The Astrophysics Spectator
The Astrophysics Spectator
Once all of the hydrogen in a gas is converted into helium-4, fusion stops until the temperature rises to about 108K. At this temperature, helium-4 is converted into heavier elements, predominantly carbon-12 and oxygen.-16, both of which are multiples of helium-4 in their proton and neutron composition. To create these isotopes, beryllium-8 must first be created from two helium-4 nuclei, but this unstable isotope, with a lifetime of only 2.6 10-16 seconds, rapidly decays back into helium-4.
The short lifetime of beryllium-8 ensures that the creation and decay of beryllium-8 are in equilibrium. This means that the density of beryllium-8 is set by the thermodynamic properties of the gas, specifically the temperature and the density of the gas; the creation and decay rated drop out of the problem. As a practical matter, because the amount of energy required to create beryllium-8 is large, 92.1 keV, the density of berylium-8 to helium-4 is minuscule: for a temperature of 108 K and a helium-4 density of 105 gm cm-3, the ratio of beryllium-8 nuclei to helium-4 nuclei will be around 10-9. The density of beryllium-8 is proportional to T-3/2 e-40 keV/T. This temperature dependence imples that a small change in temperature produces a large change in the berylium-8 density; for a temperature of 108 K (9 keV), a 15% change in temperature produces a factor of 2 change in the berylium-8 density.
While berylium-8 is present, its creation is a small energy sink. To release energy, carbon-12 and heavier elements must be created. Carbon-12 is created when helium-4 combines with beryllium-8. In this interaction, carbon-12 nucleus is left in an energetic state from which it decays, releasing a gamma-ray. The conversion of beryllium-8 into carbon-12 releases 7.37 MeV.
The conversion of helium-4 into carbon-12 is therefore accomplished through the following two reactions:
| He4 + He4 | → | Be8 |
| Be8 + He4 | → | C12 + |
The process of converting three helium-4 nuclei into a single carbon-12 nucleus releases a total of 7.27 MeV, all of which remains trapped within the star. This fusion chain can be treated as a single process; it is then called the triple-alpha process (an alpha particle is a helium-4 nucleus). The triple-alpha reaction rate is proportional to the cube of the helium-4 density. Because of the strong temperature dependence of the beryllium-8 density, the triple-alpha reaction rate is much more temperature dependent than any of the hydrogen fusion rates. Within a star, helium fusion provides sufficient energy to support a star when the core temperature rises to about 100 million degrees. The practical effect of this is that helium fusion within stars occurs over a very narrow range of temperatures.
For temperatures that enable the triple-alpha process to proceed, other nuclear reactions are possible involving helium that create elements with atomic masses that are multiples of 4. These processes are as follows:
| C12 + He4 | → | O16 + |
| O16 + He4 | → | Ne20 + |
| Ne16 + He4 | → | Mg24 + |
Each of these reactions release energy. The creation of oxygen-16 generates 7.16 MeV, while the generation of neon-20 generates 4.730 MeV. The next-two elements release even more energy, with 9.32 MeV from the creation of magnesium-24 and 9.98 from the creation of silicon-28. The creation of sulfur-32 and argon-26 generates 6.95 MeV and 6.65 MeV respectively. These large amounts of energy point to the stability of these isotopes.
Because the triple-alpha process switches on so rapidly with temperature, all stellar cores that are fusing helium have essentially the same temperature, so that the ratios of carbon-12 to oxygen-16 to neon-20 to magnesium-24 within a stellar core is essentially the same for all stellar cores.
In the universe, the third, fourth, fifth, and sixth most abundant elements are oxygen, neon, nitrogen, and carbon. The triple-alpha process and the CNO process of hydrogen fusion are responsible for this, with the triple-alpha process creating the carbon, oxygen, and neon, and the CNO process creating the nitrogen from the carbon and oxygen.
The CNO hydrogen fusion process converts carbon-12 and the oxygen-16 into four other isotopes as hydrogen is converted into helium-4. These isotopes are carbon-13, nitrogen-14, nitrogen-15, and oxygen-15. Two of these isotopes, carbon-13 and nitrogen-14, can be destroyed by combining with helium-4 during the helium fusion stage. During these reactions, neutrons are released that either combine with other isotopes to form heavier elements or decay to a proton and an electron. Because the CNO isotopes are present in only small quantities in a star, the amount of energy release through their fusion with helium-4 is generally negligible; the importance of these fusion processes is in their effect on the isotopes found in the universe. The absorption of a neutron by a nucleus can produce isotopes away from the C12 → O16 → 20 → Mg24 path.
The destruction of carbon-13 proceeds through the following reaction with helium-4:
| C13 + He4 | → | O16 + n |
In this reaction, the carbon absorbs a helium nucleus and releases a neutron to become oxygen-16, releasing 2.21 MeV of energy.
The destruction of nitrogen-14 through the absorption of helium-4 creates the unstable nucleus fluorine-18, which decays to oxygen-18. These reactions are as follows:
| N14 + He4 | → | F18 + |
| F18 | → | O18 + e+ + νe |
The energy released in these processes is 4.42 MeV.
The oxygen-18 created from nitrogen-14 can be destroyed by absorbing a helium-4 nucleus. This interaction has two branches, one that creates neon-21, and a second that creates neon-22. The first of these reactions is as follows:
| O18 + He4 | → | Ne21 + n |
This reaction is endothermic, absorbing a total of 0.699 MeV of energy from the gas.
The second reaction is as follows:
| O18 + He4 | → | Ne22 + |
| Ne22 + He4 | → | Mg25 + n |
The first of these reactions is exothermic, generating 9.67 MeV of energy. The reaction producing the magnesium-25 in endothermic, swallowing 0.48 MeV of energy.
