3).
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 equilibriumHydrostatic equilibrium occurs when compression due to gravity is balanced by a pressure gradient wihch creates a pressure gradient force in the opposite direction...
. That generally means higher temperatures than for less massive stars. As a rule of thumb, it also means higher densities. However, smaller stars, not able to reach such high temperatures, may have their cores contract until significant electron degeneracy pressureElectron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. The force provided by this pressure sets a limit on the extent to which matter can be squeezed together without it collapsing into a...
comes into play at high density. So more massive stars can also burn their fuel at lower densities than less massive ones. To get the right figures for a particular mass, and a particular stage of evolution, it is necessary to use a numerical stellar modelStars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....
computed with computer algorithms. Such models are continually being refined based on particle physics 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' events - and so bring nuclear products to the surface, and many other observations relevant to models).
Fusion reactions
The principal reactions are:
- {| border="0"
|- style="height:3em;"
||{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||+ ||{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||→ ||{{nuclideNeon-20 is an isotope of neon.Atomic mass: 19.992Excess mass: -7042 keVPercent abundance is 90.48% and spin is 0+...
||+ ||{{nuclideHelium is the chemical element with atomic number 2, and is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert monatomic gas that heads the noble gas group in the periodic table...
||+ ||4.617 MeV
|- style="height:3em;"
|{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||+ ||{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||→ ||{{nuclideSodium-23 is isotope of sodium.atomic mass: 22.9897697 u
excess mass: -9529 keV
binding energy: 186564 keV
atomic percent abundance: 100%
spin: 3/2+...
||+ ||{{nuclideHydrogen is the chemical element with atomic number 1. It is represented by the symbol H. At standard temperature and pressure, hydrogen is a colorless, odorless, nonmetallic, tasteless, highly flammable diatomic gas with the molecular formula H
2...
||+ ||2.241 MeV
|- style="height:3em;"
|{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||+ ||{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||→ ||{{nuclideMagnesium-23 is an isotope of magnesium.atomic mass: 22.9941248 u
excess mass: -5473 keV
binding energy: 181725 keV
beta decay energy: -12240 keVspin: 3/2+electrons: 12Protons-12neutrons-11...
||+ ||nThe neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutron are usually found in atomic nuclei. The nuclei of most atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of protons in a...
||- ||2.599 MeV
|- style="height:3em;"
|colspan=99|Alternatively:
|- style="height:3em;"
|{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||+ ||{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||→ ||{{nuclideMagnesium-24 is an isotope of magnesium.atomic mass: 23.9850419 u
excess mass: -13933 keV
binding energy: 198257 keV
beta decay energy: -13880 keVatomic percent abundance: 78.99%
spin: 0+...
||+ ||{{SubatomicParticle|link=yes|Gamma}} ||+ ||13.933 MeV
|- style="height:3em;"
|{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||+ ||{{nuclideCarbon-12 is the more abundant of the two stable isotopes of the element carbon, accounting for 98.89% of carbon; it contains 6 protons, 6 neutrons, and 6 electrons....
||→ ||{{nuclideOxygen-16 is the most abundant, natural, stable isotope of oxygen.atomic mass: 15.9949146 u
excess mass: -4736.998 keV
binding energy: 127619.336 keV
beta decay energy: -15417 keVatomic percent abundance: 99.762%
spin: 0+...
||+ ||2 {{nuclideHelium is the chemical element with atomic number 2, and is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert monatomic gas that heads the noble gas group in the periodic table...
||colspan=2|- 0.113 MeV
|}
Reaction Products
This sequence of reactions can be understood by thinking of the two interacting carbon nuclei as coming together to form an excited stateExcitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
of the Mg-24 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-processThe S-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay...
.
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 the 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.
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 reactionThe proton–proton chain reaction is one of several fusion reactions by which stars convert hydrogen to helium, the primary alternative being the CNO cycle...
, or the CNO cycleThe CNO cycle , or sometimes Bethe-Weizsäcker-cycle, is one of two sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton-proton chain. Theoretical models show that the CNO cycle is the dominant source of energy in stars heavier than about 1.5 times the mass...
