What prevents a star from collapsing after stellar death?

Tags:
1. Sep 28, 2014

avito009

When the star stops burning because heavier elements like Iron are formed in its core. Then the gas pressure stops and as you know the gas pressure helps keep a star in equilibrium because it provides pressure against the force of gravity. So Iron does not give off energy. So what stops the star from collapsing?

So when the core starts becoming dense due to gravity it stops becoming dense due to Pauli's Exclusion principle. Fermions (a class of particle including Protons, Neutrons and electrons) of the same type obey the Pauli exclusion principle . In layman's terms, it says that such particles cannot occupy the same, small volume of space.

Thus, if you try to force them into a small volume of space, they "push back". This "pushing" creates a pressure called "degeneracy pressure", and is what keeps white dwarfs from collapsing into black holes.

So does that mean that the same fermions like electrons cant occupy the same sub shell? Does having the same quantum state mean that the fermions cant be at the same sub-energy level. Define in laymans terms quantum state? How is it different from sub shell?

Also I read that the star does not collapse into a black hole due to quantum mechanical effects. So is the degeneracy pressure the so called quantum mechanical effect?

2. Sep 28, 2014

Staff: Mentor

When the star initially stops fusing elements in its core, the core is held up by normal gas pressure, even when the core is composed of Iron/Nickel. In lighter mass stars that will never collapse in a supernova, the core gradually cools and becomes denser until the primary repulsive method is the exclusion principle acting on electrons. In other words, the electron degeneracy holds up the star as it cools and becomes a white dwarf. It is the quantum mechanical effect you refer to in your post.

In more massive stars, the core is initially held up by plain old gas pressure. Nickel-56 is the final fusion product and is created in the silicon burning phase that occurs at around 3 billion kelvin. The release of energy, along with the conversion of gravitational potential energy into heat by contraction, is initially what keeps the core held up against the pressure of the mass above it. However, the next step in the fusion chain is the creation of zinc-60, which is an endothermic reaction. As soon as the temperature is high enough for production of zinc-60, these endothermic reactions begin to rob the core of significant amounts of energy, greatly accelerating the gravitational collapse of the core and leading to the initial stages of a supernova explosion.

In the plasma at the core of a star the electrons do not occupy orbitals like they do in normal matter. However, they do occupy energy states and these states still follow the rule that electrons cannot occupy the same state at the same time. Degeneracy pressure works because when you try to pack more electrons into a small volume the lower energy states are already taken and these new electrons must go into higher energy states. Putting an electron into a high energy state obviously requires energy, and if you don't have the energy the electron cannot be forced into this small volume into this high energy state, thus giving rise to the "repulsive force" seen in degeneracy.

3. Sep 28, 2014

Matterwave

Actually, the core of a massive star before its death is already quite degenerate, and the primary pressures keeping it from collapsing are degeneracy pressure and radiation pressure due to the emitted light (gamma rays) from the fusion reactions. The gas pressure is but a small contribution for massive stars. Even for not so massive stars, gas pressure is not often the largest source of pressure inside the core (outside the core, far from the radiative zone, then yes, gas pressure dominates).

Also I have not seen any sources that predict very much zinc-60 production. As far as I know, once Iron and Nickle populate the core, the core simply stops fusion, and will proceed to the supernova phase immediately (on the order of a few seconds). Perhaps zinc 60 is produced in the core, but probably only during the collapse or the post-bounce explosion.

4. Sep 28, 2014

Staff: Mentor

Interesting. I was mostly going off of what wikipedia said:

However, only minutes are available for the nickel-56 to decay within the core of a massive star. The star has run out of nuclear fuel and within minutes begins to contract. The potential energy of gravitational contraction heats the interior to 5 GK (430 keV) and this opposes and delays the contraction.

I thought that meant that gas pressure is still significant. Is it radiation pressure instead? Do you have links to any articles or sources that expand on this?

I was looking up zinc-60 on wiki, trying to understand the process, when I came across this note:
1. Final product of the silicon-burning process; its production is endothermic and accelerates the star's collapse
This makes sense to me. As the core contracts and the temperature rises, fusion of nickel-56 and helium-4 takes place and zinc-60 is created. Since this is an endothermic reaction, as soon as this process starts, the core's contraction accelerates in an irreversible process that leads to a supernova. This would agree with what you're last sentence above says, in that zinc-60 is only produced during the collapse since its production accelerates the collapse. It never has a chance to build up in the core. Of course, that is only my own extrapolation on this based on a limited understanding of the whole process, so I'm uncertain how accurate it is.

