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Hydrogen Fusion

The fusion of hydrogen into helium takes place through a somewhat complex network of reactions involving many isotopes that are intermediate in weight between hydrogen and helium and involving several elements that are heavier than helium. When one examines these numerous reactions, however, one finds that the conversion of hydrogen into helium predominately follows one of five paths.

The five different fusion paths can be divided into two sets of processes: the Proton-Proton (PP) process, which depends only on the amount of hydrogen and helium in the star, and the Carbon-Nitrogen-Oxygen (CNO) process, which depends on the amount of carbon, nitrogen, and oxygen in addition to the amount of hydrogen and helium in the star. The amount of carbon, nitrogen, and oxygen in a star is set by the composition of the interstellar gas at the time of the star's birth. But most of the metals (elements other than hydrogen and helium) in the interstellar gas are created and expelled by stars, so the history of star creation and evolution within a galaxy determines the effectiveness of the CNO process in a star. Because the universe had a low metal content early in its history, the first-born stars fuse hydrogen predominately through the PP process. This is one of three ways that the structure and evolution of a star depends on the age of the universe (The other two are through the influence of metals on the strength of the stellar wind in massive stars and on the transport of radiation out of a star).

The Proton-Proton Process

There are three branches to the PP process of convert hydrogen (H1) into helium (He4). The first branch does the conversion without creating any nuclei heavier than helium. The remaining two branches go through a step that creates beryllium.

The first PP branch takes hydrogen to deuterium (H2) to helium-3 (He3) to helium-4 (He4). In a chemistry-style notation with representing the gamma-ray and ν representing the electron neutrino, the fusion chain is as follows:

H1 + H1 H2 + e+ + ν
H2 + H1 He3 +
He3 + He3 He4 + 2 H1

The second and third branches of the PP chain involve the creation of beryllium-7 (Be7) and its subsequent destruction. The second branch splits from the first branch after the creation of helium-3. Helium-3 combines with helium-4 to create beryllium-7. Beryllium-7 combines with a free electron to give lithium-7 (Li7). Lithium-7 combines with hydrogen to give two helium-4 nuclei, returning the helium atom destroyed at the beginning of the offshoot.

He3 + He4 Be7 +
Be7 + e- Li7 + ν
Li7 + H1 He4 + He4

The third branch splits from the second branch after the creation of beryllium-7. In it, beryllium-7 combines with hydrogen to become boron-8 (B8). Boron-8 is unstable and decays into beryllium-8 (Be8), which rapidly decays into two helium nuclei.

Be7 + H1 B8 +
B8 Be8 + e+ + ν
Be8 2 He4

Helium is present in substantial quantities at the birth of every star, so the initial composition of the star is never an impediment to the PP process proceeding along the second and third branches. As a star converts its hydrogen to helium, increasing the density of helium in the core, these branches becomes more common.

The core temperature determines which of these branches is dominant. The first PP process branch dominates in the production of helium for core temperatures below roughly 15 million degrees (1.3 keV), the second branch dominates between 15 and 25 million degrees (1.3 to 2.2 keV), and the third branch dominates above 25 million degrees.

The total energy released in converting four hydrogen nuclei into a single Helium nucleus is the same for each of the three branches, 26.7 MeV. Much of this energy, however, is carried by the neutrino, and because neutrinos interact weakly with other particles, most of them escape from a star's core without loss of energy. The fractions of the energy lost from the core through direct emission of neutrinos for the first, second, and third branches are 2%, 4%, and 28%. The third branch produces a substantial energy output in neutrinos, making it an import source of energy loss. Neutrinos from this branch were the focus of the first experiments that measured the sun's neutrino flux and found it to be lower than expected.

The Carbon, Nitrogen, Oxygen Process

The contamination of a star by metals gives rise to the CNO process, where hydrogen nuclei are converted into helium nuclei by combining with carbon, nitrogen, and oxygen, the C, N, and O of the process's acronym. The two branches of this process cycle through a sequence that converts the elements carbon, nitrogen, and oxygen into each other's isotopes. The first cycle starts and ends with carbon-12.

C12 + H1 N13 +
N13 C13 + e+ + ν
C13 + H1 N14 +
N14 + H1 O15 +
O15 N15 + e+ + ν
N15 + H1 C12 + He4

The second branch is a similar type of cycle, and it joins onto the first. Starting with nitrogen-14, the process steps through two of the last-three reactions given above until nitrogen-15 is produced. It then proceeds as follows to convert nitrogen-15 back into nitrogen-14, with the production of fluorine-17 (F17) occurring in one of the steps:

N15 + H1 O16 +
O16 + H1 F17 +
F17 O17 + e+ + ν
O17 + H1 N14 + He4

For abundances characteristic of the Sun, the CNO process becomes important for core temperatures of roughly 15 million degrees (1.3 keV), and it provides virtually all of the conversion of hydrogen into helium above 25 million degrees (2.2 keV). The fractions of the nuclear energy loss from the core through neutrino emission in the first and second branches of the CNO process are 6% and 4%.

Hydrogen Fusion in Main-Sequence Stars

The core temperature of a star rises with its mass, so the PP process is dominate at low masses, and the CNO process is dominate at high masses. For main-sequence stars with elemental abundances similar to the Sun, the conversion of hydrogen into helium is equal for the two processes when a star is about 2 solar masses. Below about 1.2 solar masses, the contribution to the energy production from the CNO process is insignificant; this means that the Sun is powered only by the PP process. Above about 3 solar masses, virtually all of the energy generated in a star comes from the CNO process.

The mimimum mass of a star is about 0.075 solar masses. Below this mass, the core of a gravitationally-collapsing gas sphere never rises high enough for hydrogen fusion to begin. These objects are giant, cooling Jupiters that eventually get lost in space (another danger for Will Robinson). By the way, the planet Jupiter is 0.001 solar masses, so it is far below the nuclear fusion threshold.

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