L6S3

3. THERMONUCLEAR EXPLOSIONS AND ELEMENT SYNTHESIS

Energy is released when light elements fuse into heavier elements: hydrogen into helium; helium into carbon and oxygen; oxygen into silicon; silicon into iron. But since iron is the most tightly bound atomic nucleus, fusion of iron into heavier elements such as lead, uranium, etc., will not release energy. On the contrary, such fusion will absorb energy. (For the same reason, a uranium nucleus releases energy when it splits apart.) Likewise, it requires energy to tear iron nuclei apart. Iron nuclei have no more energy to release, either by fusion or fission. This point is illustrated by the curve of binding energy below.

The curve of binding energy. This graph shows that energy is released when atomic nuclei are converted by fusion reactions to make iron (⁵⁶Fe); but energy is absorbed when nuclei are converted to nuclei heavier than iron.

As we have already discussed, nuclear reactions have a temperature threshold below which the reactions cannot occur. (You can think of it as a kindling temperature.) The minimum temperatures for nuclear reactions to occur are listed in the table below:

Reaction	Temperature (K)
Hydrogen burning: 4 H ® He	(1 - 5) x 10⁷
Helium burning: 3 He ® C; He + C ® O	2 x 10⁸
Carbon/Oxygen burning: C + O ® all other elements	7 x 10⁸ - 2 x 10⁹

We have already described the reactions by which hydrogen is converted into helium (in the cores of main sequence stars) and helium is converted to carbon and oxygen (in the cores of horizontal branch stars). For single stars having mass less than about 8 Suns, those are the only reactions that will ever occur. During the AGB stage, the furious helium and hydrogen burning in shells expels most of the mass of the star as a planetary nebula, leaving behind a carbon-oxygen core that never gets hot enough for carbon burning to commence. But, as we describe in Section 5, more massive stars arrive at a stage of evolution in which the temperature rises to more than 7 x 10⁸ K, and then all hell breaks loose! The carbon and oxygen can begin to fuse, releasing more energy and raising the temperature further. A very complex network of nuclear reactions ensues, giving rise to all the known elements.

Now we come to one of the great questions of astrophysics: what accounts for the relative abundances of the heavy elements (i.e., heavier than carbon and oxygen). On Earth, and everywhere in the cosmos, some heavy elements such as silicon (found in dirt, sand, and rocks) and iron, are relatively common; but other elements, such as gold, silver, and uranium are very rare, as illustrated below.

Relative abundances of elements in the universe. Source

Today, we can be certain of the answer: the heavy elements are formed in the explosions of stars. How do we know this? The proof is a triumph of nuclear physics and astrophysics. Since the 1950s, physicists have been doing experiments to measure the rate of fusion reactions by accelerating nuclei of atoms (such as carbon, oxygen, silicon, etc.) to very high speeds in "atom-smasher" machines such as cyclotrons. The fast atomic nuclei then strike a target made of some other kind of atoms, and the physicists measure the products of the fusion reactions that occur. After measuring the rates and temperature dependence of hundreds of such fusion reactions, the physicists can incorporate their results into hundreds of equations that characterize how a mix of all sorts of elements would evolve if it was heated to billions of degrees in a supernova explosion. They then solve these equations on a computer. These calculations give a mix of elements similar to the observed abundances shown above. Such calculations leave little doubt that the heavy elements in the universe, on Earth -- indeed, in your body -- were produced by supernova explosions. As you will see in Section 6, this idea was further confirmed by observations of gamma rays from Supernova 1987A.

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