5. Sep 28, 2014

Chronos

Wiki is like a bad dog, it can't be entirely trusted.

6. Sep 28, 2014

Matterwave

Sorry, my "source" is from the lectures I went to about stellar interiors. I don't know of links to articles etc. off the top of my head.

However, the quote you got is talking about the collapse stage of the star, and it does not even state by how much this temperature increase delays the contraction. As far as I know (I attended a seminar on supernovae and compact objects over the summer), a supernova collapse happens over basically free-fall time scales (milliseconds) and I have not heard of any process that will significantly delay this (other than the main sequence fusion that "delays" the supernova for several million to perhaps a hundred million of years).

One would need to compare 5GK with the Fermi temperature of the core to see if gas pressure is significant. By the time a massive star is collapsing, it's core is already a (very small) white dwarf basically, so it's at some radius of ~1000 km with a mass of ~1.4 solar masses. I would suspect the fermi temperature to be in excess of 5GK.

We can do some order of magnitude guesses. The fermi energy is ~$\hbar^2(30N_e/V)^{2/3}/2m_e$, with a mostly iron core, N~1.5 solar mass/1 amu*1/2~10^57 (assuming electron fraction of 1/3), V~4*(1000km)^3~4*10^18 m^3 we get $E_F \approx 15MeV >>430KeV$. So I would guess that the core is highly degenerate even for temperatures in the giga-Kelvin range. The factor that I'm not sure of is the actual size of the core right before collapse, when it is very iron and nickle rich. A quick google search suggested ~1000km which is the figure I used. But even for a size of ~5000km we still get a fermi temperature higher than 5 GK.

I have not encountered this reaction in my studies, so I can't speak very much about it. I only know that once iron and nickle is reached in the core, the following fusion processes take about a day at most (to populate the core with iron and nickle), and then collapse happens in the millisecond time-scales (it's very fast because there is catastrophic failure required to produce a supernova, if the collapse were slow, there definitely would not be supernovae).

7. Sep 28, 2014

Staff: Mentor

Actually I find wiki to be extraordinarily accurate and trustworthy for an encyclopedia. I feel it's more like a friend trying to explain physics to you than a bad dog. He's trying to be accurate without making things so complicated that you can't understand him.

8. Sep 28, 2014

Staff: Mentor

My understanding is that the core contracts gradually as the silicon burning process (or any of the other fusion processes) occurs. The heating of the core doesn't stop the "collapse" because the core isn't collapsing yet, it merely opposes the contraction. Once the collapse of the core begins, nothing will give significant resistance until the core is turned into a neutron star.

Of course. I never meant to imply that the actual collapse of the core was slowed in any way.

9. Sep 28, 2014

Matterwave

I'm kind of confused on what we're talking about now. I thought we were talking about whether gas pressure was a significant contributor to the overall pressure inside the core of a massive star (esp before it goes supernova). My contention is that it is not, and radiation pressure dominates for much of the stellar interior during fusion, and degeneracy pressure is dominant once fusion reactions stop.

10. Sep 28, 2014

Staff: Mentor

Ohh, here's what looks like a very good, in depth article on the silicon burning process and the resulting collapse of the core.
http://www.ucolick.org/~woosley/ay220-11/lecture12.11.pdf [Broken]

In particular, the reactions in the core are far more complicated than I have ever read before, with dozens of different elements and isotopes present during the process.

Last edited by a moderator: May 7, 2017
11. Sep 28, 2014

Staff: Mentor

That was part of the discussion, yes. My specific post you quoted was just saying that the heating of the core resists the contraction prior to collapse. I wanted to make sure you didn't think I was saying that the heating of the core during the collapse resisted further collapse (thanks to several processes as these extremely high temperatures, heating of the core during collapse does not resist the collapse).

Page 57 of the article I linked in the post above this one has a graph of what appears to be the pressure generated in the core by radiation, ions, and electrons, although I'm not sure if it's actually the pressure or something else since the Y-axis is labeled "Entropy". The explanation on page 52 and 53 leads me to believe that entropy and pressure are at least related, so I assume that if the "entropy" of the ions, electrons, and radiation increases, then the pressure does so as well.

12. Sep 28, 2014

Matterwave

I don't follow this line of reasoning. Entropy per nucleon is not equal to the pressure... even if you make a correlation between the entropy and the pressure, it still doesn't tell you how much of the overall pressure is accounted for by gas pressure rather than degeneracy pressure or radiative pressure.

