Nuclear Fusion Reaction Pathways

Nuclear fusion reaction pathways

Main article: Stellar nucleosynthesis

Overview of the proton-proton chain

The carbon-nitrogen-oxygen cycle

A variety of nuclear fusion reactions take place in the cores of stars, that depend upon their mass and composition. When nuclei fuse, the mass of the fused product is less than the mass of the original parts. This lost mass is converted to electromagnetic energy, according to the mass–energy equivalence relationship E = mc².^[3]
The hydrogen fusion process is temperature-sensitive, so a moderate increase in the core temperature will result in a significant increase in the fusion rate. As a result, the core temperature of main sequence stars only varies from 4 million kelvin for a small M-class star to 40 million kelvin for a massive O-class star.^[141]

In the Sun, with a 10-million-kelvin core, hydrogen fuses to form helium in the proton–proton chain reaction:^[169]

4¹H → 2²H + 2e⁺ + 2ν_e(2 x 0.4 MeV)

2e⁺ + 2e⁻ → 2γ (2 x 1.0 MeV)

2¹H + 2²H → 2³He + 2γ (2 x 5.5 MeV)

2³He → ⁴He + 2¹H (12.9 MeV)

These reactions result in the overall reaction:

4¹H → ⁴He + 2e⁺ + 2γ + 2ν_e (26.7 MeV)

where e⁺ is a positron, γ is a gamma ray photon, ν_e is a neutrino, and H and He are isotopes of hydrogen and helium, respectively. The energy released by this reaction is in millions of electron volts, which is actually only a tiny amount of energy. However enormous numbers of these reactions occur constantly, producing all the energy necessary to sustain the star's radiation output. In comparison, the combustion of two hydrogen gas molecules with one oxygen gas molecule releases only 5.7 eV.

Minimum stellar mass required for fusion

Element	Solar masses
Hydrogen	0.01
Helium	0.4
Carbon	5[170]
Neon	8

In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon called the carbon-nitrogen-oxygen cycle.^[169]
In evolved stars with cores at 100 million kelvin and masses between 0.5 and 10 M_☉, helium can be transformed into carbon in the triple-alpha process that uses the intermediate element beryllium:^[169]

⁴He + ⁴He + 92 keV → ^8*Be

⁴He + ^8*Be + 67 keV → ^12*C

^12*C → ¹²C + γ + 7.4 MeV

For an overall reaction of:

3⁴He → ¹²C + γ + 7.2 MeV

In massive stars, heavier elements can also be burned in a contracting core through the neon-burning process and oxygen-burning process. The final stage in the stellar nucleosynthesis process is the silicon-burning process that results in the production of the stable isotope iron-56, an endothermic process that consumes energy, and so further energy can only be produced through gravitational collapse.^[169]
The example below shows the amount of time required for a star of 20 M_☉ to consume all of its nuclear fuel. As an O-class main sequence star, it would be 8 times the solar radius and 62,000 times the Sun's luminosity.^[171]

Fuel material	Temperature (million kelvins)	Density (kg/cm3)	Burn duration (τ in years)
H	37	0.0045	8.1 million
He	188	0.97	1.2 million
C	870	170	976
Ne	1,570	3,100	0.6
O	1,980	5,550	1.25
S/Si	3,340	33,400	0.0315[172]