Why does the core collapse happen so fast in a supernova?

[rnielsen25]

TL;DR Summary

Why does the core collapse happen in less than a second, rather than a slower contraction by the Kelvin-Helmholtz mechanism?

I just started my master's degree and I'm currently taking a course in astrophysics. However, it seems like I have misunderstood what prevents stars from collapsing (I will elaborate below). Why is it, that as soon as a massive star has finished the fusion processes, the collapse will happen in less than a second and not a slow contraction by the Kelvin-Helmholtz mechanism?
I will summarize my understanding below:

During the main phase, stars are in hydrostatic equilibrium, where a pressure gradient balances the gravitational force. This prevents stars from collapsing. The pressure is mainly caused by gas pressure, radiation pressure, and electron degeneracy pressure (Where my book explains that stars which are dominated by radiation pressure are unstable. So it's mainly the gas pressure and degeneracy pressure dominating).

Before nuclear fusion processes were discovered, we already had models that could describe how stars like the sun could shine for millions of years. This model is described by the Kelvin-Helmholtz mechanism, which essentially describes how the sun would continuously contract (very slowly), without changing temperature and emitting electromagnetic radiation in form of loss in gravitational potential energy. The mechanism can be summarized as: the star emits light and therefore cools. The temperature decrease causes the pressure to drop, which causes the star to contract. The contraction releases gravitational potential energy and thus heats the core. And then the cycle continues.
This process is also happening in Jupiter and brown dwarfs and the pre-fusion period at the birth of a star. It is my understanding that planets and brown dwarfs eventually stop their collapse when the electron degeneracy pressure balances the gravitational force.
My lecturer told me that experimentally, we do not have the precision to observe a possible contraction of the sun in such detail, that we can falsify this mechanism. But we, of course, know that this is not why stars emit light because it contradicts the age of the earth (billions of years), and nuclear fusion also explain other observations, that the contraction model doesn't.

So it is my understanding, that the fusion process releases energy and keeps the star in thermal equilibrium (producing as much energy as the star releases through radiation). This effectively prevents the contraction process from happening (Note, I do know that the radius of a star changes dramatically during the star's life cycle, i.e. when the star begins fusion of helium). However, as soon as a massive star has reached the fusion phase, where it's producing iron in the core, the fusion stops taking place (because the fusion of iron is not energetically favorable). At this stage, the star usually has an onion layer structure with iron at the core and lighter elements in the outer layers. At this point, we often learn that as the energy production stops, the core will collapse in less than a second and cause the outer layers to free fall towards the center.

But why does this process happen so fast? Couldn't the star contract slowly by the Kelvin-Helmholtz mechanism? Or what is that prevents this slower contraction? Is the explanation that massive stars emit energy at such a high rate, that if you calculated the contraction rate by the Kelvin-Helmholtz mechanism, it would in fact happen in less than a second?

 

[rnielsen25]

TL;DR Summary: Why does the core collapse happen in less than a second, rather than a slower contraction by the Kelvin-Helmholtz mechanism?

I just started my master's degree and I'm currently taking a course in astrophysics. However, it seems like I have misunderstood what prevents stars from collapsing (I will elaborate below). Why is it, that as soon as a massive star has finished the fusion processes, the collapse will happen in less than a second and not a slow contraction by the Kelvin-Helmholtz mechanism?
I will summarize my understanding below:

During the main phase, stars are in hydrostatic equilibrium, where a pressure gradient balances the gravitational force. This prevents stars from collapsing. The pressure is mainly caused by gas pressure, radiation pressure, and electron degeneracy pressure (Where my book explains that stars which are dominated by radiation pressure are unstable. So it's mainly the gas pressure and degeneracy pressure dominating).

Before nuclear fusion processes were discovered, we already had models that could describe how stars like the sun could shine for millions of years. This model is described by the Kelvin-Helmholtz mechanism, which essentially describes how the sun would continuously contract (very slowly), without changing temperature and emitting electromagnetic radiation in form of loss in gravitational potential energy. The mechanism can be summarized as: the star emits light and therefore cools. The temperature decrease causes the pressure to drop, which causes the star to contract. The contraction releases gravitational potential energy and thus heats the core. And then the cycle continues.
This process is also happening in Jupiter and brown dwarfs and the pre-fusion period at the birth of a star. It is my understanding that planets and brown dwarfs eventually stop their collapse when the electron degeneracy pressure balances the gravitational force.
My lecturer told me that experimentally, we do not have the precision to observe a possible contraction of the sun in such detail, that we can falsify this mechanism. But we, of course, know that this is not why stars emit light because it contradicts the age of the earth (billions of years), and nuclear fusion also explain other observations, that the contraction model doesn't.

