What prevents a star from collapsing after stellar death?

[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 can't occupy the same sub shell? Does having the same quantum state mean that the fermions can't 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?

 

[Drakkith]

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.

So does that mean that the same fermions like electrons can't occupy the same sub shell? Does having the same quantum state mean that the fermions can't be at the same sub-energy level. Define in laymans terms quantum state? How is it different from sub shell?

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.

 

[Matterwave]

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.

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.

 

[Drakkith]

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).

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?

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.

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.

I'll try to find more info on this process.

 

[Chronos]

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

 

[Matterwave]

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?

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 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.

I'll try to find more info on this process.

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).

 

[Drakkith]

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

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.

 

[Drakkith]

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 hundreds of millions of years).

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.

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).

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

 

[Matterwave]

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.

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.

 

[Drakkith]

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

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.

 

[Drakkith]

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.

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.

 

[Matterwave]

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.

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.

 

[Drakkith]

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.

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

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.

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.

 

[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.

 

[willem2]

However, the next step in the fusion chain is the creation of zinc-60, which is an endothermic reaction..

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.

 

[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.

 

[willem2]

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.

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

Of course, 56Fe + 4He is endothermic, a fact that is relevant to those supernovae as well.

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

 

[Ken G]

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

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

 

[Simon Bridge]

Ativo009: has this been useful so far?

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...

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

So does [degeneracy pressure] mean that the same fermions like electrons can't occupy the same sub shell?[1] Does having the same quantum state mean that the fermions can't be at the same sub-energy level.[2] Define in laymans terms quantum state?[3] How is it different from sub shell?[4] 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?[5]

Short answers in order:
[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.

 

[avito009]

Short answers in order:
[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.

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

 

[Dryson]

I'm not certain if this question should be its own topic or not but I will ask it anyway. The force of gravity upon collapsing star was mentioned in the thread. If gas pressure keeps the force of gravity from collapsing the star is the resulting collapse of a star into a black hole the result of the surrounding gravity compressing all of the gas that is remaining in the star into a singularity that then explodes outwards?

 

[Drakkith]

I'm not certain if this question should be its own topic or not but I will ask it anyway. The force of gravity upon collapsing star was mentioned in the thread. If gas pressure keeps the force of gravity from collapsing the star is the resulting collapse of a star into a black hole the result of the surrounding gravity compressing all of the gas that is remaining in the star into a singularity that then explodes outwards?

First, during the formation of a black hole, only the core of the star implodes. It's important to understand that the core does NOT explode.

Let's look at the core collapse of star into a neutron star first. When the core implodes, it rapidly shrinks until the degeneracy pressure of the nucleons becomes large enough to halt the implosion. As soon as this happens, you have a compact, rigid object with several solar masses worth of material surrounding it that is still collapsing (the layers of the star near the core). When the materials in these layers hits the core, they rebound off of it and generate a massive shockwave that, through a process not fully understood, blows the outer layers of the star away in a supernova explosion. Note that the core of the star, which is now the neutron star, does not explode.

For stars collapsing directly into black holes, it may be different, as I'm not sure there's a rigid surface for the outer layers of the star to rebound off of. Suffice it to say, the black hole does NOT explode.

 

[Dryson]

When the materials in these layers hits the core, they rebound off of it and generate a massive shockwave that, through a process not fully understood, blows the outer layers of the star away in a supernova explosion.

Could the massive shockwave possibly have something to do with gravitational fields compressing against the core that once the core has imploded the layers above the core itself come into contact with each other where the stored energy potential causes chemical reactions to occur because of the rate at which the contact occurs that then causes the shockwave to take place?

Or could it be the sudden implosion of the core that causes a vacuum to occur that causes the shockwave?

How I am envisioning this happening is by imaging a large tube, the suns core, that is pressurized that is keeping the water from caving the tube walls in. Suddenly the pressure in the tube is gone and the tubing walls cave in allowing the pressure of the water to occur the volume of the tube. As the water rushing into the tube fills the volume and comes into contact with the flow the result is that the force of the initial wave would cause reverberation back through the volume of water that came rushing in basically creating a shockwave in appearance.