, but they can also be captured by Na-23 to form
Ne-20 plus a He-4 nucleus. In fact, almost all of the Na-23 produced by the second reaction gets used up this way.
The oxygen (O-16) already produced by helium fusionHelium fusion is a kind of nuclear fusion, with the nuclei involved being helium.The fusion of helium-4 nuclei is known as the triple-alpha process, because fusion of just two helium nuclei only produces beryllium-8, which is unstable and breaks back down to two helium nuclei with a half life of...
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.
So the end result of carbon burning is a mixture mainly of oxygen, neon 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.
Neutrino Losses
NeutrinoNeutrinos are elementary particles that often travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos have a minuscule, but nonzero 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 reactionThe proton–proton chain reaction is one of several fusion reactions by which stars convert hydrogen to helium, the primary alternative being the CNO cycle...
do. But the main source of neutrinos at these high temperatures involves an exotic process in quantum theory known as pair productionPair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . This is allowed, provided there is enough energy available to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and...
. A high-energy photon, in the vicinity of an ion, can interact 'with itself' and be replaced by a pair consisting of an electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
and its anti-particle, the positronThe positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1, a spin of , and the same mass as an electron. When a low-energy positron collides with a low-energy electron, annihilation occurs, resulting in the production...
. Normally, the particle pair quickly annihilate each other, 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 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. So neutrino losses, by this and other exotic processes, play an increasingly important part in the evolution of the most massive stars.
Stellar evolution
{{main|Stellar evolution}}
During helium fusionHelium fusion is a kind of nuclear fusion, with the nuclei involved being helium.The fusion of helium-4 nuclei is known as the triple-alpha process, because fusion of just two helium nuclei only produces beryllium-8, which is unstable and breaks back down to two helium nuclei with a half life of...
, 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 and density to the carbon ignition temperature. This will raise the temperature around the core and allow helium to burn in a shell around the core.
Stars with below 4 Solar massThe solar mass , , is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxies. It is equal to the mass of the Sun, about two nonillion kilograms or about 332,950 times the mass of the Earth or 1,048 times the mass of Jupiter.The solar mass can be...
es never reach high enough core temperature to burn carbon, instead ending their lives as carbon-oxygen white dwarfA white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...
s after shell helium flashA helium flash is the sudden beginning of helium fusion in the core of intermediate mass stars of less than about 2.25 solar masses, or on the surface of an accreting white dwarf star...
es gently expel the outer envelope in a planetary nebulaA planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas and plasma ejected during the asymptotic giant branch phase of certain types of stars late in their life...
.
Those with between 4 and 8 solar masses would theoretically accumulate enough inert reaction products of carbon burning in the core to exceed the Chandrasekhar limitThe Chandrasekhar limit limits the mass of bodies made from electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of electrons. The limit is the maximum nonrotating mass which can be supported against gravitational collapse by electron degeneracy pressure...
of 1.4 solar masses and collapse catastrophically. This does not happen because such stars (on the Asymptotic Giant BranchThe asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass stars. This is a period of stellar evolution undertaken by all low to intermediate mass stars late in their life....
) are observed to have enormous mass loss rates. Instead these stars burn carbon and their new inert core of reaction products (O, Mg, Ne) never exceeds the Chandrasekhar limit.
In the late stages of carbon burning, stars with masses between 4 and 8 solar masses develop a massive stellar wind, which quickly ejects the outer envelope in a planetary nebulaA planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas and plasma ejected during the asymptotic giant branch phase of certain types of stars late in their life...
leaving behind an O-Ne-Mg white dwarfA white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...
core. The core never reaches high enough temperature and
density for further fusion burning of heavier elements than carbon.
Stars with more than 8 solar masses proceed with the neon burning processThe neon burning process is a set of nuclear fusion reactions that take place in massive stars . Neon burning requires high temperatures and densities ....
after contraction of the inert (O, Ne, Mg) core raises the temperature and density sufficiently.
See also
- Carbon detonation
- Proton–proton chain reaction
- CNO process
- neon burning