Thetriple-alpha process is a set ofnuclear fusion reactions by which threehelium-4 nuclei (alpha particles) are transformed intocarbon.[1][2]
Helium accumulates in thecores of stars as a result of theproton–proton chain reaction and thecarbon–nitrogen–oxygen cycle.
Nuclear fusion reactions of two helium-4 nuclei producesberyllium-8, which is highly unstable, and decays back into smaller nuclei with a half-life of8.19×10−17 s, unless within that time a third alpha particle fuses with the beryllium-8 nucleus[3] to produce an excitedresonance state ofcarbon-12,[4] called theHoyle state. This nearly always decays back into three alpha particles, but once in about 2421.3 times, it releases energy and changes into the stable base form of carbon-12.[5] When a star runs out ofhydrogen to fuse in its core, it begins to contract and heat up. If the central temperature rises to 108 K,[6] 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:
Nuclear fusion reactions of helium with hydrogen produceslithium-5, which also is highly unstable, and decays back into smaller nuclei with a half-life of3.7×10−22 s.
Fusing with additional helium nuclei can create heavier elements in a chain ofstellar nucleosynthesis known 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 intoneon and heavier elements. Oxygen and carbon are the main "ash" of helium-4 burning.
Material that accretes from a companion star onto the surface of aneutron star may begin this helium-burning process in a local region. The burning wave is estimated to travel at 50 to 500 km/s, traversing the surface in around one second. Within this second, the neutron star rapidly rotates, moving the brighter burning region in and out of view. This intensity modulation allows the rotational frequency to be measured, sometimes up to 300 Hz.
Some neutron stars have been measured with such an intensity modulation at 600 Hz. A suggested origin is neutron stars which rotate at 300 Hz, but have two burning regions. The second burning region is theorized to form almost immediately after the first, exactly on the opposite side of the neutron star, due to the convergence of gravitational wave from the initial thermonuclear ignition.[7]
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.
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. Thisresonance greatly increases the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted byFred Hoyle before its 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 supported Hoyle's hypothesis ofstellar nucleosynthesis, which posited that all chemical elements had originally been formed from hydrogen, the true primordial substance. Theanthropic 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.[8][9]
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.[10] In contrast, theproton–proton chain reaction produces energy at a rate proportional to the fourth power of temperature, theCNO 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, thered-giant stage.
For lower mass stars on thered-giant branch, the helium accumulating in the core is prevented from further collapse only byelectron 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 arunaway reaction. 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 production can reach approximately 1011solar luminosities which is comparable to theluminosity of a wholegalaxy,[11] 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 (the Sun is expected to burn helium at its core for about a billion years after the helium flash).[12]
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 wind driven byradiation pressure, which ultimately becomes asuperwind as the star enters theplanetary nebula phase.[13]
The triple-alpha process is highly dependent oncarbon-12 andberyllium-8 having 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.[14] Nuclear physicistWilliam Alfred Fowler had noted the beryllium-8 resonance, andEdwin Salpeter had calculated the reaction rate for8Be,12C, and16O nucleosynthesis taking this resonance into account.[15][16] 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 astrophysicistFred Hoyle 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.[14]
Hoyle went to Fowler's lab atCaltech 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.[14]) 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 generator 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 theAmerican Physical Society. A long and fruitful collaboration between Hoyle and Fowler soon followed, with Fowler even coming to Cambridge.[17]
The final reaction product lies in a 0+ state (spin 0 and positive parity). Since theHoyle state was predicted to be either a 0+ or a 2+ state, electron–positron pairs orgamma rays were expected to be seen. However, when experiments were carried out, thegamma 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 1unit 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.[18]
Carbon is a necessary component of all known life.12C, a stable isotope of carbon, is abundantly produced in stars due to three factors:
Some scholars argue the 7.656 MeV Hoyle resonance, in particular, is unlikely to be the product of mere chance.Fred Hoyle argued in 1982 that the Hoyle resonance was evidence of a "superintellect";[14]Leonard Susskind inThe Cosmic Landscape rejects Hoyle'sintelligent design argument.[22] Instead, some scientists believe that different universes, portions of a vast "multiverse", have different fundamental constants:[23] according to this controversialfine-tuning 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.[24]
