellar_evolution works. Don't forget to include at least special relativity in your model or the math doesn't fit observation (increases energy of core around 5-fold).

[Yora]

Of course, the question remains of why red giants are more luminous. I think the answer is once again related to the balance between gravity and radiation pressure. Because helium fusion requires much higher temperature and pressure than hydrogen fusion, the star's core must be compressed a great deal more as a red giant than as a main sequence star. Thus, a greater luminosity is required to support the core against gravity.

Required yes. But where does it come from? (From what I've found apparently potential energy that is lost as the helium moves closer to the center and that energy has to go somewhere.)

[NichG]

Required yes. But where does it come from? (From what I've found apparently potential energy that is lost as the helium moves closer to the center and that energy has to go somewhere.)

Well, the amount of energy produced can always be increased by increasing pressure and temperature as long as there's fuel to burn (since the burning goes faster the hotter it is). So if the current production of energy is insufficient to hold up the star, the rate of fusion will increase until it becomes sufficient.

[Yora]

Yes, but unless I am mistaken (which I might) if this were the only thing going on the star would shrink over time. But in reality the opposite is happening and the stars massively inflate.

[NichG]

Yes, but unless I am mistaken (which I might) if this were the only thing going on the star would shrink over time. But in reality the opposite is happening and the stars massively inflate.

The core shrinks over time, but holding up the core and holding up the outer layers are two different things.

[Douglas]

Let's see if I can rephrase my limited understanding of what's been said so far in this thread:

Star fuses hydrogen for a while, producing lots of helium.
Helium sinks to the core, displacing hydrogen.
Eventually there isn't enough hydrogen in the core to sustain enough fusion to keep the star from collapsing.
Star begins to collapse, heating up the core.
Core heats up enough for helium to start fusing.
Helium fusion plus the collapse heats up a shell surrounding the core.
Hydrogen fusion begins in the shell around the core.
Fusion is now occurring in a vastly larger portion of the star than before, with both the helium core and the hydrogen shell.
Total fusion energy output thus is greatly increased.
This increased energy output pushes back and reverses the collapse, pushing the outer layers further out.
The fusion in the shell, having been kickstarted by the temporary collapse, produces enough heat to sustain itself despite the expansion.
Pressure from density is replaced with pressure from higher temperatures produced by greater quantity of fusion as the star expands.


Does that sound about right? In short, star heats up, fusion region gets bigger, runaway feedback loop until expansion damps it to an equilibrium.

[BannedInSchool]

Does that sound about right? In short, star heats up, fusion region gets bigger, runaway feedback loop until expansion damps it to an equilibrium.
Without going through 'Pedia for the details again, no. The red giants have as their first stage a growing, non-fusing (but still hot) helium core with a fusing hydrogen shell around that, that hydrogen shell being possible because the core contracted. I didn't get a firm grasp on why the outer layers of the star expand, but the shell of hydrogen fusion around a more dense core is sure a different arrangement.

[Yora]

Star fuses hydrogen for a while, producing lots of helium.
"For a while" is 80% of a main sequence star's lifetime of several billion years, but yes.


Helium sinks to the core, displacing hydrogen.
The helium is being produced in the core where pressure is highest. The pressure inside a star this size is so high that plasma is rising and sinking only near the surface. Deeper inside nothing is moving much. In a red dwarf this is not the case. These are fully convective all the way through, which leads to a pretty even mixture of hydrogen and helium at all depths.


Eventually there isn't enough hydrogen in the core to sustain enough fusion to keep the star from collapsing.
Star begins to collapse, heating up the core.
This is actually happening all the time. Temperature goes down > star contracts > density goes up > temperature rises > star expands > density goes down > temperature goes down > star contracts > density goes up > ... It's a negative feedback loop that keeps going on for billions of years (in a low mass star). In practice the star is not actually pulsing in any detectable way (or it might, but only a very little), instead it always remains in a state where temperature, density, and gravity are in balance, which is called the hydrostatic equilibrium.


