Triple-alpha Process
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The triple-alpha process is a set of
nuclear fusion Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles ( neutrons or protons). The difference in mass between the reactants and products is manifest ...
reactions by which three
helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...
nuclei (
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 pr ...
s) are transformed into
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with o ...
.


Triple-alpha process in stars

Helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
accumulates in the
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 centra ...
s of stars as a result of the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle. Nuclear fusion reaction of two helium-4 nuclei produces
beryllium-8 Beryllium-8 (8Be, Be-8) is a radionuclide with 4 neutrons and 4 protons. It is an unbound resonance and nominally an isotope of beryllium. It decays into two alpha particles with a half-life on the order of 8.19 seconds. This has important r ...
, which is highly unstable, and decays back into smaller nuclei with a half-life of , unless within that time a third alpha particle fuses with the beryllium-8 nucleus to produce an excited
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
state of carbon-12, called the
Hoyle state Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
, which nearly always decays back into three alpha particles, but once in about 2421.3 times releases energy and changes into the stable base form of carbon-12. When a star runs out of
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
to fuse in its core, it begins to contract and heat up. If the central temperature rises to 108 K, six times hotter than the Sun's core, alpha particles can fuse fast enough to get past the beryllium-8 barrier and produce significant amounts of stable carbon-12. : The net energy release of the process is 7.275 MeV. As a side effect of the process, some carbon nuclei fuse with additional helium to produce a stable isotope of oxygen and energy: : + → + (+7.162 MeV) Nuclear fusion reactions of helium with hydrogen produces
lithium-5 Naturally occurring lithium (3Li) is composed of two stable isotopes, lithium-6 and lithium-7, with the latter being far more abundant on Earth. Both of the natural isotopes have an unexpectedly low nuclear binding energy per nucleon ( for li ...
, which also is highly unstable, and decays back into smaller nuclei with a half-life of . Fusing with additional helium nuclei can create heavier elements in a chain of stellar nucleosynthesis known as the
alpha process The alpha process, also known as the alpha ladder, is one of two classes of nuclear fusion reactions by which stars convert helium into heavier elements, the other being the triple-alpha process. The triple-alpha process consumes only helium, a ...
, but these reactions are only significant at higher temperatures and pressures than in cores undergoing the triple-alpha process. 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. Oxygen and carbon are the main "ash" of helium-4 burning.


Primordial carbon

The triple-alpha process is ineffective at the pressures and temperatures early in the Big Bang. One consequence of this is that no significant amount of carbon was produced in the Big Bang.


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 Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
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 Sir Fred Hoyle FRS (24 June 1915 – 20 August 2001) was an English astronomer who formulated the theory of stellar nucleosynthesis and was one of the authors of the influential B2FH paper. He also held controversial stances on other sci ...
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.


Nucleosynthesis of heavy elements

With further increases of temperature and density, fusion processes produce nuclides only up to
nickel-56 Naturally occurring nickel (28Ni) is composed of five stable isotopes; , , , and , with being the most abundant (68.077% natural abundance). 26 radioisotopes have been characterised with the most stable being with a half-life of 76,000 years, ...
(which decays later to
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
); 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
core-collapse supernova A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or when ...
e and
neutron star merger A neutron star merger is a type of stellar collision. It occurs in a fashion similar to the rare brand of type Ia supernovae resulting from merging white dwarf stars. When two neutron stars orbit each other closely, they gradually spiral i ...
s.


