Nuclear Fusion Reaction Mechanisms in Stars

Proton-Proton Chain Reaction

This is the most commonly known nuclear fusion reaction in stars. The nucleus of deuterium, called a deuteron, is formed by the combination of one proton (p) and one neutron (n). Therefore, for two protons to combine and form a deuterium nucleus, one of the protons must change into a neutron. So how can a proton change into a neutron?

• ‘Beta decay’ is when a neutron ($n$) changes into a proton ($p$) while emitting an electron ($e⁻$) and an antineutrino ($\nu_e$). The reaction equation for this is $n \rightarrow p + e^{-} + \overline{\nu_e}$.
• The process of a proton ($p$) changing into a neutron ($n$) corresponds to the reverse of beta decay. So this is called ‘inverse beta decay’. What does the inverse beta decay reaction equation look like? There’s nothing special about nuclear reaction equations. You just need to swap the positions of the proton and neutron, change the electron to a positron, and the antineutrino to a neutrino. Expressed as an equation, it’s $p \rightarrow n + e^{+} + \nu_e$.

After a deuterium nucleus is formed through the above process, a helium-3 nucleus is created through $^2_1D + p \rightarrow {^3_2He}$, and finally, two helium-3 nuclei collide to form a helium-4 nucleus and two protons.

In fact, there isn’t just one reaction path for the proton-proton chain reaction. The above case is the most representative, but there are a few other paths as well. However, the other paths don’t account for a high proportion in stars with masses less than the Sun, and in stars with masses 1.5 times that of the Sun or more, the CNO cycle, which we’ll discuss later, accounts for a much larger proportion than the proton-proton chain reaction, so we won’t cover them separately here.

This proton-proton chain reaction predominantly occurs at temperatures of about 10-14 million K. In the case of the Sun, with a core temperature of about 15 million K, the pp chain reaction accounts for 98.3%. (The remaining 1.3% is accounted for by the CNO cycle)

Carbon-Nitrogen-Oxygen Cycle (CNO Cycle)

The CNO cycle is a reaction where carbon accepts a proton and changes to nitrogen, then nitrogen accepts a proton and changes to oxygen, and so on, ultimately accepting 4 protons to produce 1 helium and returning to carbon. A characteristic of this is that carbon, nitrogen, and oxygen act as catalysts. Theoretically, this CNO cycle predominantly operates in stars with masses 1.5 times that of the Sun or more. The difference in reactions according to stellar mass lies in the temperature dependence of the proton-proton chain reaction and the CNO cycle. The former starts at relatively low temperatures around 4 million K, and its reaction rate is said to be proportional to the 4th power of temperature. The latter, on the other hand, starts at about 15 million K but is very sensitive to temperature (reaction rate proportional to the 16th power of temperature), so at temperatures above 17 million K, the CNO cycle accounts for a larger proportion.

Image source

• Author: Wikimedia user RJHall
• License: CC BY-SA 3.0

The CNO cycle also has various paths. It is broadly divided into cold CNO cycles (stellar interiors) and hot CNO cycles (novae, supernovae), and each case has three or four reaction paths. I’d like to cover all CNO cycle reactions, but that would require more than this amount of content, so I’ll only cover the most basic CN cycle*, that is, CNO-I.

*The reason it’s called the CN cycle with O omitted is that there is no stable isotope of oxygen in this reaction process.

As shown in the figure above, carbon, nitrogen, and oxygen circulate and act as catalysts. However, regardless of the reaction path, the overall reaction equation and the total amount of energy generated are the same.

More Readings

• Inkyu Park (Professor of Physics, University of Seoul), Naver Cast Physics Walk: How many neutrinos are produced in the Sun?
• Wikipedia, Proton-proton chain
• Wikipedia, CNO cycle