Core heats up enough for helium to start fusing.
Yes. But from my understanding this is not because heat produced by the fusion of hydrogen is building up over time. Instead, but I am really not 100% sure about this yet, the original hydrogen core shrinks as it is transformed into a helium core since one helium atom takes up much less space than four hydrogen atoms. While the core is shrinking a lot of mass is moving closer to the star's center of gravity. Moving towards the center of gravity means you are losing potential energy (that's just what's its called, it's an actually present energy) which ends up being turned into more heat energy.
[I am sure now. (http://physics.gmu.edu/~jevans/astr103/CourseNotes/Text/Lec27_stellarPostMSEvolLowMass.htm#18.1.)]


Helium fusion plus the collapse heats up a shell surrounding the core.
Hydrogen fusion begins in the shell around the core.
Yes, though I believe that only the combination of the two is enough to heat the hydrogen shell to fusion temperature. The energy generated by the helium fusion alone should not be sufficient by itself since it produces less heat than hydrogen fusion.


Fusion is now occurring in a vastly larger portion of the star than before, with both the helium core and the hydrogen shell.
Total fusion energy output thus is greatly increased.
This increased energy output pushes back and reverses the collapse, pushing the outer layers further out.
Yes, I believe so.


The fusion in the shell, having been kickstarted by the temporary collapse, produces enough heat to sustain itself despite the expansion.
I think fusion can not sustain itself simply because of the energy it releases. You always also need gravity that create sufficient pressure. (I believe in a fusion reactor the pressure is caused by the magnetic field instead.) Collapse is always happening but mostly very slowly because the heat in the core is pushing back. There are some events in which the collapse speeds up hugely for a short time, which is what happens during a helium flash and a supernova. But for a sun-like star the helium flash happens well into the red giant phase when it's already grown huge.


Pressure from density is replaced with pressure from higher temperatures produced by greater quantity of fusion as the star expands.
I believe what's going on in the outer layers is that the outward push of heat that comes from the contracting helium core and the hydrogen fusing layers becomes greater than the gravitational pull towards the center of the star.


Does that sound about right? In short, star heats up, fusion region gets bigger, runaway feedback loop until expansion damps it to an equilibrium.
The feedback loop is not runaway (positive feedback loop) because the expansion leads to an equilibrium (negative feedback loop).
I don't believe it's the larger fusion area that causes the expansion of an aging star, but the combined energy of fusion and core contraction. Even though the sphere in which fusion is happening is getting bigger, the helium core itself is not fusing.
My assumption is that fusion power output gows down over time, but contraction power output grows by an even bigger amount, leading to a net increase of power output.

History Channel normally makes Wikipedia make look like an established scientific journal, but this description (https://www.youtube.com/watch?v=cQmxWVCg3sY#t=43s) seems to support it.

Which is all for a low mass star (but still bigger than a red dwarf). In a high mass star the helium core will fuse and lead to a carbon core and a helium fusing layer around it. And then an oxygen core and a carbon fusing layer around that, and so on.

[BannedInSchool]

My assumption is that fusion power output gows down over time, but contraction power output grows by an even bigger amount, leading to a net increase of power output.
Mmm, I was thinking about that, and when the helium core shrinks it brings hydrogen both into the volume where there was hydrogen fusion before, that volume is experiencing more gravity because the core is more dense, and the core is even hotter than it was before. I don't know how much the helium core shrinks, but if it goes degenerate that seems like it's probably taking up a fraction of the previous fusing hydrogen core volume, but still has all the mass. That sounds a good recipe for more fusion. You know that previous hydrogen fusion core which was about half of the diameter? Well, put a hot lump in the middle that makes gravity even stronger. (Not exactly, because that would increase the mass of the star, but comparing the two internal states of the core is the point.)

