Nuclear Burning in Stars -- Nucleosynthesis

We have already met the hydrogen burning chains, the proton-proton chain and the carbon-nitrogen-oxygen cycle. We now want to introduce the other nuclear reactions available to stars. The nuclear burning chain in stars begins with hydrogen and ends with iron (Fe). The process starts with the simplest element hydrogen (1 proton) and produces more and more complex elements until the chain stops with iron (26 protons). Fe is the most tightly bound nuclear structure (in a certain sense is the easiest nucleus to hold together). Thus, when combining elements up to Fe a little bit less energy is required to hold the product nucleus together than was required to hold the individual fusing nuclei together. This is the energy released in the fusion reaction. If you try to fuse elements more massive than Fe, then the product nucleus requires more energy to hold it together than was contained in the individual fusing nuclei. In this case, you must add energy to make the fusion process go! This is not an efficient way to generate energy. Fe is the last available nuclear fuel for a star.

I have several comments on the above table:

• Each successive step in the nuclear burning chain uses the ashes of the previous process as fuel and so, each step in the chain requires higher temperatures in order for the reactions to go. This has several consequences:
  • Since we have that P ~GM**2/R**4 which implies that T ~ M/R for an ideal gas (ordinary gas pressure), this means that the more massive a star is, the less its core has to contract in order to reach the ignition temperatures ===> a smaller compression which leads to lower densities at ignition ===> less chance that the electrons in the core will become degenerate before the ignition temperature is reached.

    For lower mass stars, the compression needed to reach ignition temperature is greater ===> a greater chance that the electrons will become degenerate before ignition temperature is reached ===> core will stop contracting before the next fuel can ignite. This is what stops the burning cycle before Fe in the lower mass stars.

  • Since the amount of fuel for each successive step is smaller and the core temperatures and densities are higher, it takes a shorter amount of time for the star to use up its allotted fuel. The final stages of nuclear burning only take days to weeks to run to completion!!

• An interesting point made later is that the dominant source of energy loss from a star after around the stage of Carbon burning is through neutrino radiation and not through photon losses.