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.
When a star runs out of hydrogen to fuse in its core, it begins to collapse until the central temperature rises to 108 K, six times hotter than the sun's core. At this temperature and density, alpha particles are able to fuse rapidly enough (the half-life of 5Li is ×10−22 s and that of 8Be is 3.7×10−17 s) to produce significant amounts of carbon and restore 6.7thermodynamic equilibrium in the core
The net energy release of the process is 7.273 MeV (pJ). 1.166
As a side effect of the process, some carbon nuclei fuse with additional helium to produce a stable isotope of oxygen and 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 those elements are converted into neon and heavier elements. Both oxygen and carbon make up the 'ash' of helium-4 burning.
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.
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. These resonances 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. 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 controversially 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 (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. 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, 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 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.
The triple alpha process is highly dependent on carbon-12 and beryllium-8 having resonances with the same energy as helium-4, and before 1952, no such energy levels were known. The astrophysicist Fred Hoyle used the fact that carbon-12 is abundant in the universe as evidence for the existence of a carbon-12 resonance. This could be considered to be an example of the application of the anthropic principle: we are here, and we are made of carbon, thus the carbon must have been produced somehow. The only physically conceivable way is through a triple alpha process that requires the existence of a resonance in a given very specific location in the spectra of carbon-12 nuclei.
Hoyle went boldly into nuclear physicist William Alfred Fowler's lab at Caltech and said that there had to be a resonance of 7.69 MeV in the carbon-12 nucleus, and that all of the physicists in the world had missed it. Fred Hoyle's audacity in doing this is remarkable, and initially all the nuclear physicists in the lab were skeptical to say the least. But he was persistent and kept coming back to the lab and talked to every assistant and associate individually. Finally, a junior physicist, Ward Whaling, fresh from Rice University, who was looking for a project started believing Hoyle, and decided to look for the resonance. Fowler gave Ward permission to use an old Van de Graaff generator that no one else was using, and everyone joined in with suggestions for Ward. The experiment took 6 months, and Hoyle was back in Cambridge when his outrageous prediction was verified. They put Hoyle as first author on a paper delivered by Ward 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. By 1952, Fowler had 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 a project 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. This 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, 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 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 life that we know. 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 just above the energy level 8Be + 4He. This is necessary because the ground state of 12C is 7.3367 MeV below the energy of 8Be + 4He. Therefore, a 8Be nucleus and a 4He nucleus cannot reasonably fuse directly into a ground-state 12C nucleus. The excited Hoyle state of 12C is 7.656 MeV above the ground state of 12C. This allows 8Be and 4He to use the kinetic energy of their collision to fuse into the excited 12C, 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 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.
- Conversion of 12C + 4He to 16O is much more difficult than the production of carbon; no resonance exists for this reaction. Were this not true, insufficient carbon would exist in nature; it would almost all have converted to oxygen.
The 7.656 MeV Hoyle resonance, in particular, has been cited by physicists arguing for the existence of a multiverse where different regions of a vast multiverse have different fundamental constants. According to this controversial fine-tuning hypothesis, life can only evolve in rare patches of the multiverse where the fundamental constants are fine-tuned to support the existence of life.
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