I'm not sure where you're going with your argument now. o.o If your argument was only "hotter = more resistance to collapse" then sure that's nominally true since hotter = more gas pressure = harder to collapse. But the important thing to look at is whether this increased gas pressure is actually significant in the grand scheme of things, and it doesn't seem that way to me. But certainly I can be wrong.

13. Sep 28, 2014

Staff: Mentor

Yes, I realize that. I wasn't implying that it did.

I have no argument. That was merely my reasoning as I worked through the article. If the entropy of a hot core is higher than a cold one, then it seemed to me that the more entropy the more outward pressure. I wasn't thinking about gas pressure vs degeneracy pressure at all here.

14. Sep 28, 2014

Ken G

There is a lot of misunderstanding surrounding "degeneracy pressure." From my perspective, degeneracy pressure is gas pressure (though not "ideal gas" pressure, even though that is also a kind of misnomer because ideal vs. degeneracy is actually an issue of what sets the temperature not the pressure, given known energy). It does not augment gas pressure, or replace it, and it is not a kind of repulsion that comes from quantum mechanics. It stems simply from the fact that the particles have energy, as does all forms of gas pressure, so it's gas pressure. What's more, the electrons did not get their energy from quantum mechanics, and they did not get it from nuclear fusion-- they got it from gravity. Fusion only delayed the ultimate victory of gravity, as mentioned above.

In particular, what stops the contraction of a white dwarf is not that piling the electrons up in higher and higher levels takes too much energy than is available. (I edited this next to fix an error:) If there were a contraction, gravity would always provide exactly the right kinetic energy to keep the gas degenerate, because gravitational contraction only does work, it does not transport heat. But the key point is, the kinetic energy increase due to gravity is more than would be required to maintain force balance against the stronger gravity (if the gas is non-relativistic), so that causes the star to re-expand, and the same thing happens for an ideal gas-- this really has nothing at all to do with degeneracy.

What degeneracy actually does is make it so the star cannot lose heat, so when gravitational contraction produces an excess of energy, that energy excess always causes re-expansion, whereas loss of heat in the pre-degenerate phases precludes such re-expansion when the contraction happens slowly enough. In the case of the supernova, the electrons have gone relativistic, and then the energy released by gravity is just enough to keep the electrons in force balance (and degenerate, again because there's no heat added), so this time no re-expansion occurs. This is crucial for the collapse to occur.

As to the role of radiation pressure, this is usually important, but rarely dominant, even in the core-- except for the most massive stars. But for a typical star that will undergo a supernova, both radiation pressure and gas pressure are important, with gas pressure being perhaps somewhat dominant in many cases and most places in the star. In fact, there is a kind of a rule that radiation pressure can never produce a force that is more than about twice the force from gas pressure, or else it will induce convection that will reduce the strength of the radiative force until it is about twice the gas pressure force. So that's a pretty hard upper limit as to how dominant radiation pressure can ever get.

Last edited: Sep 28, 2014
15. Oct 2, 2014

willem2

This reaction 56Ni + 4He -> 60Zn is actually exothermic.
mass of 4He 4,002603
mass of 56Ni 55,942132
sum 55.944735
mass of 60Zn 59.941827 which is lower.

However, the only source of 4He in the core at this point will be photodisintegration, which will take more energy than is liberated by this reaction.

16. Oct 2, 2014

Ken G

Worse, 56Ni is not stable (nor is 60Zn for that matter), and given to decay to 56Fe, a process important to the glow of core-collapse supernovae. Of course, 56Fe + 4He is endothermic, a fact that is relevant to those supernovae as well.

17. Oct 2, 2014

willem2

nickle-56 has a half life of 6 days, so there is very little time for it to decay.

The reaction is exothermic, so that is not where the energy disappears. The photodisintegration that produces the 4He is where the energy disappears.

18. Oct 2, 2014

Ken G

Good point, one must take into account the full process.

19. Oct 4, 2014

Simon Bridge

Ativo009: has this been useful so far?

... has there been some topic drift? I thought the questions for consideration were:

[1] no - you can get more than one electron in a subshell
http://en.wikipedia.org/wiki/Electron_shell#Number_of_electrons_in_each_shell
... when referring to stars, the degeneracy does not usually refer to atomic states.

[2] no - electrons may have the same energy level without being in the same quantum state.

[3] the state of a quantum system.
http://en.wikipedia.org/wiki/Quantum_state

[4] subshells may be quantum states but not all quantum states are subshells.

[5] yes.

Last edited: Oct 4, 2014
20. Oct 6, 2014

avito009

Thanks Simon. Those were the answers I was looking for.