Nuclear fusion reaction pathways

A variety of different nuclear fusion reactions take place inside the cores of stars, depending upon their mass and composition, as part of stellar nucleosynthesis. The net mass of the fused atomic nuclei is smaller than the sum of the constituents. This lost mass is released as

Overview of the proton-proton chain

electromagnetic energy, according to the mass-energy equivalence relationship E = mc².^[1]

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 K for a small M-class star to 40 million K for a massive O-class star.^[104]

In the Sun, with a 10 million K core, hydrogen fuses to form helium in the proton-proton chain reaction:^[131]

4¹H → 2²H + 2e⁺ + 2ν_e (4.0 MeV + 1.0 MeV)

2¹H + 2²H → 2³He + 2γ (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.

Minimum stellar mass required for fusion

Element	Solar masses
Hydrogen	0.01
Helium	0.4
Carbon	5[132]
Neon	8

In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon—the carbon-nitrogen-oxygen cycle.^[131]

In evolved stars with cores at 100 million K and masses between 0.5 and 10 solar masses, helium can be transformed into carbon in the triple-alpha process that uses the intermediate element beryllium:^[131]

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. Fusion can not proceed any further except through an endothermic process, and so further energy can only be produced through gravitational collapse.^[131]

The example below shows the amount of time required for a star of 20 solar masses 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.^[133]

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[134]