[ace rooster]

Imagine a star as a fusion region sphere surrounded by an insulating blanket. The fusion region is at a pretty fixed temperature, because if it cools it collapses, and fusion accelerates, and if it heats up it expands, and fusion slows. Once a star has a core of helium it forces this fusion region further out. The power through the insulation is preportional to the temperature difference, and also the area, so a larger fusion region means more power through the insulation. Thats what the core sees.

All energy leaves via the surface. If the power throughput increases without a change in surface the non fusion layers of the star will accumulate energy until it does. Lower layers expand, which pushes upper layers into lower gravity, which lowers the pressure on the lower levels so they can expand further. The whole star swells until it has such a large surface area that energy stops accumulating, which means big

[SlyGuyMcFly]

Imagine a star as a fusion region sphere surrounded by an insulating blanket. The fusion region is at a pretty fixed temperature, because if it cools it collapses, and fusion accelerates, and if it heats up it expands, and fusion slows. Once a star has a core of helium it forces this fusion region further out. The power through the insulation is preportional to the temperature difference, and also the area, so a larger fusion region means more power through the insulation. Thats what the core sees.

All energy leaves via the surface. If the power throughput increases without a change in surface the non fusion layers of the star will accumulate energy until it does. Lower layers expand, which pushes upper layers into lower gravity, which lowers the pressure on the lower levels so they can expand further. The whole star swells until it has such a large surface area that energy stops accumulating, which means big

I really like this explanation. As a teacher I can really appreciate an explanation that manages to convey a complex idea in a simple way. I'm not an astrophysicist or anything like that so I can't comment on the accuracy though! I thought it had to do with Helium fusion being hotter but it seems I was quite mistaken on that count. :smallredface:

[factotum]

I thought it had to do with Helium fusion being hotter but it seems I was quite mistaken on that count. :smallredface:

Not entirely--helium fusion takes place at a much higher temperature than hydrogen fusion does, it just doesn't produce as much energy. This is why the helium burning phase of a star's existence is relatively short compared to the hydrogen one.

[ace rooster]

Not entirely--helium fusion takes place at a much higher temperature than hydrogen fusion does, it just doesn't produce as much energy. This is why the helium burning phase of a star's existence is relatively short compared to the hydrogen one.

The fact that helium fusion produces less energy is significant, but it does not account for vast difference in timescales. The main factor that needs to be considered is how fast energy is escaping from the core, because the core will collapse until energy produced equals energy out. In a red giant the core is convective, but we can get an illustration of what happens if we consider a pure radiative case instead. The rate of radiative heat transfer is proportional to the 3rd power of the temperature*, so if the core is 10x hotter it would be leaking 1000x more energy as a massively simplified estimate. 1000x more energy out means that fusion must be producing 1000x more, and hence going very fast. In reality, the swelling that the star goes through lowers the opacity, and convection starts up because of the very high temperature gradients. Both these things mean that the 1000x would be a huge underestimate.

*derivative of the 4th power. Easiest to understand by thinking of an onion where each layer exchanges energy by black body radiation.

[factotum]

Well, yes, I meant that the short helium burn time is both down to the higher temperature and the lower energy produced by helium fusion, sorry if I wasn't clear on that in my post--although I didn't know that thing about the heat transfer being related to the third power of temperature.

[ace rooster]

So convection is the actual physical movement of hot and colder atoms and molecules, not simply a redistribution of energy? Makes sense, a simple diffusion wouldn't lead to heat rising.

The Random Walk of photons inside a star is more complicated, though. It's not actually a single photon that moves from the core to the surface. What actually happens is that a fusion event of two atoms releases energy in form of a photon which then travels only an average distance of 1 cm before it hits another atom and gets absorbed. This atom goes into a higher energy state and the photon ceases to exist, a while later returns back to its previous lower energy state, with the excess energy being expelled as a new photon. This new photon will be emitted in a completely random direction which will be completely independent from the direction from which the previous photon came. So even if the previous photon was headed towards the surface the new photon might be heading towards the core. Or any imaginable direction really.
The photon released by the original fusion event starts a chain reaction of repeated absorption and emission. And with the average distance of each jump being only 1 cm and the diameter of the sun being 1.4x1011 cm it takes a really, really long time until the chain reaction leads to a photon being emitted at the surface and flying off into space. It's estimated to actually be hundreds of thousands of years on average.

