Carbon in the grand scheme

Amara Graps (
Thu, 21 Oct 1999 21:28:16 +0100

Robert J. Bradbury ( Wed, 20 Oct 1999 writes:

>I find it just too convenient that big stars like to spit
>out lots of carbon and carbon just "happens" to be both
>good for building wet nanotech *and* dry nanotech. Why
>isn't the hardest material "boron" or something that is
>*really* scarce? One could argue that common universes
>could be structured to allow the evolution of wet nanotech
>but dry nanotech would be very resource limited! Instead
>we have a playing field that seems optimal for both random
>and directed evolution of complexity.

About the occurrence of carbon in big stars.

Robert, I'm not sure if your question is:

Why carbon ?

(The answer is "because nucleosynthesis says it must be")


Why is nucleosynthesis like this in our universe ?

(I don't know the answer to that)

I'll answer to the first one. Perhaps you know about nucleosynthesis and stellar evolution, in which case, you can pass this message over, but some others here may not know these things, so I'll write a little about it.

To begin, I'll mention that the theory of stellar structure and evolution is probably the most theoretically and experimentally sound aspect of astrophysics and it has a critical role in our current understanding of the universe (stellar ages etc.).

In ordinary main-sequence stars like the Sun, the primary process for fusion is the proton-proton chain. In this reaction, four protons (these are the hydrogen nuclei) are fused into one helium nucleus (also called an alpha particle). An alpha particle has about 1% less mass than four protons. The rest of the mass is turned into gamma rays - high energy photons.

In chemical notation:

4 1H + 2 e --> 4He + 2 neutrinos + 6 photons

Fusion can only happen when the protons can get close to each other. It's a tricky business since the protons both have a positive charge, and at lower temperatures they repel each other, so then one needs to have high temperatures, like those inside of a star, so that the protons can hit each other at high speed. The proton-proton chain has several intermediate steps where electrons and antielectrons annihilate each other, more protons collide into each other, and a helium atom is made and with the helium and neutrons and protons bouncing around in the hot gas.

In chemical notation, it looks like:

1H + 1H --> 2H + antielectron + neutrino 1H + 1H --> 2H + antielectron + neutrino electron + antielectron --> photon + photon electron + antielectron --> photon + photon 2H + 1H --> 3He + photon
2H + 1H --> 3He + photon
3He + 3He --> 4He + 1H+ 1H

Or Rewriting:

6 1H + 2 e --> 4He + 2 1H + 2 neutrinos + 6 photons

Which is just our original equation above:

4 1H + 2 e --> 4He + 2 neutrinos + 6 photons

So now we have made helium. What's next?

After the exhaustion of hydrogen, the next reactions that may take place in the center of the star involve 4He to fuse into carbon. Helium burning has to take place through a nuclear process called the triple-alpha process;

3 4He --> 12C + photon

A nucleus could continue to grow by successively capturing alpha particles, and, indeed, this is the initial sequence of nucleosynthesis in heavier and heavier stars.

12C + 4He --> 16O
16O + 4He --> 20Ne
20Ne + 4He --> 24Mg

Now, why will smaller, ordinary stars like our Sun not create heavier elements than helium?

Heavier elements generally have larger electric charges. To fuse them into yet heavier elements requires overcoming greater Coulomb barriers than for elements with small electric charges; so such reactions will not be initiated until the star acquires higher temperatures (the same reasoning already discussed in the proton-proton chain introduction) Thus, helium reactions generally require higher temperatures than hydrogen reactions; carbon reactions, higher temperatures than helium reactions, etc. This pattern is a general feature of thermonuclear reactions of charged nuclei inside stars. The more massive a star, the hotter (and faster, lifetimes of massive stars are shorter) it burns, and the heavier the elements that it generates inside it.

A star spends most of its time burning hydrogen into helium, and this evolution time is called the "main sequence". After hydrogen is exhausted near the star's center, the star is left with a core consisting of helium and a small amount of heavy elements. Initially, the temperature of the core is below the E8 K required for helium ignition. But as the star contracts through gravitational contraction, the center can burn hot enough to ignite helium.

Our Sun won't burn hot enough during its evolution to fuse helium into carbon. But heavier stars will. When helium is exhausted, the next element to react is 12C which takes place temperatures around 5-10 E8 K.

So you see, an important feature in understanding nucleosynthesis is the energetics of fusion, as determined by the atomic mass excesses and the mean binding energy per nucleon. "boron" doesn't have the right atomic and binding energy to fit in the scheme of the nucleosynthesis processes (P-P chain, CNO chain), and so you see how carbon is a natural fusion product of heavier stars.

Now, a side note about Iron and those really heavy elements that you find in terrestrial planets and sometimes in humans :-)

The structure of the nucleus of and atom can be understood roughly as a balance between the attractive and repulsive parts of the strong nuclear force between protons and neutrons, modified by the electric repulsion between the protons. The strong nuclear force has a kind of attractive-repulsive duality. As long as the nucleus is not too big, the nuclear force, being short-range, tends to win over the repulsion of the electric force. It is then advantageous to add protons or neutrons to have heavier nuclei. But only if the nuclei can keep together- "binding".

But at Iron-56, the nuclear binding energy saturates - its nucleus is the largest in which the constructive short-range strong force has any advantage over the destructive long-range electric force. If one adds more protons or neutrons, then the binding energy per added particle decreses, and the nuclei becomes unstable and starts decaying or starts fissioning (uncontrolled fission chain reactions led to the A-bomb, for example). And radioactive decay, is a useful way to date rocks because unstable nuclei doesn't last for long, and so the existence of elements like uranium and thorium in something can give us that object's age.

So if you want to make elements heavier than iron, then you have to look to unusual processes to overcome all of the above physical issues. In nucleosynthesis, two processes that can make elements heavier than iron is the "s-process" and the "r-process" and the "p-process". These processes only can occur in really massive stars, where the conditions inside are extreme.

Then you need a way to push those elements out into space. An explosion will do it. The dust that you see in supernovae remnants was mostly _not_ produced in the supernovae event. It was present in the star's outer envelope before the supernovae explosion. The explosion just pushed that material outwards.

That's my stellar nucleosynthesis lesson.

Hope it was helpful,


Amara Graps                  email:
Computational Physics        vita:  finger
Multiplex Answers            URL:
      "Trust in the Universe, but tie up your camels first."
                (adaptation of a Sufi proverb)