Triple-alpha process
Encyclopedia
The triple alpha process is a set of nuclear fusion
reactions by which three helium-4
nuclei (alpha particle
s) are transformed into carbon
.
Older stars start to accumulate helium
produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle
in their cores. The products of further nuclear fusion reactions of helium with hydrogen or another helium nucleus produce lithium-5 and beryllium-8 respectively, both of which are highly unstable and decay almost instantly back into smaller nuclei. When the star starts to run out of hydrogen to fuse, the core of the star begins to collapse until the central temperature rises to . At this point helium nuclei are fusing together at a rate high enough to rival the rate at which their product, beryllium-8, decays back into two helium nuclei. This means that there are always a few beryllium-8 nuclei in the core, which can fuse with yet another helium nucleus to form carbon-12, which is stable:
The net energy release of the process is 7.275 MeV.
Because the triple-alpha process is unlikely, it requires a long period of time to produce carbon. One consequence of this is that no carbon was produced in the Big Bang
because within minutes after the Big Bang
, the temperature fell below that necessary for nuclear fusion.
Ordinarily, the probability of the triple alpha process would be 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. These resonance
s greatly increase 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. In turn, 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.
As a side effect of the process, some carbon nuclei can fuse with additional helium to produce a stable isotope of oxygen and release energy:
See alpha process for more details about this reaction and further steps in the chain of stellar nucleosynthesis.
This creates a situation in which stellar nucleosynthesis produces large amounts of carbon and oxygen but only a small fraction of these elements is converted into neon and heavier elements. Both oxygen and carbon make up the 'ash' of helium burning. The anthropic principle
has been controversially cited to explain the fact that nuclear resonances are sensitively arranged to create large amounts of carbon and oxygen in the universe.
Fusion processes produce elements only up to nickel
(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 these heavy elements. The other half are produced by rapid neutron capture, the R-process
, which probably occurs in a core-collapse supernova
.
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. The pressure in the core is thus nearly independent of temperature. A consequence of this is that once a smaller star begins burning using the triple-alpha process, the core does not expand and cool in response; the temperature can only increase, which results in the reaction rate increasing further still and becoming 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. In the core flash prodigious quantities of energy are produced, allowing the star to reach approximately 1011 solar luminosities which is comparable to a whole galaxy, although no effects will be immediately visible at the star's surface.
For higher mass stars, the helium burning occurs in a shell surrounding a degenerate carbon core. Since the helium shell is not degenerate, the increased thermal pressure due to energy released by helium burning causes the star to expand. The expansion cools the helium layer and shuts off the reaction, and the star contracts again. This cyclical process causes the star to become strongly variable, and results in it blowing off material from its outer layers.
and beryllium-8 having resonances with the same energy as helium-4
, and before 1952 no such energy level was known. Astrophysicist Fred Hoyle
used the fact that carbon-12 is abundant in the universe as evidence for the existence of the carbon-12 resonance, in what is an example of the application of the Anthropic Principle
: we are here, and we are made of carbon, so carbon must have originated somehow and the only physically conceivable way is through triple alpha processes that requires the existence of a resonance in a given very specific location in the spectra of carbon-12 nuclei. Hoyle suggested the idea to nuclear physicist William (Willy) A. Fowler
, who conceded that it was possible that this energy level had been missed in previous work. By 1952, Fowler had already discovered the beryllium-8 resonance, and Edwin Salpeter calculated the reaction rate taking this resonance into account. This helped to explain the rate of the process, but the rate calculated by Salpeter was still somewhat too low. A few years later, after an undertaking by his research group at the Kellogg Radiation Laboratory at the California Institute of Technology
, Fowler discovered a carbon-12 resonance near 7.65 MeV, which has eliminated the final discrepancy between the nuclear theory and the theory of stellar evolution.