 

[Drakkith]

The first paragraph in your post above isn't correct, but your second one is pretty much spot on. The core collapses faster than the outer layers, leaving a large, low pressure region between where the core used to be and the outer layers. Gravity accelerates the material of the outer layers inwards and it hits the newly formed neutron star at a high velocity and rebounds off of the surface.

 

[Dryson]

The first paragraph in your post above isn't correct, but your second one is pretty much spot on. The core collapses faster than the outer layers, leaving a large, low pressure region between where the core used to be and the outer layers. Gravity accelerates the material of the outer layers inwards and it hits the newly formed neutron star at a high velocity and rebounds off of the surface.

Is it possible to convert the above process into a propulsive thrust system or would the release of energy be too great?

 

[Drakkith]

No. It doesn't even make sense given the context or the scale involved here. Also, if you want to quote someone's post, click the Reply button to quote a single post, +Quote button to add the post to the quote queue, or you can highlight individual sections of the text and then click Reply or +Quote.

 

[Simon Bridge]

... using a supernova for propulsion?
A kind of extreme surfing for Real men?!

 

[Matterwave]

Even the neutrino flux close by to the supernova would kill you many times over (not to mention the material that is floating around at trillions of Kelvin). See this XKCD what if: http://what-if.xkcd.com/73/

 

[Dryson]

Does the magnetization of iron that is formed in the core of a sun aid in keeping the gas pressure from collapsing the sun or does the magnetization of the iron actually assist in the collapse of the sun?

What level of magnetization would the iron be at compared to normal magnetized iron on planet Earth?

 

[Drakkith]

The core of a star is far too hot for iron to magnetize. You don't even have atoms, just a plasma of ions and electrons.

 

[Dryson]

Is there the smallest probability that the intense heat would cease allowing the formation of iron that becomes magnetic for a moment thus either assisting in the collapse or preventing the collapse of the core only for a moment?

I was reading in this article that the core is comprised of inert iron.

http://abyss.uoregon.edu/~js/ast122/lectures/lec18.html

Just from welding I know that active gas interacts with the metal being where as inert gas does not interact with metal that is being welded but is used to clean the weld area of and protect the weld area from contaminants such as oxygen.

Does inert iron core apply in the same manner where it would shield rather than interact?

Or is it the iron ash in the core that causes the actual collapse?

Does the iron ash have magnetic properties?

 

[Drakkith]

No, there is not.

 

[Matterwave]

The resulting Neutron star may very well have a very strong magnetic field (see: magnetar http://en.wikipedia.org/wiki/Magnetar )...but this process is very different than the magnetization of Iron that we find here on Earth. I couldn't tell you much about it since I never studied this subject though.

 

[Simon Bridge]

Does the magnetization of iron that is formed in the core of a sun...

Does Iron form in the core of the Sun?
I guess that's where the fusion happens so...

I was reading in this article that the core is comprised of inert iron.

The lecture referenced [1. L18] is about stellar death, which is when stars are much cooler.
The Sun is not near that stage just yet so we would not expect a considerable buildup of iron anywhere.
Earlier in the same series there is a section on the interior structure of main sequence stars:
i.e. [1] lectures 12 and 14.

... you can see from your own source material that we do not expect inert iron in a star as young as the Sun.

Stars do have magnetic fields - these do not come from magnetized iron.
iirc: magnetic effects in stars are much weaker than coulomb effects - we would normally see the effects as disturbances on the surface.
Stars that are collapsing into degeneracy have already overcome coulomb pressure so magnetic effects are not going to be important.
In quantum systems, the magnetic field is included as part of the overall potential - determining the states. Thus - the magnetic field's impact on stellar collapse past this point is already accounted for under the label "Pauli pressure" at the education level of those lectures you are reading.

[1] Readings: Schneier & Arney: Unit 66 U Oregon. (Lecture Series)
http://abyss.uoregon.edu/~js/ast122/

 

[Drakkith]

To be clear, I think Dryson was using "sun" to mean all stars, not just our own Sun.

