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I'm a high school student with a question about supernovas and the life cycle of stars. I understand that supernovas occur in massive stars when they run out of fuel and collapse, resulting in a powerful explosion. However, I wonder why this process does not occur for less massive stars. If these stars also run out of fuel and begin to contract, why do they not explode in a manner similar to massive stars, but instead form planetary nebulae through the shedding of layers? Why does the contraction of a less massive star not result in an explosion, just a less intense one compared to massive stars?

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2 Answers 2

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The short answer is that electron degeneracy pressure is able to support the core of a low-mass star (less than 8 solar masses) indefinitely but not the core of a more massive star, which becomes unstable and collapses, triggering a supernova.

Details

The weight of a star is supported by a pressure gradient. The gas at the centre of the star must have a pressure that is high enough to support the layers above it.

This pressure can arise in several ways. There is the pressure of a perfect gas, where the kinetic energy of the gas particles is proportional to the temperature. This is what currently supports the weight of the Sun. In massive stars there can also be radiation pressure - the typical photon momentum in a the centre becomes so large that it provides a significant pressure term. Finally, there is electron degeneracy pressure - this is a consequence of the Pauli Exclusion Principle, which forbids indistinguishable electrons from occupying the same quantum states.

Electron degeneracy pressure becomes very important in the cores of stars towards the ends of their lives. The plasma density becomes so high in the core that the electrons must occupy a large range of energy states, as dictated by the Pauli Exclusion Principle. As a result of this energy they exert a pressure but importantly, this degeneracy pressure would be maintained even if the gas cooled.

Now, in stars there is a broad division into high-mass stars (those above 8 solar masses) and lower mass stars. For stars in the lower mass category, electron degeneracy pressure becomes dominant after core helium burning, when the core composition is a mixture of carbon and oxygen nuclei and lots of free electrons. The core, which is always less than about 1.2 solar masses, compresses a bit, but never achieves temperatures sufficient to ignite carbon because electron degeneracy pressure halts the contraction. The core cools, the outer layers of the star are lost gradually over millions of years in stellar winds and the cooling core is left behind as a remnant - a white dwarf - that will simply continue to cool off while supported by degenerate electrons.

In more massive stars, the core does reach temperatures high enough to ignite carbon and subsequently to ignite fusion reactions in heavier elements too. The endgame for such stars is a core of nickel and iron in which further fusion reactions are energetically unfavorable and is compressed to the point that is supported by electron degeneracy pressure.

The big difference between the evolution of the high-mass and lower mass stars, in addition to the core composition, is that in higher mass stars the core quickly becomes too massive (bigger than about 1.2 to 1.3 solar masses) to be supported by electron degeneracy pressure. An instability is triggered by the capture of electrons by nuclei, the core collapses suddenly, which releases the gravitational potential energy that is responsible for a supernova. In lower mass stars, the core is less massive, never reaches this instability limit and is able to be supported by electron degeneracy and thus there is no collapse.

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  • $\begingroup$ "a white dwarf - that will simply continue to cool off while supported by degenerate electrons." Isn't it specifically non-degenerate electrons? Doesn't electron degeneracy pressure arise from the fact that electrons resist degenerating, and if you don't overcome that pressure, then degeneration doesn't happen? In more or less the same way that many buildings are supported by non-crumbling concrete? Or have I completely misunderstood? $\endgroup$
    – Arthur
    Commented May 10, 2023 at 9:22
  • $\begingroup$ @Arthur degeneracy pressure arises because the electrons are in a degenerate state, filling all available energy levels up to their Fermi Energy. This non-zero kinetic energy is what leads to pressure. Degeneracy pressure is not "overcome" at any point it just gets bigger as you squeeze the density higher. $\endgroup$
    – ProfRob
    Commented May 10, 2023 at 11:25
  • $\begingroup$ Fair enough. I just thought it was weird to call it "degenerate" before they break and collapse under the pressure. But if this is what "degenerate" means in this context, then that's what it means. $\endgroup$
    – Arthur
    Commented May 10, 2023 at 11:37
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Well, there is a limit called the Chandrasekhar Limit which tells us that if a star's mass is more than $1.44$ times the mass of our Sun, if will die in a big explosion called a supernova and turn into a neutron star. If the mass of the star is less than the Chandrasekhar Limit, then it would 'implode' and turn into a white dwarf.

To explain a bit more, what happens when a star loses out on hydrogen fuel, is that it starts to fuse other elements like helium (product of nuclear fusion of hydrogen), oxygen, silicon, etc. And that fusion continues outwards, thus star expands. Once it runs out of all its fuel, its outward pressure drops significantly. At one point the gravity would be more and thus would cause the star to collapse. This is an implosion. Now, if the star's mass is more than the limit, then once the star collapses, the atoms inside get so close to each other that they start to repel away. This repulsion continues to build up, and the core gets very dense, until a point when the repulsion is more than the gravity and suddenly all of the matter, except for the core, gets spewed away into space, creating an explosion which we call a supernova. The core that remains is called a Neutron star, which is the densest of the stellar objects known till date. Now, if the star's mass is less than the limit, then the repulsion won't be enough to cause the explosion and thus the star just 'implodes' and doesn't 'explode'. This creates a very tiny ball of very dense material, called a white dwarf.

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  • $\begingroup$ The Chandrasekhar limit refers to the mass after the explosion, not before. It's just the maximum mass of a white dwarf. $\endgroup$
    – Sten
    Commented May 10, 2023 at 6:49
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    $\begingroup$ The dividing line between stars that explode and those that become white dwarfs is about 8 solar masses. $\endgroup$
    – ProfRob
    Commented May 10, 2023 at 7:05
  • $\begingroup$ @Sten, it seems like it is actually true that it refers to the maximum stable mass of a white dwarf, but I'm a bit confused at this point. Does the mass of the star change as it shrinks into a white dwarf? If it doesn't, then it shouldn't make a difference, right? $\endgroup$ Commented May 10, 2023 at 19:06
  • $\begingroup$ Yes, the mass shrinks. Most is blown off and is what forms the so called planetary nebula $\endgroup$ Commented May 10, 2023 at 19:08
  • $\begingroup$ @NathanOliver, thank you for letting me know that. So, is it that any star of mass less than 8 solar masses would turn into a white dwarf of mass less than 1.44 solar masses and any star of mass more than 8 solar masses would turn into a white dwarf of mass more than 1.44 solar masses and further into a supernova? $\endgroup$ Commented May 10, 2023 at 19:14

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