CNO cycle

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The CNO cycle (for carbon-nitrogen-oxygen), or sometimes Bethe-Weizsäcker-cycle, is one of two fusion reactions by which stars convert hydrogen to helium, the other being the proton-proton chain.

The proton-proton chain is more important in stars the mass of the sun or less. Only 1.7% of ⁴He nuclei being produced in the Sun are born in the CNO cycle. However theoretical models show that the CNO cycle is the dominant source of energy in heavier stars. The CNO process was proposed by Carl von Weizsäcker^[1] and Hans Bethe^[2] independently in 1938 and 1939, respectively.

The reactions of the CNO cycle are ^[3]:

12C + 1H	→	13N + γ	+1.95 MeV
13N	→	13C + e+ + νe	+2.22 MeV
13C + 1H	→	14N + γ	+7.54 MeV
14N + 1H	→	15O + γ	+7.35 MeV
15O	→	15N + e+ + νe	+2.75 MeV
15N + 1H	→	12C + 4He	+4.96 MeV

The net result of the cycle is to fuse four protons into an alpha particle plus two positrons (annihilating with electrons and releasing energy in the form of gamma rays) plus two neutrinos which escape from the star carrying away some energy. The carbon, nitrogen, and oxygen nuclei serve as catalysts and are regenerated.

In a minor branch of the reaction, occurring in the Sun core just 0.04% of the time, the final reaction shown above does not produce ¹²C and ⁴He, but instead produces ¹⁶O and a photon and continues as follows:

15N + 1H	→	16O + γ	+12.13 MeV
16O + 1H	→	17F + γ	+0.60 MeV
17F	→	17O + e+ + νe	+2.76 MeV
17O + 1H	→	14N + 4He	+1.19 MeV

Like the carbon, nitrogen, and oxygen involved in the main branch, the fluorine produced in the minor branch is merely catalytic and at steady state, does not accumulate in the star.

The main branch of the CNO cycle is known as CNO-I, the minor branch as CNO-II. There exist also two subdominant branches of CNO-III and CNO-IV which are significant only for heavy stars. They are started when the last reaction in CNO-II results in oxygen-18 and gamma instead of nitrogen-14 and alpha:

17O + 1H	→	18F
18F	→	18O + e+ + νe + γ.

While the total number of "catalytic" CNO nuclei is conserved in the cycle, in stellar evolution the relative proportions of the nuclei are altered. When the cycle is run to equilibrium, the ratio of the ¹²C/¹³C nuclei is driven to 3.5, and ¹⁴N becomes the most numerous nucleus, regardless of initial composition. During a star's evolution, convective mixing episodes bring material in which the CNO cycle has operated from the star's interior to the surface, altering the observed composition of the star. Red giant stars are observed to have lower ¹²C/¹³C and ¹²C/¹⁴N ratios than main sequence stars, which is considered to be proof of nuclear energy generation in stars by hydrogen fusion.

See also

• Triple-alpha process
• Proton-proton chain

References

1. ^ C. F. von Weizsäcker. Physik. Zeitschr. 39 (1938) 633.
2. ^ H. A. Bethe. Physical Review 55 (1939) 436.
3. ^ "Introductory Nuclear Physics", Kenneth S. Krane, John Wiley & Sons, New York, 1988, p.537