The final reaction product lies in a 0+ state. Since the Hoyle State was predicted to be either a 0+ or a 2+ state, electron-positron pairs or gamma rays were expected to be seen. However, when experiments were carried out the gamma emission reaction channel was not observed. This meant the state must be a 0+ state as a gamma emission carries away at least 1 unit of angular momentum as photon are particles with intrinsic spin of 1. The electron-positron pair is favoured because they are fermion
s, and their combined spins (0) can couple to a reaction that has a change in angular momentum of 0.
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
reactions by which three helium-4
Helium-4
Helium-4 is a non-radioactive isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth. Its nucleus is the same as an alpha particle, consisting of two protons and two neutrons. Alpha decay of heavy...
nuclei (alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...
s) are transformed into carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...
.
Older stars start to accumulate helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle
CNO cycle
The CNO cycle is one of two sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain. Unlike the proton–proton chain reaction, the CNO cycle is a catalytic cycle. Theoretical models show that the CNO cycle is the dominant source of energy in stars...
in their cores. The products of further nuclear fusion reactions of helium with hydrogen or another helium nucleus produce lithium-5 and beryllium-8 respectively, both of which are highly unstable and decay almost instantly back into smaller nuclei. When the star starts to run out of hydrogen to fuse, the core of the star begins to collapse until the central temperature rises to . At this point helium nuclei are fusing together at a rate high enough to rival the rate at which their product, beryllium-8, decays back into two helium nuclei. This means that there are always a few beryllium-8 nuclei in the core, which can fuse with yet another helium nucleus to form carbon-12, which is stable:
| + → | (−93.7 keV) |
| + → + + | (+7.367 MeV) |
The net energy release of the process is 7.275 MeV.
Because the triple-alpha process is unlikely, it requires a long period of time to produce carbon. One consequence of this is that no carbon was produced in the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
because within minutes after the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
, the temperature fell below that necessary for nuclear fusion.
Ordinarily, the probability of the triple alpha process would be 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
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
of 12C. These resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
s greatly increase 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
Fred Hoyle
Sir Fred Hoyle FRS was an English astronomer and mathematician noted primarily for his contribution to the theory of stellar nucleosynthesis and his often controversial stance on other cosmological and scientific matters—in particular his rejection of the "Big Bang" theory, a term originally...
before its actual observation, based on the physical necessity for it to exist, in order for carbon to be formed in stars. In turn, prediction and then discovery of this energy resonance and process gave very significant support to Hoyle's hypothesis of stellar nucleosynthesis
Stellar nucleosynthesis
Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...
, which posited that all chemical elements had originally been formed from hydrogen, the true primordial substance.
As a side effect of the process, some carbon nuclei can fuse with additional helium to produce a stable isotope of oxygen and release energy:
- + → + γ (+7.162 MeV)
See alpha process for more details about this reaction and further steps in the chain of stellar nucleosynthesis.
This creates a situation in which stellar nucleosynthesis produces large amounts of carbon and oxygen but only a small fraction of these elements is converted into neon and heavier elements. Both oxygen and carbon make up the 'ash' of helium burning. The anthropic principle
Anthropic principle
In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...
has been controversially cited to explain the fact that nuclear resonances are sensitively arranged to create large amounts of carbon and oxygen in the universe.
Fusion processes produce elements only up to nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...
(which decays later to iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
); heavier elements (those beyond Ni) are created mainly by neutron capture. The slow capture of neutrons, the S-process
S-process
The S-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay...
, produces about half of these heavy elements. The other half are produced by rapid neutron capture, the R-process
R-process
The r-process is a nucleosynthesis process, likely occurring in core-collapse supernovae responsible for the creation of approximately half of the neutron-rich atomic nuclei that are heavier than iron. The process entails a succession of rapid neutron captures on seed nuclei, typically Ni-56,...
, which probably occurs in a core-collapse supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
.
Reaction rate and stellar evolution
The triple-alpha steps is strongly dependent on the temperature and density of the stellar material. The energy released by the reaction is approximately proportional to the temperature to the 30th power, and the density squared. Contrast this to the PP chain which produces energy at a rate proportional to the fourth power of temperature and directly with density.This strong temperature dependence has consequences for the late stage of stellar evolution, the red giant
Red giant
A red giant is a luminous giant star of low or intermediate mass in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower...
stage.