The Sun will never create iron in its core since it is not nearly massive enough to get that far in the nucleosynthesis process.

 

[Ken G]

Note also that it is not just an issue of the age of the Sun, the Sun will never produce any iron. That only happens in much more massive stars. You don't necessarily have to be massive enough to go supernova, the highest mass stars that don't supernova can make white dwarfs with iron in them, but that's still much more massive than the Sun. The Sun will never get hot enough to fuse anything past carbon and oxygen in any significant quantity.

 

[Monsterboy]

If nickel and iron are one of the last elements to be formed in the stars then how did we come across elements as heavy as uranium etc ?

 

[Ken G]

A common and good question. The difference is in what types of nucleosynthesis release net heat, so play a key role in stellar evolution and can delay the ultimate fate of the star, and what types simply are caused by a hot environment, as stars often encounter during late stages. So when the focus is only on fusion up to iron, it means the focus is on powering the star and affecting the evolutionary timescales. If core collapse occurs, all bets are off on past nucleosynthesis, as a huge amount of gravitational energy is released, and a super bright radiation field appears that can disrupt nuclei and undo essentially all the products of past nucleosynthesis in the central regions of the star. These new nuclear effects can result in all kinds of nuclei, much of which can be spewed out in the supernova bounce. But there's no concern that they do not release heat, because there is plenty of heat to go around.

 

[Drakkith]

Look up the R-process on wikipedia. I'm on my phone right now, otherwise I'd post the link myself.

 

[Matterwave]

If nickel and iron are one of the last elements to be formed in the stars then how did we come across elements as heavy as uranium etc ?

There are 2 processes (and a third, tentative process) generally thought to be attributable for the formation of matter heavier than iron and nickel. They are the R-process, the S-process, and the tentative P-process.

The others have mentioned the R-process, which is thought to occur in supernovae environments. It stands for the rapid capture of neutrons onto seed nuclei. The neutrons are captured "rapidly" meaning they are captured far faster than beta decay is allowed to happen. As such, you build up very very neutron rich, unstable, nuclei which then decay via many beta-decays into stable nuclei. The S-process, which is thought to occur in a variety of astrophysical environments, chief among them being in asymptotic giant branch stars, is the slow capture of neutrons by seed nuclei (usually starting from something much lighter than iron, since AGB stars were not massive enough to create iron in the first place). The nuclei capture neutrons very slowly, much slower than the beta decay process, and the nuclei basically move up the valley of stability 1 nucleon at a time, always staying in the valley of stability.

These two processes, which although not entirely understood, are quite well studied, but are not able to explain every nuclei that we see (they do explain many/most of the heavier elements). There are some proton rich nuclei which should not be able to form from either the R-process or the S-process, because, essentially to get to those nuclei via the S or R process, you must pass by stable nuclei which won't decay in the right way to those nuclei. These are the so called "p-process nuclei". These nuclei were first conjectured to be created by a "proton-capture process" (hence the name p-process), but the viability of such a process is...tenuous. There is current active research into how these "p-process nuclei" are formed (probably by some modified version of proton capture), and this is the least understood of the processes.

 

[Ken G]

Thank you for that extremely cogent summary, I had never even heard of the p-process though I knew that the R-process is hard or impossible to do in the laboratory and a lot about it is not yet understood.

 

[BrandonP]

"What prevents a star from collapsing after stellar death?"

If an object becomes smaller than its Schwarzschild radius,
then it will collapse into a black hole.

If not, then it won't.

That's really all there is to it.

 

[Murtuza Tipu]

Your first paragraph is not quite right. Gas pressure does not "stop" upon formation of an iron core, it is merely that the star cannot generate further heat from nuclear reactions and becomes unstable to collapse. i.e. The star does collapse! Perhaps what you mean is what halts the collapse (sometimes) before the star disappears inside its own event horizon and becomes a black hole? The answer is the degeneracy pressure of neutrons that are formed (endothermically) in electron capture events as the star collapses.

