CNO cycle

The CNO cycle is a series of nuclear fusion reactions which convert four hydrogen nuclei to a helium nucleus, releasing energy in the process. The CNO cycle dominates the nuclear reactions in stars with more than three times the mass of the Sun. Low-mass stars generate energy via the proton-proton chain. The CNO cycle was theorized independently by Hans Bethe and Carl von Weizsäcker in 1938.

The following particles are involved:

• H¹ - hydrogen 1 (proton)
• He⁴ - helium 4 (alpha particle)
• C¹² - carbon 12
• C¹³ - carbon 13
• N¹⁴ - nitrogen 14
• N¹⁵ - nitrogen 15
• O¹⁵ - oxygen 15
• O¹⁶ - oxygen 16
• O¹⁷ - oxygen 17
• F¹⁷ - fluorine 17
• e⁺ - positron (anti-electron)
• nu - neutrino
• gamma - photon (gamma ray)

The CNO cycle is also called the CNO bi-cycle because the reaction of N¹⁵ with a proton can have two different results. The two reaction cycles and energy generated by each are as follows:

CNO - 1

1. C¹² + H¹ -> N¹³ + gamma (1.944 MeV)
2. N¹³ -> C¹³ + e⁺ + nu(1) (2.221 MeV) (radioactive decay)
3. C¹³ + H¹ -> N¹⁴ + gamma (7.550 MeV)
4. N¹⁴ + H¹ -> O¹⁵ + gamma (7.293 MeV)
5. O¹⁵ -> N¹⁵ + e⁺ + nu(2) (2.761 MeV) (radioactive decay)
6. N¹⁵ + H¹ -> C¹² + He⁴ (4.965 MeV)

CNO - 2

1. C¹² + H¹ -> N¹³ + gamma (1.944 MeV)
2. N¹³ -> C¹³ + e⁺ + nu(1) (2.221 MeV) (radioactive decay)
3. C¹³ + H¹ -> N¹⁴ + gamma (7.550 MeV)
4. N¹⁴ + H¹ -> O¹⁵ + gamma (7.293 MeV)
5. O¹⁵ -> N¹⁵ + e⁺ + nu(2) (2.761 MeV) (radioactive decay)
6. N¹⁵ + H¹ -> O¹⁶ + gamma (12.126 MeV)
7. O¹⁶ + H¹ -> F¹⁷ + gamma (0.601 MeV)
8. F¹⁷ -> O¹⁷ + e⁺ + nu(3) (2.762 MeV) (radioactive decay)
9. O¹⁷ + H¹ -> N¹⁴ + He⁴ (1.193 MeV)

The latter cycle is much less frequent, with reaction (6) having a probability of 4 x 10^-4. Both cycles result in the formation of an alpha particle, along with a release of heat. The first cycle is a catalytic series, with the C¹² serving only to catalyze the formation of helium. The second cycle is not truly catalytic, but the N¹⁴ produced can then participate in the first cycle (see reaction (4)).

Each cycle also results in the formation of two or three neutrinos, having mean energies of: nu(1) = 0.710 MeV, nu(2) = 1.00 MeV, and nu(3) = 0.94 MeV.

As mentioned above, the CNO cycle is most important in massive stars. It is interesting to note that the rate of energy production by the two cycles is temperature dependent. The temperature dependence goes as T^4.5 for the proton-proton chain but T²⁰ for the CNO cycle. This is the reason why massive stars evolve faster; since they are more massive, they have higher core temperatures and thus burn their hydrogen faster.

Sources: D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, and P. Foukal, Solar Astrophysics