Inastrophysics, thecarbon–nitrogen–oxygen (CNO)cycle, sometimes calledBethe–Weizsäcker cycle, afterHans Albrecht Bethe andCarl Friedrich von Weizsäcker, is one of the two known sets offusionreactions by whichstars converthydrogen tohelium, the other being theproton–proton chain reaction (p–p cycle), which is more efficient at theSun's core temperature. The CNO cycle is hypothesized to be dominant in stars that are more than 1.3 times asmassive as the Sun.[1]
Unlike the proton-proton reaction, which consumes all its constituents, the CNO cycle is acatalytic cycle. In the CNO cycle, fourprotons fuse, usingcarbon,nitrogen, andoxygen isotopes as catalysts, each of which is consumed at one step of the CNO cycle, but re-generated in a later step. The end product is onealpha particle (astablehelium nucleus), twopositrons, and twoelectron neutrinos.
There are various alternative paths and catalysts involved in the CNO cycles, but all these cycles have the same net result:
The positrons will almost instantlyannihilate with electrons, releasing energy in the form ofgamma rays. The neutrinos escape from the star carrying away some energy.[2] One nucleus goes on to become carbon, nitrogen, and oxygen isotopes through a number of transformations in a repeating cycle.
The proton–proton chain is more prominent in stars the mass of the Sun or less. This difference stems from temperature dependency differences between the two reactions; pp-chain reaction starts at temperatures around4×106 K[3] (4 megakelvins), making it the dominant energy source in smaller stars. A self-maintaining CNO chain starts at approximately15×106 K, but its energy output rises much more rapidly with increasing temperatures[1] so that it becomes the dominant source of energy at approximately17×106 K.[4]
The Sun has acore temperature of around15.7×106 K, and only1.7% of4
He nuclei produced in the Sun areborn in the CNO cycle.
TheCNO-I process was independently proposed byCarl von Weizsäcker[5][6] andHans Bethe[7][8] in the late 1930s.
The first reports of the experimental detection of the neutrinos produced by the CNO cycle in the Sun were published in 2020 by theBOREXINO collaboration. This was also the first experimental confirmation that the Sun had a CNO cycle, that the proposed magnitude of the cycle was accurate, and that von Weizsäcker and Bethe were correct.[2][9][10]
Under typical conditions found in stars, catalytic hydrogen burning by the CNO cycles is limited byproton captures. Specifically, the timescale forbeta decay of theradioactive nuclei produced is faster than the timescale for fusion. Because of the long timescales involved, the cold CNO cycles convert hydrogen to helium slowly, allowing them to power stars in quiescent equilibrium for many years.
The first proposed catalytic cycle for the conversion of hydrogen into helium was initially called the carbon–nitrogen cycle (CN-cycle), also referred to as the Bethe–Weizsäcker cycle in honor of the independent work ofCarl Friedrich von Weizsäcker in 1937–38[5][6] andHans Bethe. Bethe's 1939 papers on the CN-cycle[7][8] drew on three earlier papers written in collaboration withRobert Bacher andMilton Stanley Livingston[11][12][13] and which came to be known informally asBethe's Bible. It was considered the standard work on nuclear physics for many years and was a significant factor in his being awarded the1967 Nobel Prize in Physics.[14] Bethe's original calculations suggested the CN-cycle was the Sun's primary source of energy.[7][8] This conclusion arose from a belief that is now known to be mistaken, that theabundance of nitrogen in the sun is approximately 10%; it is actually less than half a percent.[15] The CN-cycle, named as it contains no stable isotope of oxygen, involves the following cycle of transformations:[15]
This cycle is now understood as being the first part of a larger process, the CNO-cycle, and the main reactions in this part of the cycle (CNO-I) are:[15]
| 12 6C | + | 1 1H | → | 13 7N | + | γ | + | 1.95 MeV | |||
| 13 7N | → | 13 6C | + | e+ | + | ν e | + | 1.20 MeV | (half-life of 9.965 minutes[16]) | ||
| 13 6C | + | 1 1H | → | 14 7N | + | γ | + | 7.54 MeV | |||
| 14 7N | + | 1 1H | → | 15 8O | + | γ | + | 7.35 MeV | |||
| 15 8O | → | 15 7N | + | e+ | + | ν e | + | 1.73 MeV | (half-life of 122.24 seconds[16]) | ||
