What is the truth about radiation pressure in stars?

[amarante]

Thanks Ken G. Now I got it. ;)

 

[Ken G]

Excellent. To be honest, I had not realized how confusing the term "radiative core" is, this goes a long way toward helping me to understand where the confusion is coming from!

 

[amarante]

Excellent. To be honest, I had not realized how confusing the term "radiative core" is, this goes a long way toward helping me to understand where the confusion is coming from!

Actually, I think I was confused about the energy transport and momentum transfer. Now it is all clear.

 

[Pigkappa]

Here they are talking about a core-collapse supernova, and again we find the patently wrong information that when fusion stops, radiation stops holding up the core of the star. At least they are talking about massive stars here, but most stars that go supernova also do not have cores that are primarily held up by radiation pressure (instead it is usually ideal gas pressure or electron degeneracy pressure). At best they are leaving out most of the story-- what really happens is, fusion ends, hydrostatic equilibrium is just fine for awhile, but gradually the energy losses from the core force the core to (gradually) contract, nothing dramatic there, and little to do with radiation pressure.

I 'm not sure it works this way. It is true (I think) that most stars that go supernova do not have cores that are primarily held up by radiation pressure and "gradually the energy losses from the core force the core to (gradually) contract", but it isn't true that radiation pressure has little to do with it.

I think that this is what happens. When the fusion stops, no more photons are produced. Then the radiation pressure drops and the core begins to contract. This is a very slow contraction because the radiation pressure wasn't too important, but it's the only pressure which can be reduced (the electron, nuclei and nucleons gas pressure depends on the chemical composition, T and density of the core and they don't change just because the fusion stopped).
Since the core has started to contract, its temperature and density rise and this changes the equilibrium between free \alpha particles and Fe nuclei and the reaction Fe + \gamma \rightarrow 13 \alpha + 4n happens, some of the \alpha particles break up releasing free protons, and some of the protons capture some electrons thus reducing their pressure contribute.
The radiation pressure variation is important because it allows the contraction to start.

I'm facing this topic for my 3rd-year thesis (a minor presentation we have to make which is kinda pointless) and the Stellar Physics course is at the 4th year, so I hope I didn't mess up anything.

 

[Ken G]

I 'm not sure it works this way. It is true (I think) that most stars that go supernova do not have cores that are primarily held up by radiation pressure and "gradually the energy losses from the core force the core to (gradually) contract", but it isn't true that radiation pressure has little to do with it.

Most stars that go supernova do not have cores that are primarily held up by radiation pressure, and radiation pressure plays little role anywhere in the supernova process.

I think that this is what happens. When the fusion stops, no more photons are produced.

Right away this is incorrect. Photons are not just produced by fusion, they are produced by hot gas. If you don't want to make photons, you'd have to instantly cool the gas to absolute zero. Generally, what instead happens is the gas begins to heat up, thereby producing more photons. Your understanding is exactly the misconception I am pointing to, so I'm glad that you are willing to share it, because it supports my claim that this misconception is quite widespread.

Then the radiation pressure drops and the core begins to contract.

Again, no, radiation pressure depends only on one thing in the core: its temperature. Period. So if you think the radiation pressure drops, you are claiming the core temperature drops. That is not usually true.

This is a very slow contraction because the radiation pressure wasn't too important, but it's the only pressure which can be reduced (the electron, nuclei and nucleons gas pressure depends on the chemical composition, T and density of the core and they don't change just because the fusion stopped).

And right there is your core misconception: radiation pressure is not fundamentally different from other forms of pressure, they all depend (in different ways) on the local plasma properties like T and density and composition, it's just that radiation pressure is particularly simple because it only depends on T (we are talking about a thermal radiation field here, the equations for it can be found anywhere).

I'm facing this topic for my 3rd-year thesis (a minor presentation we have to make which is kinda pointless) and the Stellar Physics course is at the 4th year, so I hope I didn't mess up anything.

I'm glad we had this talk!

 

[Pigkappa]

Right away this is incorrect. Photons are not just produced by fusion, they are produced by hot gas.

Again, no, radiation pressure depends only on one thing in the core: its temperature. Period. So if you think the radiation pressure drops, you are claiming the core temperature drops. That is not usually true.

And right there is your core misconception: radiation pressure is not fundamentally different from other forms of pressure, they all depend (in different ways) on the local plasma properties like T and density and composition, it's just that radiation pressure is particularly simple because it only depends on T (we are talking about a thermal radiation field here, the equations for it can be found anywhere).
I'm glad we had this talk!

Yeah, ok, I meant that less photons are produced. My fault.

And right there is your core misconception: radiation pressure is not fundamentally different from other forms of pressure, they all depend (in different ways) on the local plasma properties like T and density and composition, it's just that radiation pressure is particularly simple because it only depends on T (we are talking about a thermal radiation field here, the equations for it can be found anywhere).
I'm glad we had this talk!

Then why does the core start to contract? "There's less energy so it contracts" isn't a dynamical explanation, we need to find out which pressure source (radiation, ions and electron gas, or whatever) starts to drop.

 

[Ken G]

Yeah, ok, I meant that less photons are produced. My fault.

Again, radiation pressure depends only on one thing: temperature. If you think the core radiation pressure drops when fusion ends, then you think the core temperature goes down after hydrogen fusion ends. If that were true, the Sun would never fuse anything past helium. But you are right that there does have to be some transient initial drop to get it started, it is after that that we will see the rise.

Then why does the core start to contract? "There's less energy so it contracts" isn't a dynamical explanation, we need to find out which pressure source (radiation, ions and electron gas, or whatever) starts to drop.