For lower mass stars, the helium accumulating in the core is prevented from further collapse only by electron degeneracy
Degenerate matter
Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...
pressure. The pressure in the core is thus nearly independent of temperature. A consequence of this is that once a smaller star begins burning using the triple-alpha process, the core does not expand and cool in response; the temperature can only increase, which results in the reaction rate increasing further still and becoming a runaway
Thermal runaway
Thermal runaway refers to a situation where an increase in temperature changes the conditions in a way that causes a further increase in temperature, often leading to a destructive result...
reaction. This process, known as the helium flash
Helium flash
A helium flash is the runaway fusion of helium in the core of low mass stars of less than about 2.25 solar masses and greater than about 0.5 solar mass, or on the surface of an accreting white dwarf star. They may also occur in the outer layers of larger stars in shell flashes...
, lasts a matter of seconds but burns 60–80% of the helium in the core. In the core flash prodigious quantities of energy are produced, allowing the star to reach approximately 1011 solar luminosities which is comparable to a whole galaxy, although no effects will be immediately visible at the star's surface.
For higher mass stars, the helium burning occurs in a shell surrounding a degenerate carbon core. Since the helium shell is not degenerate, the increased thermal pressure due to energy released by helium burning causes the star to expand. The expansion cools the helium layer and shuts off the reaction, and the star contracts again. This cyclical process causes the star to become strongly variable, and results in it blowing off material from its outer layers.
Discovery
The triple alpha process is highly dependent on carbon-12Carbon-12
Carbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
and beryllium-8 having resonances with the same energy as helium-4
Helium-4
Helium-4 is a non-radioactive isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth. Its nucleus is the same as an alpha particle, consisting of two protons and two neutrons. Alpha decay of heavy...
, and before 1952 no such energy level was known. Astrophysicist Fred Hoyle
Fred Hoyle
Sir Fred Hoyle FRS was an English astronomer and mathematician noted primarily for his contribution to the theory of stellar nucleosynthesis and his often controversial stance on other cosmological and scientific matters—in particular his rejection of the "Big Bang" theory, a term originally...
used the fact that carbon-12 is abundant in the universe as evidence for the existence of the carbon-12 resonance, in what is an example of the application of the Anthropic Principle
Anthropic principle
In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...
: we are here, and we are made of carbon, so carbon must have originated somehow and the only physically conceivable way is through triple alpha processes that requires the existence of a resonance in a given very specific location in the spectra of carbon-12 nuclei. Hoyle suggested the idea to nuclear physicist William (Willy) A. Fowler
William Alfred Fowler
William Alfred "Willy" Fowler was an American astrophysicist and winner of the Nobel Prize for Physics in 1983. He should not be confused with the British astronomer Alfred Fowler....
, who conceded that it was possible that this energy level had been missed in previous work. By 1952, Fowler had already discovered the beryllium-8 resonance, and Edwin Salpeter calculated the reaction rate taking this resonance into account. This helped to explain the rate of the process, but the rate calculated by Salpeter was still somewhat too low. A few years later, after an undertaking by his research group at the Kellogg Radiation Laboratory at the California Institute of Technology
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
, Fowler discovered a carbon-12 resonance near 7.65 MeV, which has eliminated the final discrepancy between the nuclear theory and the theory of stellar evolution.
The final reaction product lies in a 0+ state. Since the Hoyle State was predicted to be either a 0+ or a 2+ state, electron-positron pairs or gamma rays were expected to be seen. However, when experiments were carried out the gamma emission reaction channel was not observed. This meant the state must be a 0+ state as a gamma emission carries away at least 1 unit of angular momentum as photon are particles with intrinsic spin of 1. The electron-positron pair is favoured because they are fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s, and their combined spins (0) can couple to a reaction that has a change in angular momentum of 0.