Nuclear Reactions: Powering Stars

As we’ve said before (somewhere), stars produce energy through nuclear fusion, combining lighter elements to produce heavier elements. This is as opposed to nuclear fission, used in nuclear power plants here on Earth, which usually involves bombarding heavy elements with neutrons until they become unstable and decay into lighter nuclei, releasing energy in the process. The problem with using fission as an energy source is that it tends to produce some nasty radioactive byproducts along the way — not so with fusion, which is why achieving controlled fusion is one of the “holy grails” of science. But enough about the earth and our energy woes, we’re here to talk about stars.

First, we’re going to assume you’re familiar with the notation for nuclear isotopes, but if you’re not (or if you’ve forgotten), here’s a quick refresher. In normal nuclear notation, which is used in most of the diagrams below, the top number represents the number of nucleons (neutrons + protons), while the bottom number is the number of protons (aka the element’s atomic number). Isotope notation, which we are forced to use because of technical limitations, is simply the element’s name followed by the number of nucleons.

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Stars which are approximately the size of our Sun, or smaller, mostly use the proton-proton chain to produce their energy. This is the most basic of the nuclear fusion reactions that power stars.

Proton-Proton Chain

Credit: Windows to the Universe

First, two protons fuse into deuterium, a “heavy” isotope of hydrogen. One of the protons is converted to a neutron through beta-plus decay, causing a positron (a positively charged electron) to be released, as well as a neutrino. The deuterium then combines with another proton to form He-3 and release a gamma ray. Finally, two He-3 nuclei react to form a helium nucleus and two protons. And don’t forget about the positrons — they will collide with electrons and annihilate, releasing more energy.

Note that this is the so-called PPI chain, which takes place around 70% of the time. The PPII and PPIII chains contain further reactions, but in the end, all three branches of the proton-proton chain convert hydrogen into helium.

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Stars over ~1.3 M(sun) mostly rely on the CNO cycle for their energy because these more massive stars tend to have higher core temperatures, and the CNO cycle becomes much more effective at higher temperatures than the P-P chain. The name “CNO” refers to the three elements whose different isotopes drive the cycle.

CNO Cycle

Credit: Australia Telescope Outreach & Education

It starts with a C-12 nucleus, which combines with a proton to produce  N-13 and a gamma-ray photon. One of the protons in N-13 beta-decays into a neutron, spitting out a positron and a neutrino in the process. So now we have C-13, which fuses with a proton to form N-14 (and a gamma ray), and then another proton to form O-15 (and another gamma ray). A proton in O-15 beta-decays into a neutron, producing N-15 and ejecting another positron and another neutrino. N-15 combines with yet another proton…but this time, the nucleus splits apart into an alpha particle (He-4) and C-12.

And then the cycle starts all over again.

This is the simplest iteration of the cold CNO cycle, which is the type that generally powers stars (it’s termed “cold” because it takes place at relatively low temperatures). There are three other branches of the cold CNO cycle, all of which are relatively rare — a nucleus fails to emit an alpha particle and instead stays together as a heavier element, which is then used as a catalyst for further reactions. In the hot CNO cycles, taking place under conditions of higher temperature and pressure, certain nuclei capture protons before they can beta-decay, leading to a different series of reactions.

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The P-P chain and the CNO cycle both convert hydrogen into helium, which is all well and good for most of a star’s lifetime. But for most stars, the pressure and temperature at the core eventually rise high enough to ignite helium fusion.

Triple-Alpha Process

Credit: Australia Telescope Outreach and Education

Enter the triple-alpha process, which fuses together helium nuclei (aka alpha particles) into progressively heavier elements as shown in the diagram above. The triple-alpha process is extremely unlikely because Be-8 is extremely unstable, but under high enough temperature and pressure, Be-8 is created fast enough to continuously exist in a small amount. If Be-8 manages to fuse with another alpha particle before it disintegrates, stable C-12 is produced. The endpoint of the process is considered to be C-12 (which is three alpha particles fused together, hence the name), although stable O-16 and Ne-20 can be produced by smashing more alpha particles into the C-12 nuclei.

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Further nuclear reactions take place in stars above 8-11 M(sun). In the first stage, carbon burning, two C-12 nuclei react to form a variety of products, most often forming N-20 and spitting out an alpha particle. Neon burning involves Ne-20 either disintegrating into O-16 and an alpha particle, or capturing an alpha particle to become Mg-24. Then in oxygen burning, two O-16 nuclei fuse to form several products, most notably Si-28 and S-32. Finally, silicon burning repeatedly adds alpha particles to a silicon nucleus until it becomes Ni-56 (which will eventually decay into Fe-56). But when the star tries to fuse Ni-56 into Zn-60, energy is consumed instead of produced, and the core promptly collapses.

Elements heavier than iron are produced in supernova explosions through neutron capture processes, since neutrons are much easier to add to a nucleus than protons are. The S-process (slow) involves the capture of only one neutron at a time, which then beta-decays into a proton, producing a new element. On the other hand, in the R-process (rapid), many neutrons are captured at once, which then begin to beta-decay into protons.

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Even with all this talk of these different reactions, we still haven’t really explained how stars can even produce energy from nuclear fusion. The answer can be found in Einstein’s famous equation E=mc^2. In certain fusion reactions, the end product has slightly less mass than the sum of its components. This missing mass is termed the “mass defect” and it shows up because nuclei require slightly less energy per nucleon to bind themselves together as the number of nucleons increases. Well, at least up to iron — for elements heavier than iron, it actually takes more energy per nucleon to bind a nucleus together, which is why fusion reactions to form elements heavier than iron consume energy instead of producing it. The energy released through fusion reactions can be calculated through E=mc^2; while the yield from one reaction is small, the sheer number of atoms in a star makes the total quite significant.

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TL;DR — Sun-sized and smaller stars mostly produce energy through the P-P chain, which turns 6 protons into an alpha particle and 2 protons. More massive stars use the CNO cycle, which uses C-12 as a catalyst for a series of reactions that also turn hydrogen into helium. Stars that burn helium (which is most of them) do so through the triple-α process, which keeps smashing alpha particles together to form heavier elements. If the star is massive enough, elements up to iron can be produced; elements heavier than iron are produced in supernovae. The mass defect explains how stars produce energy through nuclear reactions.

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Sources and links for further reading:

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