CNO cycle - Lecture notes 1 PDF

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Carbon-Nitrogen-Oxygen Cycle-1...

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CNO cycle

Carbon-Nitrogen-Oxygen Cycle-1 The CNO cycle (for carbon–nitrogen–oxygen) is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain reaction. Unlike the latter, the CNO cycle is a catalytic cycle. It is dominant in stars that are more than 1.3 times as massive as the Sun.[1] In the CNO cycle, four protons fuse, using carbon, nitrogen, and oxygen isotopes as catalysts, to produce one alpha particle, two positrons and two electron neutrinos. Although there are various paths and catalysts involved in the CNO cycles, all these cycles have the same net result: 4 1 1H + 2 e− → 42He + 2 e+ + 2 e− + 2 νe + 3 γ + 24.7 MeV → 42He + 2 νe + 3 γ + 26.7 MeV

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 to become carbon, nitrogen, and oxygen isotopes through a number of transformations in an endless loop. Theoretical models suggest that the CNO cycle is the dominant source of energy in stars whose mass is greater than about 1.3 times that of the Sun.[1] 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[2] (4 megakelvins), making it the dominant energy source in smaller stars. A selfmaintaining CNO chain starts at approximately 15×106 K, but its energy output rises much more rapidly with increasing temperatures.[1] At approximately 17×106 K, the CNO cycle starts becoming the dominant source of energy.[3] 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[4] and Hans Bethe[5] in 1938 and 1939, respectively.

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 honorarily referred to as the Bethe–Weizsäcker cycle, because it does not involve a stable isotope of oxygen. Bethe's original calculations suggested the CN-cycle was the Sun's primary source of energy, owing to the belief at the time that the Sun's composition was 10% nitrogen;[5] the solar abundance of nitrogen is now known to be less than half a percent. This cycle is now recognized as the first part of the larger CNO nuclear burning network. The main reactions of the CNO-I cycle are 12 6C →13 7N →13 6C →14 7N →15 8O →15 7N →12 6C

12 1 13 6C + 1H → 7N + γ 13 7N

13 → 6C + e+

+ 1.95 MeV

+ ν + 1.20 MeV (half-life of 9.965 minutes[7]) e

13 1 14 6C + 1H → 7N + γ

+ 7.54 MeV

14 1 15 7N + 1H → 8O + γ

+ 7.35 MeV

15 8O

15 → 7N + e+

15 1 12 4 7N + 1H → 6C + 2He

+ ν + 1.73 MeV (half-life of 122.24 seconds[7]) e + 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; it should be noted that 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.[8] 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.[9] 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 electron 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 1.20 MeV, and the neutrino emitted during the decay of oxygen-15 can have an energy from zero up to 1.73 MeV. On average, about 1.7 MeV of the total energy output is taken away by neutrinos for each loop of the cycle, leaving about 25 MeV available for producing luminosity.[10]

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 15 7N shown above does not produce carbon-12 and an alpha particle, but instead produces oxygen-16 and a photon and continues: 15 7N →16 8O →17 9F →17 8O →14 7N →15 8O →15 7N

1 16 15 + 1H → 8O + γ 7N 16 1 17 8O + 1H → 9F + γ 17 9F

17 → 8O + e+

+ 12.13 MeV

+ 0.60 MeV

+ ν + 2.76 MeV (half-life of 64.49 seconds) e

1 14 4 17 8O + 1H → 7N + 2He

+ 1.19 MeV

14 1 15 7N + 1H → 8O + γ

+ 7.35 MeV

15 8O

15 → 7N + e+

+ ν + 2.75 MeV (half-life of 122.24 seconds) e

Like the carbon, nitrogen, and oxygen involved in the main branch, the fluorine produced in the minor branch is merely an intermediate product and at steady state, 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 gamma instead of nitrogen-14 and alpha, and continues 17 1 18 8O + 1H → 9F + γ

17 8O →18 9F →18 8O →15 7N →16 8O →17 9F →17 8O

18 9F

18 → 8O + e+

+ 5.61 MeV

+ ν + 1.656 MeV (half-life of 109.771 minutes) e

18 1 15 4 8O + 1H → 7N + 2He

+ 3.98 MeV

15 1 16 7N + 1H → 8O + γ

+ 12.13 MeV

16 1 17 8O + 1H → 9F + γ

+ 0.60 MeV

17 9F

17 → 8O + e+

+ ν + 2.76 MeV (half-life of 64.49 seconds) e

CNO-IV

A proton reacts with a nucleus causing release of an alpha particle. 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 gamma instead of nitrogen-15 and alpha, and continues 19 9F →16 8O →17 9F →17 8O →18 9F →18 8O →19 9F