The analogy of filled "shells" is not too bad. In quantum mechanics we find that there are a finite number of possible quantum states per unit momentum per unit volume (often called "phase space"). In a "normal" gas, the occupation of these quantum states is governed by Maxwell-Boltzmann statistics - progressively fewer of these states are filled, according to .

In a Fermi gas at very high density or very low temperature, we reach a situation where the Pauli exclusion principle limits the occupation of these states to 2 particles per energy/momentum state (one for each spin); particles that might otherwise have occupied very low energy states are forced to occupy states of higher energy and momentum. In a "completely degenerate" gas, which is a good approximation for the electrons in a White Dwarf star or the neutrons in a Neutron star (the relevant case here), all the energy states are filled up to something termed the Fermi energy, with zero occupation at even higher energies.

Pressure is caused by particles having momentum (this is just basic kinetic theory). The large number of fermions with non-zero (even relativistic in some cases) momentum is the reason that a degenerate gas exerts a pressure, even if its temperature is reduced to close-to-zero. In fact, once a gas of fermions approaches complete degeneracy, a change in temperature has almost no effect on its pressure.

One point I will take issue with in your question, is the statement that "such particles cannot occupy the same small volume of space". In fact, the restriction is on the occupation of phase space. In a neutron star, the neutrons are almost touching each other, with separations of m. You can cram lots of particles into a small volume, but only at the expense of giving them large momenta.

 

[Drakkith]

Pressure is caused by particles having momentum (this is just basic kinetic theory). The large number of fermions with non-zero (even relativistic in some cases) momentum is the reason that a degenerate gas exerts a pressure, even if its temperature is reduced to close-to-zero. In fact, once a gas of fermions approaches complete degeneracy, a change in temperature has almost no effect on its pressure.

Question. If a group of fermions is degenerate with many of them having relativistic momentum, and a small amount of energy is added to raise the temperature, what happens to the momentum of the fermions?

 

[avito009]

If an object becomes smaller than its Schwarzschild radius,
then it will collapse into a black hole.

But I thought the maximum size of a stable white dwarf, approximately 3 × 1030 kg (about 1.4 times the mass of the Sun). Stars with mass higher than the Chandrasekhar limit ultimately collapse under their own weight and become neutron stars or black holes. Stars with a mass below this limit are prevented from collapsing by the degeneracy pressure of their electrons.

So who is right Brandon or Me?

 

[Drakkith]

But I thought the maximum size of a stable white dwarf, approximately 3 × 1030 kg (about 1.4 times the mass of the Sun). Stars with mass higher than the Chandrasekhar limit ultimately collapse under their own weight and become neutron stars or black holes. Stars with a mass below this limit are prevented from collapsing by the degeneracy pressure of their electrons.

So who is right Brandon or Me?

A white dwarf is not smaller than its Shwarzchild radius so it doesn't collapse.

 

[Ken G]

So you are both right, though your answer is more useful because it can help us understand why and when stars can go below their Schwarzschild radii.

 

[avito009]

A white dwarf is not smaller than its Shwarzchild radius so it doesn't collapse.

So correct me if I am wrong. If a star has mass greater than the Chandrasekhar Limit, due to this greater mass the gravitational force is more (Moon has lesser gravity than Earth because mass of Moon is lesser than mass of Earth. So grater the mass greater the gravitational pull). So degeneracy pressure provided by the electrons is weaker than the inward pull of gravity. So when this mass is very less the schwarzschild radius is also less. So when the radius of the star falls below the schwarzschild radius then we get a black hole.

Am I right?

 

[Drakkith]

So when this mass is very less the schwarzschild radius is also less.

Exactly. You'd need to compress the Moon to a much smaller volume than the Sun in order for it to form a black hole.

 

[Murtuza Tipu]

Have a look at this applet (it is designed for electrons in WDs, but will do here). It shows occupation index vs energy for fermions. To get the momentum distribution, you multiply this by the density of momentum states g(p) = 8pi p^2/h^3. Look at what happens when you increase the temperature whilst keeping the density constant. You get a partial degeneracy and a tail of particles with energies higher than the Fermi energy.geogebratube.org/student/b87651#material/28528