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. In contrast, the proton–proton chain reaction produces energy at a rate proportional to the fourth power of temperature, the
CNO cycle The CNO cycle (for carbon–nitrogen–oxygen; sometimes called Bethe–Weizsäcker cycle after Hans Albrecht Bethe and Carl Friedrich von Weizsäcker) is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, ...
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 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 o ...
stage. For lower mass stars on the
red-giant branch The red-giant branch (RGB), sometimes called the first giant branch, is the portion of the giant branch before helium ignition occurs in the course of stellar evolution. It is a stage that follows the main sequence for low- to intermediate-mass sta ...
, the helium accumulating in the core is prevented from further collapse only by electron degeneracy pressure. The entire degenerate core is at the same temperature and pressure, so when its density becomes high enough, fusion via the triple-alpha process rate starts throughout the core. The core is unable to expand in response to the increased energy production until the pressure is high enough to lift the degeneracy. As a consequence, the temperature increases, causing an increased reaction rate 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 The solar luminosity (), is a unit of radiant flux (Power (physics), power emitted in the form of photons) conventionally used by astronomers to measure the luminosity of stars, galaxy, galaxies and other celestial objects in terms of the output o ...
which is comparable to the luminosity of a whole galaxy, although no effects will be immediately observed at the surface, as the whole energy is used up to lift the core from the degenerate to normal, gaseous state. Since the core is no longer degenerate, hydrostatic equilibrium is once more established and the star begins to "burn" helium at its core and hydrogen in a spherical layer above the core. The star enters a steady helium-burning phase which lasts about 10% of the time it spent on the main sequence (our Sun is expected to burn helium at its core for about a billion years after the helium flash). 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 process continues cyclically, and stars undergoing this process will have periodically variable radius and power production. These stars will also lose material from their outer layers as they expand and contract.


Discovery

The triple-alpha process is highly dependent on carbon-12 and
beryllium-8 Beryllium-8 (8Be, Be-8) is a radionuclide with 4 neutrons and 4 protons. It is an unbound resonance and nominally an isotope of beryllium. It decays into two alpha particles with a half-life on the order of 8.19 seconds. This has important r ...
having resonances with slightly more energy than
helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...
. Based on known resonances, by 1952 it seemed impossible for ordinary stars to produce carbon as well as any heavier element.Kragh, Helge (2010) When is a prediction anthropic? Fred Hoyle and the 7.65 MeV carbon resonance. http://philsci-archive.pitt.edu/5332/ Nuclear physicist
William Alfred Fowler William Alfred Fowler ( ) was an American nuclear physicist, later astrophysicist, who, with Subrahmanyan Chandrasekhar, won the 1983 Nobel Prize in Physics. He is known for his theoretical and experimental research into nuclear reactions with ...
had noted the beryllium-8 resonance, and
Edwin Salpeter Edwin Ernest Salpeter (3 December 1924 – 26 November 2008,) was an Austrian–Australian–American astrophysicist. Life Born in Vienna to a Jewish family, Salpeter emigrated from Austria to Australia while in his teens to escape the Nazis. He ...
had calculated the reaction rate for 8Be, 12C, and 16O nucleosynthesis taking this resonance into account. However, Salpeter calculated that red giants burned helium at temperatures of 2·108 K or higher, whereas other recent work hypothesized temperatures as low as 1.1·108 K for the core of a red giant. Salpeter's paper mentioned in passing the effects that unknown resonances in carbon-12 would have on his calculations, but the author never followed up on them. It was instead astrophysicist
Fred Hoyle Sir Fred Hoyle FRS (24 June 1915 – 20 August 2001) was an English astronomer who formulated the theory of stellar nucleosynthesis and was one of the authors of the influential B2FH paper. He also held controversial stances on other sci ...
who, in 1953, used the abundance of carbon-12 in the universe as evidence for the existence of a carbon-12 resonance. The only way Hoyle could find that would produce an abundance of both carbon and oxygen was through a triple-alpha process with a carbon-12 resonance near 7.68 MeV, which would also eliminate the discrepancy in Salpeter's calculations. Hoyle went to Fowler's lab at
Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
and said that there had to be a resonance of 7.68 MeV in the carbon-12 nucleus. (There had been reports of an excited state at about 7.5 MeV.) Fred Hoyle's audacity in doing this is remarkable, and initially the nuclear physicists in the lab were skeptical. Finally, a junior physicist,
Ward Whaling Ward may refer to: Division or unit * Hospital ward, a hospital division, floor, or room set aside for a particular class or group of patients, for example the psychiatric ward * Prison ward, a division of a penal institution such as a priso ...
, fresh from
Rice University William Marsh Rice University (Rice University) is a Private university, private research university in Houston, Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranke ...
, who was looking for a project decided to look for the resonance. Fowler gave Whaling permission to use an old
Van de Graaff generator A Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate electric charge on a hollow metal globe on the top of an insulated column, creating very high electric potentials. It produces very high voltage ...
that was not being used. Hoyle was back in Cambridge when Fowler's lab discovered a carbon-12 resonance near 7.65 MeV a few months later, validating his prediction. The nuclear physicists put Hoyle as first author on a paper delivered by Whaling at the summer meeting of the American Physical Society. A long and fruitful collaboration between Hoyle and Fowler soon followed, with Fowler even coming to Cambridge. The final reaction product lies in a 0+ state (spin 0 and positive parity). Since the
Hoyle state Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
was predicted to be either a 0+ or a 2+ state, electron–positron pairs or
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
s were expected to be seen. However, when experiments were carried out, the gamma emission reaction channel was not observed, and this meant the state must be a 0+ state. This state completely suppresses single gamma emission, since single gamma emission must carry away at least 1 unit of angular momentum.
Pair production Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifi ...
from an excited 0+ state is possible because their combined spins (0) can couple to a reaction that has a change in angular momentum of 0.


