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The carbon-burning process or carbon fusion 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 that take place in the cores of massive
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s (at least 8 \beginM_\odot\end at birth) that combines carbon into other elements. It requires high temperatures (> 5×108 K or 50
keV Kev can refer to: Given name * Kev Adams, French comedian, actor, screenwriter and film producer born Kevin Smadja in 1991 * Kevin Kev Carmody (born 1946), Indigenous Australian singer-songwriter * Kev Coghlan (born 1988), Scottish Grand Prix motor ...
) and
densities Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter Rho (letter), rho), although the Latin letter ''D'' ca ...
(> 3×109 kg/m3). These figures for temperature and density are only a guide. More massive stars burn their nuclear fuel more quickly, since they have to offset greater gravitational forces to stay in (approximate)
hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary ...
. That generally means higher temperatures, although lower densities, than for less massive stars. To get the right figures for a particular mass, and a particular stage of evolution, it is necessary to use a numerical
stellar model This glossary of astronomy is a list of definitions of terms and concepts relevant to astronomy and cosmology, their sub-disciplines, and related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outsid ...
computed with computer algorithms. Such models are continually being refined based on
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the ...
experiments (which measure nuclear reaction rates) and astronomical observations (which include direct observation of mass loss, detection of nuclear products from spectrum observations after convection zones develop from the surface to fusion-burning regions – known as
dredge-up A dredge-up is any one of several stages in the evolution of some stars. By definition, during a ''dredge-up'', a convection zone extends all the way from the star's surface down to the layers of material that have undergone fusion. Consequently, th ...
events – and so bring nuclear products to the surface, and many other observations relevant to models).


Fusion reactions

The principal reactions are: :


Reaction products

This sequence of reactions can be understood by thinking of the two interacting carbon nuclei as coming together to form an
excited state In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to a ...
of the 24Mg nucleus, which then decays in one of the five ways listed above. The first two reactions are strongly exothermic, as indicated by the large positive energies released, and are the most frequent results of the interaction. The third reaction is strongly endothermic, as indicated by the large negative energy indicating that energy is absorbed rather than emitted. This makes it much less likely, yet still possible in the high-energy environment of carbon burning. But the production of a few neutrons by this reaction is important, since these neutrons can combine with heavy nuclei, present in tiny amounts in most stars, to form even heavier isotopes in the
s-process The slow neutron-capture process, or ''s''-process, is a series of reactions in nuclear astrophysics that occur in stars, particularly asymptotic giant branch stars. The ''s''-process is responsible for the creation (nucleosynthesis) of approximat ...
.Rose (1998), pp. 229–234 The fourth reaction might be expected to be the most common from its large energy release, but in fact it is extremely improbable because it proceeds via electromagnetic interaction, as it produces a gamma ray photon, rather than utilising the strong force between nucleons as do the first two reactions. Nucleons look a lot bigger to each other than they do to photons of this energy. However, the 24Mg produced in this reaction is the only magnesium left in the core when the carbon-burning process ends, as 23Mg is radioactive. The last reaction is also very unlikely since it involves three reaction products, as well as being endothermic — think of the reaction proceeding in reverse, it would require the three products all to converge at the same time, which is less likely than two-body interactions. The protons produced by the second reaction can take part in the proton–proton chain reaction, or 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, ...
, but they can also be captured by 23Na to form 20Ne plus a 4He nucleus. In fact, a significant fraction of the 23Na produced by the second reaction gets used up this way. In stars between 9 and 11
solar mass The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass ...
es, the oxygen (O-16) already produced by
helium fusion The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon. Triple-alpha process in stars Helium accumulates in the cores of stars as a result of the proton–pro ...
in the previous stage of stellar evolution manages to survive the carbon-burning process pretty well, despite some of it being used up by capturing He-4 nuclei.Camiel (1992), pp.97–98 So the end result of carbon burning is a mixture mainly of oxygen, neon, sodium and magnesium. The fact that the mass-energy sum of the two carbon nuclei is similar to that of an excited state of the magnesium nucleus is known as 'resonance'. Without this resonance, carbon burning would only occur at temperatures one hundred times higher. The experimental and theoretical investigation of such resonances is still a subject of research. A similar resonance increases the probability 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. Triple-alpha process in stars Helium accumulates in the cores of stars as a result of the proton–pro ...
, which is responsible for the original production of carbon.


