Triple-alpha process

Overview of the triple-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]

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.^[3] 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 10⁸ K^[4] (8.6 keV). At this point helium nuclei begin to fuse together faster than their product, beryllium-8, decays back into two helium nuclei.

Once beryllium-8 is produced a little faster than it decays, the number of beryllium-8 nuclei in the stellar core increases to a large number. Then in its core there will be many beryllium-8 nuclei that can fuse with another helium nucleus to form carbon-12, which is stable:

4 2He + 4 2He → 8 4Be	(−91.8 keV)
8 4Be + 4 2He → 12 6C	(+7.367 MeV)

The net energy release of the process is 1.166 pJ (7.273 MeV).

Because the triple-alpha process is unlikely, it 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. 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:

12
6C + 4
2He → 16
8O + 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-4 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 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 these heavy elements. 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.^[5] 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 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. The core flash allows the star's energy production to reach approximately 10¹¹ solar luminosities which is comparable to the luminosity of a whole galaxy,^[6] although no effects will be immediately observed in electromagnetic radiation.

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-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.^[7] By 1952, Fowler had discovered the beryllium-8 resonance, and Edwin Salpeter calculated the reaction rate taking this resonance into account.^[8][9]

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.^[10]

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:

1. The decay lifetime of a ⁸Be nucleus is four orders of magnitude larger than the time for two ⁴He nuclei (alpha particles) to scatter.^[11]
2. 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.^[12]
3. 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.^[11]

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.

References

1. Appenzeller; Harwit; Kippenhahn; Strittmatter; Trimble, eds. (1998). Astrophysics Library (3rd ed.). New York: Springer. ISBN.
2. Ostlie, D.A. & Carroll, B.W. (2007). An Introduction to Modern Stellar Astrophysics. Addison Wesley, San Francisco. ISBN 0-8053-0348-0.
3. G. Audia,§, O. Bersillonb, J. Blachotb and A.H. Wapstrac, http://www.nndc.bnl.gov/amdc/nubase/Nubase2003.pdf/ The NUBASE evaluation of nuclear and decay properties, (2001)
4. Wilson, Robert (1997). "Chapter 11: The Stars- their Birth, Life, and Death". Astronomy through the ages the story of the human attempt to understand the universe. Basingstoke: Taylor & Francis. ISBN 9780203212738.
5. Carroll, Bradley W.; Ostlie, Dale A. (2006). An Introduction to Modern Astrophysics (2nd ed.). Addison-Wesley, San Francisco. pp. 312–313. ISBN 0-8053-0402-9.
6. Carroll, Bradley W.; Ostlie, Dale A. (2006). An Introduction to Modern Astrophysics (2nd ed.). Addison-Wesley, San Francisco. pp. 461–462. ISBN 0-8053-0402-9.
7. Fred Hoyle, A Life in Science, Simon Mitton, Cambridge University Press, 2011, pages 205 - 209.
8. Salpeter, E. E. (1952). "Nuclear Reactions in Stars Without Hydrogen". The Astrophysical Journal 115: 326–328. Bibcode:1952ApJ...115..326S. doi:10.1086/145546.
9. Salpeter, E. E. (2002). "A GENERALIST LOOKS BACK". Annu. Rev. Astron. Astrophys. 40: 1–25. Bibcode:2002ARA&A..40....1S. doi:10.1146/annurev.astro.40.060401.093901.
10. Cook, CW; Fowler, W.; Lauritsen, C.; Lauritsen, T. (1957). "12B, 12C, and the Red Giants". Physical Review 107 (2): 508–515. Bibcode:1957PhRv..107..508C. doi:10.1103/PhysRev.107.508.
11. Uzan, Jean-Philippe (April 2003). "The fundamental constants and their variation: observational and theoretical status". Reviews of Modern Physics 75 (2): 403–455. arXiv:hep-ph/0205340. Bibcode:2003RvMP...75..403U. doi:10.1103/RevModPhys.75.403.
12. Livio, M.; Hollowell, D.; Weiss, A.; Truran, J. W. (27 July 1989). "The anthropic significance of the existence of an excited state of 12C". Nature 340 (6231): 281–284. Bibcode:1989Natur.340..281L. doi:10.1038/340281a0.