| 15 7N | + | 1 1H | → | 12 6C | + | 4 2He | + | 4.96 MeV |
where the carbon-12 nucleus used in the first reaction is regenerated in the last reaction. After the twopositrons emittedannihilate with two ambient electrons producing an additional2.04 MeV, the total energy released in one cycle is 26.73 MeV; in some texts, authors are erroneously including the positron annihilation energy in with thebeta-decayQ-value and then neglecting the equal amount of energy released by annihilation, leading to possible confusion. All values are calculated with reference to the Atomic Mass Evaluation 2003.[17]
The limiting (slowest) reaction in the CNO-I cycle is theproton capture on14
7N. In 2006 it was experimentally measured down to stellar energies, revising the calculated age ofglobular clusters by around 1 billion years.[18]
Theneutrinos emitted in beta decay will have a spectrum of energy ranges, because althoughmomentum is conserved, the momentum can be shared in any way between the positron and neutrino, with either emitted at rest and the other taking away the full energy, or anything in between, so long as all the energy from the Q-value is used. The totalmomentum received by the positron and the neutrino is not great enough to cause a significant recoil of the muchheavier daughter nucleus[a] and hence, its contribution to kinetic energy of the products, for the precision of values given here, can be neglected. Thus the neutrino emitted during the decay of nitrogen-13 can have an energy from zero up to1.20 MeV, and the neutrino emitted during the decay of oxygen-15 can have an energy from zero up to1.73 MeV. On average, about 1.7 MeV of the total energy output is taken away by neutrinos for each loop of the cycle, leaving about25 MeV available for producingluminosity.[19]
In a minor branch of the above reaction, occurring in the Sun's core 0.04% of the time, the final reaction involving15
7N shown above does not produce carbon-12 and an alpha particle, but instead produces oxygen-16 and a photon and continues
In detail:
| 15 7N | + | 1 1H | → | 16 8O | + | γ | + | 12.13 MeV | |||
| 16 8O | + | 1 1H | → | 17 9F | + | γ | + | 0.60 MeV | |||
| 17 9F | → | 17 8O | + | e+ | + | ν e | + | 2.76 MeV | (half-life of 64.49 seconds) | ||
| 17 8O | + | 1 1H | → | 14 7N | + | 4 2He | + | 1.19 MeV | |||
| 14 7N | + | 1 1H | → | 15 8O | + | γ | + | 7.35 MeV | |||
| 15 8O | → | 15 7N | + | e+ | + | ν e | + | 2.75 MeV | (half-life of 122.24 seconds) |
Like the carbon, nitrogen, and oxygen involved in the main branch, thefluorine produced in the minor branch is merely an intermediate product; at steady state, it does not accumulate in the star.
This subdominant branch is significant only for massive stars. The reactions are started when one of the reactions in CNO-II results in fluorine-18 and a photon instead of nitrogen-14 and an alpha particle, and continues
In detail:
| 17 8O | + | 1 1H | → | 18 9F | + | γ | + | 5.61 MeV | |||
| 18 9F | → | 18 8O | + | e+ | + | ν e | + | 1.656 MeV | (half-life of109.771 min) | ||
| 18 8O | + | 1 1H | → | 15 7N | + | 4 2He | + | 3.98 MeV | |||
| 15 7N | + | 1 1H | → | 16 8O | + | γ | + | 12.13 MeV | |||
| 16 8O | + | 1 1H | → | 17 9F | + | γ | + | 0.60 MeV | |||
| 17 9F | → | 17 8O | + | e+ | + | ν e | + | 2.76 MeV | (half-life of64.49 s) |
Like the CNO-III, this branch is also only significant in massive stars. The reactions are started when one of the reactions in CNO-III results in fluorine-19 and a photon instead of nitrogen-15 and an alpha particle, and continues
In detail:
| 18 8O | + | 1 1H | → | 19 9F | + | γ | + | 7.994 MeV | |||
| 19 9F | + | 1 1H | → | 16 8O | + | 4 2He | + | 8.114 MeV | |||
| 16 8O | + | 1 1H | → | 17 9F | + | γ | + | 0.60 MeV | |||
| 17 9F | → | 17 8O | + | e+ | + | ν e | + | 2.76 MeV | (half-life of 64.49 seconds) | ||
| 17 8O | + | 1 1H | → | 18 9F | + | γ | + | 5.61 MeV | |||
| 18 9F | → | 18 8O | + | e+ | + | ν e | + | 1.656 MeV | (half-life of 109.771 minutes) |
In some instances18
9F can combine with a helium nucleus to start a neon-sodium cycle, in which:[20][21]
20
10Ne → 21
11Na → 21
10Ne → 22
11Na → 22
10Ne → 23
11Na → 20
10Ne
The sodium-23 can also turn into magesium-24 after proton bombardment, initiating the magnesium-aluminum cycle.