To see why it starts to contract, you need to look at the sources of pressure, yes, but you should look at the dominant sources of pressure. That is usually either ideal gas pressure, or degeneracy pressure-- it is only radiation pressure for the most massive stars. So yes, at first there must be a small decrease in that dominant pressure, which initiates contraction, but very quickly the temperature will begin to rise as gravitational energy is released. The dominant pressure, and the radiation pressure also, generally increases as the contraction continues-- it is slightly weaker than gravity, but both are increasing with time. And in any event, the important pressure that is doing this is usually not radiation pressure, that's the key point that is so wrong in so many places.

To address how the temperature and pressure can rise even as the core contracts, I brought up the example of a decaying orbit, so let's look at that again. If you have a particle in a circular orbit, and you turn on a drag force very slowly, so that the drag is at first imperceptible, and then gradually more and more until it reaches some constant drag that is nevertheless quite small, what will be the motion of the object? The answer is, the object will be in a nearly circular orbit, but will gradually spiral in. Will the object's velocity ever be slower than it started? Depending on how fast you "turn on" the drag, you might get a small initial decrease that "gets the ball rolling", but after that the object's velocity (and so kinetic energy) will always be increasing, the whole time.

So one could ask, why does a retarding force on the object cause it to speed up continually? The answer is there are two forces, the drag, and gravity, and gravity overrules the drag and causes the kinetic energy to increase, not decrease. That's also why cores get hotter, and radiation pressure increases, when fusion stops. Although there does have to be a short phase in which the pressure drops at first, it is the dominant pressure that drops, and it very quickly starts to rise after that initial almost imperceptible transient.

 

[Pigkappa]

Ok but you still didn't tell why the pressure drops in a short phase. This is really important because this is what allows the collapse to start.



If it's not because of the radiation pressure, I think the reason might be the following: when the fusion reaction stops, the equilibrium in the reaction Fe + \gamma \rightleftarrows 13 \alpha + 4n is shifted to the right (because the other source of Fe, the nuclear fusion, has stopped, and therefore there are less Fe ions) ===> more alpha particles ===> more free protons which can absorb electrons.

I'm not really sure this is the real cause anyway.

Again, radiation pressure depends only on one thing: temperature

This is true only in conditions of thermal equilibrium; I don't really know whether the fusion reaction stops suddenly or not...

 

[Ken G]

Ok but you still didn't tell why the pressure drops in a short phase. This is really important because this is what allows the collapse to start.

In most of the situations that the erroneous texts I cited were talking about, the dominant pressure is garden variety ideal gas pressure. So that would be the pressure that drops imperceptibly when the fusion ends (because of a tiny drop in temperature). But again, once the contraction begins, that initial tiny drop is replaced by a very substantial rise.

In other situations (like core collapse supernovae), there's no pressure drop at all, instead there is additional "ash" being added to the degenerate core, so it is the rising gravity that contracts it, not falling pressure.

If it's not because of the radiation pressure, I think the reason might be the following: when the fusion reaction stops, the equilibrium in the reaction Fe + \gamma \rightleftarrows 13 \alpha + 4n is shifted to the right (because the other source of Fe, the nuclear fusion, has stopped, and therefore there are less Fe ions) ===> more alpha particles ===> more free protons which can absorb electrons.

No, the physics is much simpler than that, it's garden variety falling ideal gas pressure (for the core contraction of the Sun after fusion ends), or increasing gravity (for the core collapse of a degenerate core going past the Chandrasekhar mass.

This is true only in conditions of thermal equilibrium; I don't really know whether the fusion reaction stops suddenly or not...

Thermal equlibrium is an excellent assumption in the core of the Sun, and certainly none of the texts that I pointed out the errors in were assuming anything else. Fusion does not stop suddenly, but it makes no real difference, because the fusion rate stops faster than the evolutionary time of the core (which is called the Kelvin-Helmholtz timescale, the energy transport timescale).

 

[Pigkappa]

I'm sorry i can't quote the right parts of your post but I'm writing from a smartphone. I didn't know the fusion stopping time scale was bigger than KH, I'm sadly weak in Nuclear physics.

I don't understand why the gravity rises just before the collapse starts. Where does the new
mass come from?

 

[ibysaiyan]

I'm sorry i can't quote the right parts of your post but I'm writing from a smartphone. I didn't know the fusion stopping time scale was bigger than KH, I'm sadly weak in Nuclear physics.

I don't understand why the gravity rises just before the collapse starts. Where does the new
mass come from?

I haven't been through each post but replying back to this quote.Is this to do with type II supernovae ? If so then the extra mass I assume comes from the surrounding material which actually slams into the rigid core (held by neutron degeneracy pressure)

Just a thought.Someone correct me if I am mistaken.

~ibysaiyan
Regards

 

[Drakkith]

I'm sorry i can't quote the right parts of your post but I'm writing from a smartphone. I didn't know the fusion stopping time scale was bigger than KH, I'm sadly weak in Nuclear physics.

I don't understand why the gravity rises just before the collapse starts. Where does the new
mass come from?

I think it comes from non-fusing material that builds up in the middle of the core. Over time the core becomes denser and denser as it fills with non-fusing materials, increasing the gravity of the core. (Though not the star overall)

 

[Ken G]

Exactly.

 

[Chronos]

Iron [and to some degree nickel] is the predominant 'ash' that accumulates in the core of a type II supernova. The collapse mechanics are unclear, but, at some critical density this ash stuff goes 'poof' and converts to a hodge podge of heavier elements in a brief, but, spectacular fireworks display.