Neutrino losses

Neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
losses start to become a major factor in the fusion processes in stars at the temperatures and densities of carbon burning. Though the main reactions don't involve neutrinos, the side reactions such as the proton–proton chain reaction do. But the main source of neutrinos at these high temperatures involves a process in quantum theory known as
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 specific ...
. A high energy
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 ...
which has a greater energy than the
rest mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
of two
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s ( mass-energy equivalence) can interact with electromagnetic fields of the atomic nuclei in the star, and become a particle and
anti-particle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
pair of an electron and positron. Normally, the positron quickly annihilates with another electron, producing two photons, and this process can be safely ignored at lower temperatures. But around 1 in 1019 pair productions end with a weak interaction of the electron and positron, which replaces them with a
neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
and anti-neutrino pair. Since they move at virtually the speed of light and interact very weakly with matter, these neutrino particles usually escape the star without interacting, carrying away their mass-energy. This energy loss is comparable to the energy output from the carbon fusion. Neutrino losses, by this and similar processes, play an increasingly important part in the evolution of the most massive stars. They force the star to burn its fuel at a higher temperature to offset them. Fusion processes are very sensitive to temperature so the star can produce more energy to retain
hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary ...
, at the cost of burning through successive nuclear fuels ever more rapidly. Fusion produces less energy per unit mass as the fuel nuclei get heavier, and the core of the star contracts and heats up when switching from one fuel to the next, so both these processes also significantly reduce the lifetime of each successive fusion-burning fuel. Up to the helium burning stage the neutrino losses are negligible. But from the carbon burning stage onwards, the reduction in stellar lifetime due to energy lost in the form of neutrinos roughly matches the increased energy production due to fuel change and core contraction. In successive fuel changes in the most massive stars, the reduction in lifetime is dominated by the neutrino losses. For example, a star of 25 solar masses burns hydrogen in the core for 107 years, helium for 106 years and carbon for only 103 years.


Stellar evolution

During
helium fusion The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon. Triple-alpha process in stars Helium accumulates in the cores of stars as a result of the proton–pro ...
, stars build up an inert core rich in carbon and oxygen. The inert core eventually reaches sufficient mass to collapse due to gravitation, whilst the helium burning moves gradually outward. This decrease in the inert core volume raises the temperature to the carbon ignition temperature. This will raise the temperature around the core and allow helium to burn in a shell around the core. Outside this is another shell burning hydrogen. The resulting carbon burning provides energy from the core to restore the star's
mechanical equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero ...
. However, the balance is only short-lived; in a star of 25 solar masses, the process will use up most of the carbon in the core in only 600 years. The duration of this process varies significantly depending on the mass of the star.Anderson, Scott R.
''Open Course: Astronomy: Lecture 19: Death of High-Mass Stars''
GEM (2001)
Stars of below 8–9
solar mass The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass ...
es never reach high enough core temperature to burn carbon, instead ending their lives as carbon-oxygen
white dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes fro ...
s after shell
helium flash A helium flash is a very brief thermal runaway nuclear fusion of large quantities of helium into carbon through the triple-alpha process in the core of low mass stars (between 0.8 solar masses () and 2.0 ) during their red giant phase (the Sun is ...
es gently expel the outer envelope in a
planetary nebula A planetary nebula (PN, plural PNe) is a type of emission nebula consisting of an expanding, glowing shell of ionized gas ejected from red giant stars late in their lives. The term "planetary nebula" is a misnomer because they are unrelated to ...
. In stars with masses between 8 and 12 solar masses, the carbon-oxygen core is under
degenerate Degeneracy, degenerate, or degeneration may refer to: Arts and entertainment * Degenerate (album), ''Degenerate'' (album), a 2010 album by the British band Trigger the Bloodshed * Degenerate art, a term adopted in the 1920s by the Nazi Party i ...
conditions and carbon ignition takes place in a ''carbon flash'', that lasts just milliseconds and disrupts the stellar core. In the late stages of this nuclear burning they develop a massive stellar wind, which quickly ejects the outer envelope in a
planetary nebula A planetary nebula (PN, plural PNe) is a type of emission nebula consisting of an expanding, glowing shell of ionized gas ejected from red giant stars late in their lives. The term "planetary nebula" is a misnomer because they are unrelated to ...
leaving behind an O-Ne-Na-Mg
white dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes fro ...
core of about 1.1 solar masses. The core never reaches high enough temperature for further fusion burning of heavier elements than carbon. Stars of more than 12 solar masses start carbon burning in a non-degenerate core, and after carbon exhaustion proceed with the
neon-burning process The neon-burning process is a set of nuclear fusion reactions that take place in evolved massive stars with at least 8 Solar masses. Neon burning requires high temperatures and densities (around 1.2×109 K or 100 keV and 4×109 kg/m3). At such h ...
once contraction of the inert (O, Ne, Na, Mg) core raises the temperature sufficiently.Ryan (2010), pp.147–148


See also

*
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, an ...
*
Carbon detonation Carbon detonation or carbon deflagration is the violent reignition of thermonuclear fusion in a white dwarf star that was previously slowly cooling. It involves a runaway thermonuclear process which spreads through the white dwarf in a matter of s ...
*
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, ...
*
Neon-burning process The neon-burning process is a set of nuclear fusion reactions that take place in evolved massive stars with at least 8 Solar masses. Neon burning requires high temperatures and densities (around 1.2×109 K or 100 keV and 4×109 kg/m3). At such h ...
* Proton–proton chain reaction *
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. Triple-alpha process in stars Helium accumulates in the cores of stars as a result of the proton–pro ...


References

{{Nuclear processes Nucleosynthesis