Triple-alpha process

"Helium burning" redirects here. Not to be confused withalpha process.

Overview of the triple-alpha process

Thetriple-alpha processis a set ofnuclear fusionreactions by which threehelium-4nuclei (alpha particles) are transformed intocarbon.

Triple-alpha process in stars

Comparison of the energy output (ε) ofproton–proton(PP),CNOandTriple-αfusion processes at different temperatures (T). The dashed line shows the combined energy generation of the PP and CNO processes within a star.

Heliumaccumulates in thecoresof stars as a result of theproton–proton chain reactionand thecarbon–nitrogen–oxygen cycle.

Nuclear fusion reaction of two helium-4 nuclei producesberyllium-8,which is highly unstable, and decays back into smaller nuclei with a half-life of8.19×10⁻¹⁷s,unless within that time a third alpha particle fuses with the beryllium-8 nucleusto produce an excitedresonancestate ofcarbon-12,called theHoyle state,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 ofhydrogento fuse in its core, it begins to contract and heat up. If the central temperature rises to 10⁸K,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.

4 2He +4 2He →8 4Be	(−0.0918 MeV)
8 4Be +4 2He →12 6C + 2 γ	(+7.367 MeV)

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:

¹²
₆C
+⁴
₂He
→¹⁶
₈O
+
γ
(+7.162 MeV)

Nuclear fusion reactions of helium with hydrogen produceslithium-5,which also is highly unstable, and decays back into smaller nuclei with a half-life of3.7×10⁻²²s.

Fusing with additional helium nuclei can create heavier elements in a chain ofstellar nucleosynthesisknown as thealpha process,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 intoneonand heavier elements. Oxygen and carbon are the main "ash" of helium-4 burning.

Primordial carbon

Main article:Big Bang nucleosynthesis

The triple-alpha process is ineffective at the pressures and temperatures early in theBig 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 anexcited stateof¹²C.Thisresonancegreatly increases the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted byFred Hoylebefore 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 ofstellar nucleosynthesis,which posited that all chemical elements had originally been formed from hydrogen, the true primordial substance. Theanthropic principlehas 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 producenuclidesonly up tonickel-56(which decays later toiron); heavier elements (those beyond Ni) are created mainly by neutron capture. The slow capture of neutrons, thes-process,produces about half of elements beyond iron. The other half are produced by rapid neutron capture, ther-process,which probably occurs incore-collapse supernovaeandneutron star mergers.

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, theproton–proton chain reactionproduces energy at a rate proportional to the fourth power of temperature, theCNO cycleat 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, thered-giantstage.

For lower mass stars on thered-giant branch,the helium accumulating in the core is prevented from further collapse only byelectron degeneracypressure. 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 arunawayreaction. This process, known as thehelium flash,lasts a matter of seconds but burns 60–80% of the helium in the core. During the core flash, the star'senergy productioncan reach approximately 10¹¹solar luminositieswhich is comparable to theluminosityof a wholegalaxy,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 equilibriumis 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 (the Sun is expected to burn helium at its core for about a billion years after the helium flash).

In higher mass stars, which evolve along theasymptotic giant branch,carbon and oxygen accumulate in the core as helium is burned, while hydrogen burning shifts to further-out layers, resulting in an intermediate helium shell. However, the boundaries of these shells do not shift outward at the same rate due to differing critical temperatures and temperature sensitivities for hydrogen and helium burning. When the temperature at the inner boundary of the helium shell is no longer high enough to sustain helium burning, the core contracts and heats up, while the hydrogen shell (and thus the star's radius) expand outward. Core contraction and shell expansion continue until the core becomes hot enough to reignite the surrounding helium. This process continues cyclically – with a period on the order of 1000 years – and stars undergoing this process have periodically variable luminosity. These stars also lose material from their outer layers in astellar winddriven byradiation pressure,which ultimately becomes asuperwindas the star enters theplanetary nebulaphase.

Discovery

The triple-alpha process is highly dependent oncarbon-12andberyllium-8having resonances with slightly more energy thanhelium-4.Based on known resonances, by 1952 it seemed impossible for ordinary stars to produce carbon as well as any heavier element.Nuclear physicistWilliam Alfred Fowlerhad noted the beryllium-8 resonance, andEdwin Salpeterhad calculated the reaction rate for⁸Be,¹²C, and¹⁶O nucleosynthesis taking this resonance into account.However, Salpeter calculated that red giants burned helium at temperatures of 2·10⁸K or higher, whereas other recent work hypothesized temperatures as low as 1.1·10⁸K 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 astrophysicistFred Hoylewho, 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 atCaltechand 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, fresh fromRice University,who was looking for a project decided to look for the resonance. Fowler permitted Whaling to use an oldVan de Graaff generatorthat 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 theAmerican 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 theHoyle statewas predicted to be either a 0+ or a 2+ state, electron–positron pairs orgamma rayswere expected to be seen. However, when experiments were carried out, thegamma emissionreaction 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 1unit of angular momentum.Pair productionfrom 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

Main article:Fine-tuned universe

Carbon is a necessary component of all known life.¹²C, a stable isotope of carbon, is abundantly produced in stars due to three factors:

1. The decay lifetime of a⁸Benucleus is four orders of magnitude larger than the time for two⁴He nuclei (alpha particles) to scatter.
2. An excited state of the¹²C nucleus exists a little (0.3193 MeV) above the energy level of⁸Be +⁴He. This is necessary because the ground state of¹²C is 7.3367 MeV below the energy of⁸Be +⁴He; a⁸Be nucleus and a⁴He nucleus cannot reasonably fuse directly into a ground-state¹²C nucleus. However,⁸Be and⁴He use thekinetic energyof their collision to fuse into the excited¹²C (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 of¹²C observed in nature.The Hoyle state has been measured to be about 7.65 MeV above the ground state of¹²C.
3. In the reaction¹²C +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 Hoyleargued in 1982 that the Hoyle resonance was evidence of a "superintellect";Leonard SusskindinThe Cosmic Landscaperejects Hoyle'sintelligent designargument.Instead, some scientists believe that different universes, portions of a vast "multiverse",have different fundamental constants:according to this controversialfine-tuninghypothesis, 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.