Improbability and fine-tuning

Carbon is a necessary component of all known life. 12C, a stable isotope of carbon, is abundantly produced in stars due to three factors: # The decay lifetime of a 8Be nucleus is four orders of magnitude larger than the time for two 4He nuclei (alpha particles) to scatter. # An excited state of the 12C nucleus exists a little (0.3193 MeV) above the energy level of 8Be + 4He. This is necessary because the ground state of 12C is 7.3367 MeV below the energy of 8Be + 4He; a 8Be nucleus and a 4He nucleus cannot reasonably fuse directly into a ground-state 12C nucleus. However, 8Be and 4He use the
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...
of their collision to fuse into the excited 12C (kinetic energy supplies the additional 0.3193 MeV necessary to reach the excited state), which can then transition to its stable ground state. According to one calculation, the energy level of this excited state must be between about 7.3 MeV and 7.9 MeV to produce sufficient carbon for life to exist, and must be further "fine-tuned" to between 7.596 MeV and 7.716 MeV in order to produce the abundant level of 12C observed in nature. The Hoyle state has been measured to be about 7.65 MeV above the ground state of 12C. # In the reaction 12C + 4He → 16O, there is an excited state of oxygen which, if it were slightly higher, would provide a resonance and speed up the reaction. In that case, insufficient carbon would exist in nature; almost all of it would have converted to oxygen. Some scholars argue the 7.656 MeV Hoyle resonance, in particular, is unlikely to be the product of mere chance.
Fred Hoyle Sir Fred Hoyle FRS (24 June 1915 – 20 August 2001) was an English astronomer who formulated the theory of stellar nucleosynthesis and was one of the authors of the influential B2FH paper. He also held controversial stances on other sci ...
argued in 1982 that the Hoyle resonance was evidence of a "superintellect";
Leonard Susskind Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicis ...
in '' The Cosmic Landscape'' rejects Hoyle's
intelligent design Intelligent design (ID) is a pseudoscientific argument for the existence of God, presented by its proponents as "an evidence-based scientific theory about life's origins". Numbers 2006, p. 373; " Dcaptured headlines for its bold attempt to ...
argument. Instead, some scientists believe that different universes, portions of a vast " multiverse", have different fundamental constants: according to this controversial
fine-tuning In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to fit with certain observations. This had led to the discovery that the fundamental constants and quantities fall into suc ...
hypothesis, life can only evolve in the minority of universes where the fundamental constants happen to be fine-tuned to support the existence of life. Other scientists reject the hypothesis of the multiverse on account of the lack of independent evidence.


References

{{DEFAULTSORT:Triple-Alpha Process Nucleosynthesis