Sorry If this seems like I'm jumping back a bit, but only just got round to answering this.

The first point is correct, and is best thought of as the movement of energy by movement of high energy matter. Convection occurs when you get super adiabatic temperature gradients resulting in instability. Importantly, this means that you can get temperature gradients where a higher region is 'cooler' than a lower region, provided the pressure difference is enough to account for it.* Convection is generally pretty good at clamping to the adiabat hard. In the core of our sun the temperature gradient is not great enough for convection to occur. If you have any questions about convection in particular, I am glad to answer if I can, because it is one of the few things that I think it important for people to understand.

The second point is mostly wrong though. Photons last a very long time, because there are very few atoms in the innards of a star. The temperatures involved will entirely ionise helium, and even very heavy metals, leaving you with free nucliae and free electrons rather than any atoms. The photons generally scatter off free electrons, which don't really have energy levels in the same way. They give up energy as they do so, lengthening their wavelength, but it is rarely absorbed.

* As a side note, this is why 'global warming' will probably not mean much in the way of actual warming. The atmosphere is pretty much at the adiabat, so any extra energy at the surface will mean more convection, rather than dramatically higher temperatures. Convection drives weather systems, so climate change will mean more extreme storms and weather systems. These will probably include higher temperatures, but the temperature change will not be the most dramatic effect. I far prefer the phrase 'climate change' to 'global warming' for this reason.


The third power thing is an interesting informative hack, but simplifies considerably. Opacity changes with wavelength, and the continuous gradient means that black body spectra cannot be assumed. I've never looked into it in much detail, and don't know how much in error it is. All the errors I know about suggest it is an underestimate, though possibly not in the limit which stars approach. Opaque structures where blackbody radiative heat transfer dominates conductive are pretty much restricted to stars anyway, so I don't expect getting it wrong to upset my life too much.

[Yora]

I looked it up and the mean distance for each photon travelled is almost always listed as 1cm. Except one article (http://futurism.com/how-the-sun-works/) that said that this is actually much bigger than the real distance which is much smaller than that.

If you have a source that gives a much larger mean distance, please share.

[Tirunedeth]

I looked it up and the mean distance for each photon travelled is almost always listed as 1cm. Except one article (http://futurism.com/how-the-sun-works/) that said that this is actually much bigger than the real distance which is much smaller than that.

If you have a source that gives a much larger mean distance, please share.

My precise source is Fundamental Astronomy, Fifth Edition, by Hannu Karttunen, Pekka Kroger, Heikki Oja, Markku Poutanen, and Karl J. Donner, page 241. They make an estimate of the mean free path based on the mean density of the sun (1410 kg/m3) and the absorption coefficient at about half the radius of the sun (10 m2/kg), and give a value for the mean free path of on the order of 10-4 m (1/10 of a millimeter). Repeating the calculation with their numbers gives me 7x10-5 m, which agrees with their order of magnitude estimate.

Of course, I'm going to take a wild guess that you don't have this particular astronomy textbook sitting around, and don't want to buy it just to check one calculation (which doesn't even go into that much detail). Here (http://adsabs.harvard.edu/full/1992ApJ...401..759M)'s another source, which goes into a bit more detail. In particular, it has a graph of the mean free path vs. radius on the second page; it gives values less than half a centimeter for pretty much the entire Sun, and values of around 1/10 of a cm near the core. That's somewhat greater than the 10-4 cm from Fundamental Astronomy, but less than the 1 cm which does, indeed, seem to be commonly quoted for the mean free path in the solar interior.