So it is my understanding, that the fusion process releases energy and keeps the star in thermal equilibrium (producing as much energy as the star releases through radiation). This effectively prevents the contraction process from happening (Note, I do know that the radius of a star changes dramatically during the star's life cycle, i.e. when the star begins fusion of helium). However, as soon as a massive star has reached the fusion phase, where it's producing iron in the core, the fusion stops taking place (because the fusion of iron is not energetically favorable). At this stage, the star usually has an onion layer structure with iron at the core and lighter elements in the outer layers. At this point, we often learn that as the energy production stops, the core will collapse in less than a second and cause the outer layers to free fall towards the center.

But why does this process happen so fast? Couldn't the star contract slowly by the Kelvin-Helmholtz mechanism? Or what is that prevents this slower contraction? Is the explanation that massive stars emit energy at such a high rate, that if you calculated the contraction rate by the Kelvin-Helmholtz mechanism, it would in fact happen in less than a second?

So I tried to estimate the contraction rate for Betelgeuse using the Kelvin-Helmholtz mechanism. I used it's estimated mass, radius and luminosity. This gave me a contraction rate (dR/dt) around -600 m/s. This rate is a lot faster than the sun's case and corresponds to a lifetime of around 28 years (assuming the entire radius of Betelgeuse would contract to a singularity at this rate). But still much slower than a second and a free fall collapse.

 

[willem2]

At near-supernova temperatures and pressures, nuclear reactions will produce neutrino's. This will rob the core of the star of energy, and the neutrino's are radiated away much more easily. The energy loss wil increase the rate of collapse, and the temperature and pressure, and this will increase the neutrino production, and make the contraction faster.

 

[Drakkith]

But why does this process happen so fast? Couldn't the star contract slowly by the Kelvin-Helmholtz mechanism? Or what is that prevents this slower contraction?

I believe the Kelvin-Helmoltz mechanism merely gives the amount of energy provided by gravity for a star or planet. It was proposed as a possible solution to how the Sun powers itself, though we now know that fusion is the main energy source for the Sun and other stars. I don't think the Kelvin-Helmholtz mechanism itself tells you how fast something contracts. For that you need to know the power output somehow.

The key to understanding how collapse happens so fast is to recognize that the normal mechanisms that support are star against gravitational collapse are disrupted or overpowered during a core collapse. There are a variety of ways this happens: electron capture (for example in Super-AGB stars), loss of electron degeneracy pressure (in the collapse of iron/nickel cores) and electron-positron pair instability (in super-massive stars) are some examples.

For iron/nickel cores, which are degenerate, the pressures become so high that it is simply more energetically favorable for electrons to be captured by nuclei and the entire mess turning into a sea of neutrons than for the core to remain held up by electron degeneracy pressure. The cause of the collapse here is the removal of electron-electron repulsion from the core. Electrons, being lighter in mass than neutrons, are 'larger' in some sense of the word and will try to stay further apart from other electrons than neutrons will stay apart from other neutrons. So the whole core collapses to a tiny fraction of its original size as the electrons and nuclei turn into neutrons.

In super-AGB stars (super-asymptotic giant branch), a similar mechanism to that which occurs in iron/nickel cores occurs with the exception that super-AGB stars have oxygen and neon in their cores. Unlike iron and nickel, oxygen and neon release a lot of energy when they fuse. When the core collapse occurs, the core temperature and density spikes, igniting a runaway fusion reaction that blows the star apart. This collapse is called an electron capture supernova (though it is still a core collapse supernova).

In certain super massive stars, the core is primarily held up not by degeneracy pressure from electrons, but by pressure from light itself in the form of gamma rays. These gamma rays can be energetic enough to produce electron-positron pairs that temporarily rob the star of support until they annihilate with each other to produce more gamma rays that then hold up the star. In pair instability supernovas the star undergoes pulsations or fluctuations that cause the production and energy of gamma rays to spike. This increase in energy makes it more likely for the gamma rays to interact with nuclei in the core and produce electron-positron pairs. Then this increase in the production of matter-antimatter pairs robs the star of support, letting the outer layers to collapse inward, exerting more pressure on the core, which compresses it and heats it up, which then causes even more energetic gamma rays to be created, which then creates even more matter-antimatter pairs, etc etc. The whole thing quickly turns into a runaway collapse that blows the whole star apart as oxygen and possibly some heavier elements undergo runaway fusion. The cause of the extremely fast collapse is the sudden loss of support by gamma rays.