Section 2.4 - Stellar Nucleosynthesis and Degenerate Matter

Concocting the Periodic Table of Elements

When the Universe was born out of the Big Bang, most of the matter produced was hydrogen, the simplest atom - one proton, one electron. From the previous section, we learned that for most of their lives, stars power themselves through the thermonuclear fusion of hydrogen into helium. Since stars make up the vast majority of all matter in the Universe, hydrogen and helium are by far the most abundant elements. But the periodic table has more than just hydrogen and helium; all the heavier atoms had to be cooked up in the nuclear furnace at the core of a star too. 

The Triple Alpha Process

As stars run out of hydrogen, they expand into red giants and start fusing helium into heavier elements through the triple alpha process (named as such because helium nuclei are also known as alpha particles)

This reaction is particularly awesome - if two helium-4 nuclei fuse, that would make beryllium-8, but that's an extremely unstable nucleus that will immediately break apart again. In order to form a stable nucleus that won't decay, three helium nuclei need to all merge at the same time to form carbon-12. This would be exceedingly unlikely under normal circumstances, but it's possible given the immense heat and pressure inside of a star. For there, stable isotopes of nitrogen and oxygen can be formed from the CNO cycle. 

From the previous section we learned that for small stars without enough mass to continue nuclear fusion beyond oxygen, the process stops and they die off as white dwarves. For this reason, white dwarves are made of mostly carbon and oxygen (although it's a bit more complicated than that, discussed further below).   

This process is why apart from hydrogen and helium, carbon, nitrogen, and oxygen (elements 6, 7, and 8) are relatively abundant while lithium, beryllium, and boron (elements 3, 4, and 5) are quite rare. Our bodies are primarily made of hydrogen, carbon, nitrogen, and oxygen, 4 of the 5 most abundant elements in the Universe

Fusing up to Iron

We saw this diagram in the previous section. If a star is large enough, it can keep fusing oxygen into heavier and heavier elements, but only up to a point. That point occurs at iron-56 (26 protons, 30 neutrons) for a very interesting reason related to the interaction between the strong force and the electromagnetic force (see here for a refresher on the four forces).

The stability of a nucleus is a tradeoff between the attractive strong force and the repulsive electromagnetic force between positive protons. Let me explain:

  • For small nuclei, each additional proton increases the stability of the nucleus because it adds to the amount of strong force present (recall that the strong force is what binds atomic nuclei)
  • But for large nuclei, each additional proton actually reduces the stability of the nucleus. That's because the strong force has very, very limited range. As the nucleus gets really large, each additional proton isn't able to add much more to the total strong force, but it increases the repulsion caused by the electromagnetic force

So based on the two above statements, there must be an inflection point. That transition occurs at iron-56, which is the most stable nucleus, and is also why iron is relatively abundant in the Universe. But for this reason, nuclei beyond iron can't be formed by nuclear fusion anymore.

For nuclei smaller than iron, each additional nucleon (proton or electron) increases the stability of the nucleus. But beyond iron-56, each additional nucleon detracts from the nucleus' stability

Onward to Uranium!

Uranium is generally considered the heaviest naturally occurring element in nature; the superheavy stuff beyond that is artificially synthesized. Getting from iron to uranium involves neutron capture resulting from supernovae. When a star explodes, it can blast existing iron atoms with neutrons, and since neutrons are neutral, they can more easily interact with existing nuclei. From here, two processes occur:

  • s-process (slow): when a neutron strikes a nucleus, one of two things can happen. If the isotope is stable, the neutron will stick. If the isotope is unstable, the neutron will undergo beta decay, transforming into a proton and an electron and forming the next element in the process
  • r-process (rapid): similar to the s-process, but the neutrons bombard the existing nuclei so quickly that there isn't enough time for beta decay. As a result, the nuclei formed are generally very neutron heavy

And there you have it - everything we see in the Universe was once inside the heart of a star. We are all made of stardust!

If you wish to make an apple pie from scratch, you must first invent the Universe" - Carl Sagan

Degenerate Matter

There's one last concept related to white dwarves and neutron stars that I think is worth discussing. At extreme densities, there's a state of matter known as degenerate matter where particles must occupy extremely high states of kinetic energy to satisfy the Pauli exclusion principle (see the section on quantum mechanics if you need a refresher). 

At low densities (left), there are a lot of combinations of position and momentum available, but as the particles are squeezed together (right) they have to keep getting faster and faster to maintain the Pauli exclusion principle

A lot of strange things start to happen to degenerate matter. For example, degenerate gases don't obey ideal gas laws of pressure and temperature, and higher masses of degenerate matter counter-intuitively occupy smaller volumes

Electron degeneracy in white dwarves is what prevents them from collapsing further. The more you try to compress matter in a white dwarf, the more and more the electrons come up against the limit set by the Pauli Exclusion Principle because there aren't many free energy states left. As a result, the electrons speed up and exert an outward pressure that counteracts further gravitational contraction

The Chandrasekhar Limit

The problem with electron degeneracy is there's a fundamental limit to how fast the electrons can speed up to keep exerting pressure, and that's the speed of light

Astrophysicist Subrahmanyan Chandrasekhar demonstrated the Chandrasekhar Limit, which states that the maximum mass of a stable white dwarf is ~1.4x the mass of the Sun. Beyond that, the white dwarf must explode and collapse into a neutron star

By extension, a neutron star is supported by neutron degeneracy, and there is an analogous limit to a neutron star's mass called the Tolman-Oppenheimer-Volkoff Limit. The current estimate for the limit is about 2.17 solar masses. Beyond that, the neutron star will collapse into a black hole.