19 1 16 4 9F + 1H → 8O + 2He

+ 8.114 MeV

16 1 17 8O + 1H → 9F + γ

+ 0.60 MeV

17 9F

17 → 8O + e+

17 1 18 8O + 1H → 9F + γ 18 9F

18 → 8O + e+

18 1 19 8O + 1H → 9F + γ

+ ν + 2.76 MeV (half-life of 64.49 seconds) e + 5.61 MeV

+ ν + 1.656 MeV (half-life of 109.771 minutes) e + 7.994 MeV

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 captures a proton instead of decaying, leading to the total sequence 12 6C →13 7N →14 8O →14 7N →15 8O →15 7N →12 6C

12 1 13 6C + 1H → 7N + γ

+ 1.95 MeV

14 1 13 7N + 1H → 8O + γ

+ 4.63 MeV

14 8O

14 → 7N + e+

14 1 15 7N + 1H → 8O + γ 15 8O

15 → 7N + e+

15 1 12 4 7N + 1H → 6C + 2He

13

7N

+ ν + 5.14 MeV (half-life of 70.641 seconds) e + 7.35 MeV

+ ν + 2.75 MeV (half-life of 122.24 seconds) e + 4.96 MeV

HCNO-II The notable difference between the CNO-II cycle and the HCNO-II cycle is that 17 9F captures a proton instead of decaying, and neon is produced in a subsequent reaction on 18 9F , leading to the total sequence 15 7N →16 8O →17 9F →18 10Ne →18 9F →15 8O →15 7N

15 7N

1 16 + 1H → 8O

+ γ

+ 12.13 MeV

16 8O

1 17 + 1H → 9F

+ γ

+ 0.60 MeV

17 9F

1 18 + 1H → 10Ne + γ

+ 3.92 MeV

18 10Ne

18 → 9F

18 9F

1 15 + 1H → 8O

15 8O

15 → 7N

+ e+ 4 + 2He

+ e+

(half-life + ν + 4.44 MeV seconds) e

of

1.672

of

122.24

+ 2.88 MeV (half-life + ν + 2.75 MeV seconds) e

HCNO-III An alternative to the HCNO-II cycle is that 189F captures a proton moving towards higher mass and using the same helium production mechanism as the CNO-IV cycle as 18 9F →19 10Ne →19 9F →16 8O →17 9F →18 10Ne →18 9F

18 9F 19 10Ne

1 19 + 1H → 10Ne + γ 19 → 9F

+ e+

+ 6.41 MeV

+ ν + 3.32 MeV (half-life of 17.22 seconds) e

19 9F

1 16 + 1H → 8O

4 + 2He

+ 8.11 MeV

16 8O

1 17 + 1H → 9F

+ γ

+ 0.60 MeV

17 9F

1 18 + 1H → 10Ne + γ

+ 3.92 MeV

18 10Ne

18 → 9F

+ e+

+ ν + 4.44 MeV (half-life of 1.672 seconds) e

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 carbon12/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.

Proton-Proton Fusion This is the nuclear fusion process which fuels the Sun and other stars which have core temperatures less than 15 million Kelvin. A reaction cycle yields about 25 MeV of energy.

Proton-Proton Cycle The fusion of hydrogen in lower temperature stars like our Sun involve the following reactions yielding positrons, neutrinos, and gamma rays.

The solar neutrino problem

which can be followed by either The latter of these reactions is part of what is usually called the proton-proton cycle, which yields about 25 MeV and can be combined to the form

Step 1. Proton Fusion

The fusing of two protons which is the first step of the proton-proton cycle created great problems for early theorists because they recognized that the interior temperature of the sun (some 14 million Kelvins) would not provide nearly enough energy to overcome the coulomb barrier of electric repulsion between two protons. Next step

With the development of quantum mechanics, it was realized that on this scale the protons must be considered to have wave properties and that there was the possibility of tunneling through the coulomb barrier. Proton-proton cycle

Eddington and his fusion critics Arthur Eddington thought that nuclear processes must be involved to account for the radiant energy of the sun, but was criticized because the temperature was seen to be not hot enough when considered by classical physics alone. His tongue-in-cheek reply to his critics: "I am aware that many critics consider the stars are not hot enough. The critics lay themselves open to an obvious retort; we tell them to go and find a hotter place." Proton-proton cycle

Step 2. Deuterium formation The second step of the proton-proton cycle . This step involves the weak interaction because it involves the transmutation of one of the protons to a neutron in order to form deuterium. This process requires energy and produces a positron and an electron neutrino. Next step

In the proton-proton fusion process, deuterium is produced by the weak interaction in a quark transformation which converts one of the protons to a neutron. The neutrinos quickly escape the sun, requiring only about 2 seconds to exit the sun compared to perhaps a million years for a photon to traverse from the center to the surface of the sun. The neutrino flux can be calculated, but earlier measurements of the neutrino flux measured only about a third of the expected number. This is called the solar neutrino problem. It is now presumed to be solved with the evidence for neutrino oscillation at the Sudbury Neutrino Observatory and at the Super Kamiokande neutrino detector. Proton-proton cycle

Step 3. Deuterium-proton fusion

The third step of the proton-proton cycle . Next step

Step 4. Helium-3 fusion

The fourth step of the proton-proton cycle .

