CNO cycle
The CNO cycle (for
Unlike the proton-proton reaction, which consumes all its constituents, the CNO cycle is a catalytic cycle. In the CNO cycle, four protons fuse, using carbon, nitrogen, and oxygen 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 one alpha particle (a stable helium nucleus), two positrons, and two electron neutrinos.
There are various alternative paths and catalysts involved in the CNO cycles, but all these cycles have the same net result:
- 4 1
1H
+ 2
e−
- → 4
2He
+ 2
e+
+ 2
e−
+ 2
ν
e + 3
γ
+ 24.7 MeV - → 4
2He
+ 2
ν
e + 7
γ
+ 26.7 MeV
- → 4
The positrons will almost instantly annihilate with electrons, releasing energy in the form of gamma 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 around 4×106 K[3] (4 megakelvin), making it the dominant energy source in smaller stars. A self-maintaining CNO chain starts at approximately 15×106 K, but its energy output rises much more rapidly with increasing temperatures[1] so that it becomes the dominant source of energy at approximately 17×106 K.[4]
The Sun has a core temperature of around 15.7×106 K, and only 1.7% of 4
He
nuclei produced in the Sun are
born in the CNO cycle.
The CNO-I process was independently proposed by Carl von Weizsäcker[5][6] and Hans 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 the BOREXINO 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]
Cold CNO cycles
Under typical conditions found in stars, catalytic hydrogen burning by the CNO cycles is limited by proton captures. Specifically, the timescale for beta decay of the radioactive 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.
CNO-I
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 of
- 15→ 12
7N
6C
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 two positrons emitted annihilate with two ambient electrons producing an additional 2.04 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 the beta-decay Q-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 the proton capture on 14
7N
. In 2006 it was experimentally measured down to stellar energies, revising the calculated age of globular clusters by around 1 billion years.[18]
The
CNO-II
In a minor branch of the above reaction, occurring in the Sun's core 0.04% of the time, the final reaction involving
7N
- 15→ 15
8O
7N
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, the fluorine produced in the minor branch is merely an intermediate product; at steady state, it does not accumulate in the star.
CNO-III
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
- 17→ 17
9F
8O
In detail:
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 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 of 64.49 s)
CNO-IV
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 instances 18
9F
can combine with a helium nucleus to start a sodium-neon cycle.[20]
Hot CNO cycles
Under conditions of higher temperature and pressure, such as those found in novae and X-ray bursts, the rate of proton captures exceeds the rate of beta-decay, pushing the burning to the proton 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 of proton captures, they are also called the beta-limited CNO cycles.[clarification needed]
HCNO-I
The difference between the CNO-I cycle and the HCNO-I cycle is that 13
7N
captures a proton instead of decaying, leading to the total sequence
- 15→12
7N
6C
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
HCNO-II
The notable difference between the CNO-II cycle and the HCNO-II cycle is that , leading to the total sequence
- 15→15
8O
7N
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)
HCNO-III
An alternative to the HCNO-II cycle is that 18
9F
captures a proton moving towards higher mass and using the same helium production mechanism as the CNO-IV cycle as
- 18
9F
→18→18
10Ne
9F
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)
Use in astronomy
While the total number of "catalytic" nuclei are 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 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 do main sequence stars, which is considered to be convincing evidence for the operation of the CNO cycle.[21]
See also
- Aneutronic fusion
- Cold fusion
- Fusion power
- Nuclear fusion
- Proton–proton chain, as found in stars like the Sun
- Stellar nucleosynthesis, the whole topic
- Triple-alpha process, how 12
C
is produced from lighter nuclei
Footnotes
- ^ Note: It is not important how invariant masses of e and ν are small, because they are already small enough to become relativistic. What is important is that the daughter nucleus is heavy compared to p⁄c .
References
- ^ ISBN 0-470-09220-3.
- ^ S2CID 227174644.
- ISBN 3-540-25124-3.
- ^
Schuler, S.C.; King, J.R.; The, L.-S. (2009). "Stellar Nucleosynthesis in the Hyades open cluster". S2CID 10626836.
- ^ a b von Weizsäcker, Carl F. (1937). "Über Elementumwandlungen in Innern der Sterne I" [On transformations of elements in the interiors of stars I]. Physikalische Zeitschrift. 38: 176–191.
- ^ a b von Weizsäcker, Carl F. (1938). "Über Elementumwandlungen in Innern der Sterne II" [On transformations of elements in the interiors of stars II]. Physikalische Zeitschrift. 39: 633–646.
- ^ a b c
PMID 17835673.
- ^ PMID 17835673.
- S2CID 227174644.
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;
- ^ "Neutrinos yield first experimental evidence of catalyzed fusion dominant in many stars". phys.org. Retrieved 26 November 2020.
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."
- .
- .
- .
- . Retrieved 26 November 2018.
- ^ a b c
Krane, Kenneth S. (1988). Introductory Nuclear Physics. ISBN 0-471-80553-X.
- ^ ISBN 9783642103681.
- ^ Wapstra, Aaldert; Audi, Georges (18 November 2003). "The 2003 Atomic Mass Evaluation". Atomic Mass Data Center. Archived from the original on 28 September 2011. Retrieved 25 October 2011.
- ^
Lemut, A.; Bemmerer, D.; Confortola, F.; Bonetti, R.; Broggini, C.; Corvisiero, P.; et al. (LUNA Collaboration) (2006). "First measurement of the 14N(p,γ)15O cross section down to 70 keV". S2CID 16875233.
- ^
Scheffler, Helmut; Elsässer, Hans (1990). Die Physik der Sterne und der Sonne [The Physics of the Stars and the Sun]. ISBN 3-411-14172-7.
- ^ Depalo, Rosanna. "The neon-sodium cycle: Study of the 22Ne(p, γ)23Na reaction at astrophysical energies" (PDF). Archived from the original (PDF) on 28 July 2020. Retrieved 16 April 2020.
- .
Further reading
- Bethe, H. A. (1939). "Energy Production in Stars". PMID 17835673.
- Iben, I. (1967). "Stellar Evolution Within and off the Main Sequence". .