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The CNO cycle (for carbonnitrogenoxygen; sometimes called Bethe–Weizsäcker cycle after
Hans Albrecht Bethe Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel Prize ...
and
Carl Friedrich von Weizsäcker Carl Friedrich Freiherr von Weizsäcker (; 28 June 1912 – 28 April 2007) was a German physicist and philosopher. He was the longest-living member of the team which performed nuclear research in Germany during the Second World War, under W ...
) is one of the two known sets of
fusion Fusion, or synthesis, is the process of combining two or more distinct entities into a new whole. Fusion may also refer to: Science and technology Physics *Nuclear fusion, multiple atomic nuclei combining to form one or more different atomic nucl ...
reactions by which
star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ma ...
s convert hydrogen to helium, the other being the proton–proton chain reaction (p–p cycle), which is more efficient at the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
's core temperature. The CNO cycle is hypothesized to be dominant in stars that are more than 1.3 times as massive as the Sun. Unlike the proton-proton reaction, which consumes all its constituents, the CNO cycle is a
catalytic cycle In chemistry, a catalytic cycle is a multistep reaction mechanism that involves a catalyst. The catalytic cycle is the main method for describing the role of catalysts in biochemistry, organometallic chemistry, bioinorganic chemistry, materials ...
. 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 Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produce ...
(a stable helium nucleus), two
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collides ...
s, and two electron neutrinos. There are various alternative paths and catalysts involved in the CNO cycles, all these cycles have the same net result: :4   +   2 ::   →     +     +   ::   →     +     +   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. One nucleus goes on to become carbon, nitrogen, and oxygen isotopes through a number of transformations in an endless loop. 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 megakelvin), making it the dominant energy source in smaller stars. A self-maintaining CNO chain starts at approximately , but its energy output rises much more rapidly with increasing temperatures so that it becomes the dominant source of energy at approximately . The Sun has a
core Core or cores may refer to: Science and technology * Core (anatomy), everything except the appendages * Core (manufacturing), used in casting and molding * Core (optical fiber), the signal-carrying portion of an optical fiber * Core, the central ...
temperature of around , and only of nuclei produced in the Sun are born in the CNO cycle. The CNO-I process was independently proposed by Carl von Weizsäcker and Hans Bethe 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. 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.


Cold CNO cycles

Under typical conditions found in stars, catalytic hydrogen burning by the CNO cycles is limited by
proton capture Proton capture is a nuclear reaction in which an atomic nucleus and one or more protons collide and merge to form a heavier nucleus. Since protons have positive electric charge, they are repelled electrostatically by the positively charged nucl ...
s. Specifically, the timescale for
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For e ...
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 Carl Friedrich von Weizsäcker in 1937–38 and Hans Bethe. Bethe's 1939 papers on the CN-cycle drew on three earlier papers written in collaboration with Robert Bacher and Milton Stanley Livingston and which came to be known informally as ''"Bethe's Bible"''. It was considered the standard work on nuclear physics for many years and was a significant factor in his being awarded the 1967 Nobel Prize in Physics. Bethe's original calculations suggested the CN-cycle was the Sun's primary source of energy. This conclusion arose from a belief that is now known to be mistaken, that the abundance of nitrogen in the sun is approximately 10%; it is actually less than half a percent. The CN-cycle, named as it contains no stable isotope of oxygen, involves the following cycle of transformations: :   →     →     →     →     →     →   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: : 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 , 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 In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For exam ...
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. The limiting (slowest) reaction in the CNO-I cycle is the
proton capture Proton capture is a nuclear reaction in which an atomic nucleus and one or more protons collide and merge to form a heavier nucleus. Since protons have positive electric charge, they are repelled electrostatically by the positively charged nucl ...
on . In 2006 it was experimentally measured down to stellar energies, revising the calculated age of globular clusters by around 1 billion years. The neutrinos emitted in beta decay will have a spectrum of energy ranges, because although momentum 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 total momentum received by the positron and the neutrino is not great enough to cause a significant recoil of the much heavier daughter nucleus 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 to , and the neutrino emitted during the decay of oxygen-15 can have an energy from zero up to . On average, about 1.7 MeV of the total energy output is taken away by neutrinos for each loop of the cycle, leaving about available for producing luminosity.


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 shown above does not produce carbon-12 and an alpha particle, but instead produces oxygen-16 and a photon and continues : In detail: : Like the carbon, nitrogen, and oxygen involved in the main branch, the
fluorine Fluorine is a chemical element with the symbol F and atomic number 9. It is the lightest halogen and exists at standard conditions as a highly toxic, pale yellow diatomic gas. As the most electronegative reactive element, it is extremely reactiv ...
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 : → → → → → → In detail: :


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: : In some instances can combine with a helium nucleus to start a sodium-neon cycle.


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 nuclear drip line is the boundary beyond which atomic nuclei decay by the emission of a proton or neutron. An arbitrary combination of protons and neutrons does not necessarily yield a stable nucleus. One can think of moving up and/or to ...
. 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 capture Proton capture is a nuclear reaction in which an atomic nucleus and one or more protons collide and merge to form a heavier nucleus. Since protons have positive electric charge, they are repelled electrostatically by the positively charged nucl ...
s, they are also called the beta-limited CNO cycles.


HCNO-I

The difference between the CNO-I cycle and the HCNO-I cycle is that captures a proton instead of decaying, leading to the total sequence :→→→→→→ In detail: :


HCNO-II

The notable difference between the CNO-II cycle and the HCNO-II cycle is that captures a proton instead of decaying, and neon is produced in a subsequent reaction on , leading to the total sequence :→→→→→→ In detail: :


HCNO-III

An alternative to the HCNO-II cycle is that captures a proton moving towards higher mass and using the same helium production mechanism as the CNO-IV cycle as :→→→→→→ In detail: :


Use in astronomy

While the total number of "catalytic" nuclei are conserved in the cycle, in
stellar evolution Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, which is cons ...
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 A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses ()) in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around or ...
stars are observed to have lower carbon-12/carbon-13 and carbon-12/nitrogen-14 ratios than do
main sequence In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar H ...
stars, which is considered to be convincing evidence for the operation of the CNO cycle.


See also

* Proton–proton chain reaction, as found in stars like the Sun *
Stellar nucleosynthesis Stellar nucleosynthesis is the creation (nucleosynthesis) of chemical elements by nuclear fusion reactions within stars. Stellar nucleosynthesis has occurred since the original creation of hydrogen, helium and lithium during the Big Bang. A ...
, the whole topic * Triple-alpha process, how is produced from lighter nuclei


Footnotes


References


Further reading

* * {{DEFAULTSORT:Cno Cycle Nuclear fusion reactions Carbon Nitrogen Oxygen Fluorine Neon Nucleosynthesis