Next step

Step 5. Alpha particle formation

The fifth step of the proton-proton cycle . Alpha particles are the end product of the proton-proton fusion cycle. They are formed by the fusion of two helium-3 nuclei.

Proton-proton cycle

Triple-alpha process "Helium burning" redirects here. It is not to be confused with alpha process.

The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon.[1][2] Triple-alpha process in stars Helium accumulates in the core of stars as a result of the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle. Further nuclear fusion reactions of helium with hydrogen or another alpha particle produce lithium-5 and beryllium-8 respectively. Both products are highly unstable and decay, almost instantly, back into smaller nuclei, unless a third alpha particle fuses with a beryllium before that time to produce a stable carbon-12 nucleus.[3]

When a star runs out of hydrogen to fuse in its core, it begins to collapse until the central temperature rises to 108 K,[4] six times hotter than the sun's core. At this temperature and density, alpha particles can fuse fast enough (the half-life of 5Li is 3.7×10−22 s and that of 8Be is 6.7×10−17 s) to produce significant amounts of carbon and restore thermodynamic equilibrium in the core 4 2He + 4 2He (−91.8 keV) → 8 4Be 8 4Be + 4 2He → 12 (+7.367 MeV) 6C + 2 γ

The net energy release of the process is 7.273 MeV (1.166 pJ). As a side effect of the process, some carbon nuclei fuse with additional helium to produce a stable isotope of oxygen and energy: 12 6C + 2He → 8O + γ (+7.162 MeV)

4 16

This creates a situation in which stellar nucleosynthesis produces large amounts of carbon and oxygen but only a small fraction of those elements are converted into neon and heavier elements. Both oxygen and carbon make up the 'ash' of helium-4 burning. Primordial carbon Because the triple-alpha process is unlikely, it normally needs a long time to produce much carbon. One consequence of this is that no significant amount of carbon was produced in the Big Bang because within minutes after the Big Bang, the temperature fell below the critical point for nuclear fusion. Resonances Ordinarily, the probability of the triple alpha process is extremely small. However, the beryllium-8 ground state has almost exactly the energy of two alpha particles. In the second step, 8Be + 4He has almost exactly

the energy of an excited state of 12C. This "resonance" greatly increases the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted by Fred Hoyle before its actual observation, based on the physical necessity for it to exist, in order for carbon to be formed in stars. The prediction and then discovery of this energy resonance and process gave very significant support to Hoyle's hypothesis of stellar nucleosynthesis, which posited that all chemical elements had originally been formed from hydrogen, the true primordial substance. The anthropic principle has been cited to explain the fact that nuclear resonances are sensitively arranged to create large amounts of carbon and oxygen in the universe.[5][6] Nucleosynthesis of heavy elements With further increases of temperature and density, fusion processes produce nuclides only up to nickel-56 (which decays later to iron); heavier elements (those beyond Ni) are created mainly by neutron capture. The slow capture of neutrons, the s-process, produces about half of elements beyond iron. The other half are produced by rapid neutron capture, the r-process, which probably occurs in a core-collapse supernova. Reaction rate and stellar evolution The triple-alpha steps are strongly dependent on the temperature and density of the stellar material. The power released by the reaction is approximately proportional to the temperature to the 40th power, and the density squared.[7] In contrast, the PP chain produces energy at a rate proportional to the fourth power of temperature, the CNO cycle at about the 17th power of the temperature, and both are linearly proportional to the density. This strong temperature dependence has consequences for the late stage of stellar evolution, the red giant stage. For lower mass stars, the helium accumulating in the core is prevented from further collapse only by electron degeneracy pressure. As the temperature rises, increased pressure in the core would normally result in an expansion, reduction of density, and thus reduction in reaction rate. However, due to the high pressure at the center of the star this does not occur and energy production continues unmoderated. As a consequence, the temperature increases, causing the reaction rate further increase in a positive feedback cycle that becomes a runaway reaction. This process, known as the helium flash, lasts a matter of seconds but burns 60–80% of the helium in the core. During the core flash, the star's energy production can reach approximately 1011 solar luminosities which is comparable to the luminosity of a whole galaxy,[8] although no effects will be immediately observed at the surface, as it is hidden by the star's overlying layers. For higher mass stars, carbon collects in the core, displacing the helium to a surrounding shell where helium burning occurs. In this helium shell, the pressures are lower and the mass is not supported by electron degeneracy. Thus, as opposed to the center of the star, the shell is able to expand in response to increased thermal pressure in the helium shell. Expansion cools this layer and slows the reaction, causing the star to contract again. This proces...