Why are the elements formed in main sequence stars not in some simple pattern?

[nhnifong]

The elements formed in a main sequence star are these,

H  (1)  
He (2)  
C  (6)  
O  (8)  
Ne (10)  
Si (14)
Fe (26)

What I don't understand is why are they restricted to these? Why don't the elements in between these get formed accidently?

And for the elements past Iron, I know that they cannot be formed exothermically, but there's no shortage of energy around, they should be getting formed accidently as well in a heavy star, even if they don't contribute to it's energy production.

Why are they not in a simple pattern, such as the Integers, powers of two, or the Fibonacci sequence?

[Brotoro]

The elements formed inside the cores of high mass stars are NOT restricted to those that you listed. Those are just some major products along the way that can hang around for a while until the temperature and pressure builds up to the point where the fusion of those elements can occur (given a massive enough star...except for iron on the bottom, which is dead end for fusion energy production).

The jump from helium to carbon, for example, occurs because two heliums would form boron 8, which is unstable and immediately breaks apart into two heliums. Once the temperature gets up to around 100 million Kelvin, the reactions happen fast enough that the boron 8 has a substantial chance of being hit with another helium before breaking apart, and you get carbon as a result of this "triple alpha" process. Oxygen is also formed at this stage when some of the carbon fuses with another helium.

If the star is massive enough, it can go on to carbon burning which can produce neon, magnesium, sodium, oxygen (for example, two carbons fusing together can make a neon by spitting out an alpha particle--helium nucleus--after the reaction).

If the star is massive enough, it can go on to neon burning, which leaves behind mainly oxygen and magnesium. More massive still, and the star can start fusing the oxygen, which gives you several elements, but mainly silicon and sulphur.

Once you get to the stage where you can burn silicon, the temperatures in the core of the star are getting so high that the gamma rays have enough energy to knock some of the nuclei apart into alpha particles...and at a high enough temperature, the silicon and sulphur will start fusing with those alpha particles in a rapid chain of reactions that cook up nickel 56...which decays to iron 56.

As always in the shorthand of stellar astrophysics, "burning" as used above refers to thermonuclear fusion.

Edited November 19, 2013 by Brotoro

[nhnifong]

Interesting, I didn't consider that fusion and fission were both happening in stars....

Why is a iron a dead end? I've heard that it's not exothermic to fuse iron, but why should that stop it from happening?

[Awaras]

It probably does happen, but not often enough to produce more than trace amounts of heavier stuff. Untill the boom, of course.

[Brotoro]

Interesting, I didn't consider that fusion and fission were both happening in stars....

Why is a iron a dead end? I've heard that it's not exothermic to fuse iron, but why should that stop it from happening?

I wouldn't call it "nuclear fission" since that might confuse people. When two oxygen atoms fuse, for example they bring in so much energy that the resulting sulfur nucleus that you might expect to result usually sheds the excess energy by spitting out an alpha particle or neutron or proton, etc. (by can rarely stay together as a sulfur nucleus and emit all of the energy as a gamma ray). This is more of a decay than a nuclear fission. In the case of nuclei that are broken apart by gamma rays into the alpha particles that fuel the silicon burning, the term to use is "photodissociation", not fission.

I said that iron is a dead end for fusion energy production (because it sits at the peak of the curve of binding energy). Nuclear reactions that absorb energy (instead of liberating energy) can and do occur in stars in relatively small numbers, but are not going to help the star fight off gravitational collapse. In a supernova explosion where lots of energy is being released and there are lots of neutrons flying around, a large number of these energy-absorbing reactions can occur and cook up lots of heavy elements.

[K^2]

This isn't the whole answer, but it's a big part of it.

These are binding energies of stable nuclei. Note that iron has the highest binding energy. That means to make iron into a heavier element you have to add energy. Up to iron, energy is released as elements fuse together.

From this graph, He⁴, C¹², O¹⁶, and Ne²⁰ immediately stand out. You expect to see a lot of these four elements in a star, and you, in fact, do.

The reasons why it works this way are a bit complicated. So first of all, neutrons and protons are fermions. That means that two cannot be in exactly the same state. They can, however, differ only by a spin. So at the lowest energy state, you can have two neutrons and two protons. That's He⁴. This group of four is so tightly bound because of that, that it behaves almost like a single particle. In fact, it has a name. Alpha particle. Well, if you consider heavier nuclei, the protons and neutrons in it still like to keep that tight packing, so they are often found in groups of four. Consequently, C¹² nucleus can almost be pictured as three He⁴ nuclei bound together. There are a lot of experiments that confirm this.

Ne²⁰ is the next interesting case. Just like with electron shell, once you fill out the ground state, at a higher level you have two vacancies for particles with no angular momentum, and six for particles with orbital angular momentum. Levels are nowhere as neatly arranged as in the atomic orbitals, but up to this point you can use roughly the same rule of thumb. As the result, Ne²⁰ has a full shell, giving it a total of 10 protons and 10 neutrons, and a rather high binding energy.

After that more complicated effects take over, and the curve becomes fairly uniform as it peaks at Fe⁵⁶ and then comes down.

So why did I say that this isn't the whole story? Take a look at beryllium. You expected to see Be⁸, didn't you? Pants to that, says nuclear physics, laughs wildly in your face, and jumps out of the window. The fact is, a He⁴ is so stable that a Be⁸ almost instantly falls apart into a pair of these. Oddly enough, a stray neutron in Be⁹ prevents that decay, making it the only stable isotope of beryllium.