Under conditions of higher temperature and pressure, such as those found innovae andX-ray bursts, the rate of proton captures exceeds the rate of beta-decay, pushing the burning to theproton drip line. The essential idea is that a radioactive species will capture a proton before it can beta decay, opening new nuclear burning pathways that are otherwise inaccessible. Because of the higher temperatures involved, these catalytic cycles are typically referred to as the hot CNO cycles; because the timescales are limited by beta decays instead ofproton captures, they are also called the beta-limited CNO cycles.[clarification needed]
The difference between the CNO-I cycle and the HCNO-I cycle is that13
7N captures a proton instead of decaying, leading to the total sequence
In detail:
| 12 6C | + | 1 1H | → | 13 7N | + | γ | + | 1.95 MeV | |||
| 13 7N | + | 1 1H | → | 14 8O | + | γ | + | 4.63 MeV | |||
| 14 8O | → | 14 7N | + | e+ | + | ν e | + | 5.14 MeV | (half-life of 70.641 seconds) | ||
| 14 7N | + | 1 1H | → | 15 8O | + | γ | + | 7.35 MeV | |||
| 15 8O | → | 15 7N | + | e+ | + | ν e | + | 2.75 MeV | (half-life of 122.24 seconds) | ||
| 15 7N | + | 1 1H | → | 12 6C | + | 4 2He | + | 4.96 MeV |
The notable difference between the CNO-II cycle and the HCNO-II cycle is that17
9F captures a proton instead of decaying, and neon is produced in a subsequent reaction on18
9F, leading to the total sequence
In detail:
| 15 7N | + | 1 1H | → | 16 8O | + | γ | + | 12.13 MeV | |||
| 16 8O | + | 1 1H | → | 17 9F | + | γ | + | 0.60 MeV | |||
| 17 9F | + | 1 1H | → | 18 10Ne | + | γ | + | 3.92 MeV | |||
| 18 10Ne | → | 18 9F | + | e+ | + | ν e | + | 4.44 MeV | (half-life of 1.672 seconds) | ||
| 18 9F | + | 1 1H | → | 15 8O | + | 4 2He | + | 2.88 MeV | |||
| 15 8O | → | 15 7N | + | e+ | + | ν e | + | 2.75 MeV | (half-life of 122.24 seconds) |
An alternative to the HCNO-II cycle is that18
9F captures a proton moving towards higher mass and using the same helium production mechanism as the CNO-IV cycle as
In detail:
| 18 9F | + | 1 1H | → | 19 10Ne | + | γ | + | 6.41 MeV | |||
| 19 10Ne | → | 19 9F | + | e+ | + | ν e | + | 3.32 MeV | (half-life of 17.22 seconds) | ||
| 19 9F | + | 1 1H | → | 16 8O | + | 4 2He | + | 8.11 MeV | |||
| 16 8O | + | 1 1H | → | 17 9F | + | γ | + | 0.60 MeV | |||
| 17 9F | + | 1 1H | → | 18 10Ne | + | γ | + | 3.92 MeV | |||
| 18 10Ne | → | 18 9F | + | e+ | + | ν e | + | 4.44 MeV | (half-life of 1.672 seconds) |
While the total number of "catalytic" nuclei are conserved in the cycle, instellar evolution the relative proportions of the nuclei are altered. When the cycle is run to equilibrium, the ratio of the carbon-12/carbon-13 nuclei is driven to 3.5, and nitrogen-14 becomes the most numerous nucleus, regardless of initial composition. During a star's evolution, convective mixing episodes moves material, within 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 carbon-12/carbon-13 and carbon-12/nitrogen-14 ratios than domain sequence stars, which is considered to be convincing evidence for the operation of the CNO cycle.[22]
This result therefore paves the way towards a direct measurement of the solar metallicity using CNO neutrinos. Our findings quantify the relative contribution of CNO fusion in the Sun to be of the order of 1 per cent;
Pocar points out, "Confirmation of CNO burning in our sun, where it operates at only one percent, reinforces our confidence that we understand how stars work."
