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Supernovae

Nuclear Reactions in Thermonuclear Supernovae

The energetics of a thermonuclear supernova are easy to understand; carbon and oxygen within a white dwarf are converted into nickel, releasing more than enough energy to blow the star apart.  The reactions themselves, however, are not simple, involving many small steps that build up and tear apart atomic nuclei.  This complexity is reflected in the richness of the chemical composition of our world.

The principle characteristic of the reactions in a thermonuclear supernova is that they go fast, consuming a white dwarf's carbon (12C) and oxygen (16O) in less than 1 second.  This means that beta decays (decays that emit an electron or positron along with a neutrino), which are slow by their nature, play no part in the explosion.  This is very different from the reactions in the Sun, where the timescale for converting hydrogen into helium is governed by the emission of a positron and a neutrino in conversion of two hydrogen nuclei into a deuterium nucleus.  In the thermonuclear reactions present in an exploding white dwarf, these reactions take too long , and are therefore bypassed as atomic nuclei combine to form heavier nuclei.  As a consequence, the number of protons and the number of neutrons in a white dwarf do not change during the explosion.

The conversion of carbon and oxygen into nickel (56Ni) loosely follows the path 12C → 16O → 20Ne → 24Mg → 28Si → 32S → 36Ar → 40Ca → 44Ti → 48Cr → 52Fe → 56Ni.  Each nucleus in this chain has a composition that is a multiple of the helium nucleus, and with each step in the chain, the number of nucleons increases by two protons and two neutrons.  The flow of atomic nuclei along this path, however, is very complex, involving reactions that combine pairs of carbon or oxygen nuclei, as well as reactions that combine atomic nuclei with protons, neutrons, and helium-4 nuclei (4He).[1]  Unlike in the thermonuclear fusion of a main-sequence star, where the reactions flow only in the direction that generates energy as nuclei combine to create higher mass nuclei with lower mass per nucleon, the reactions in a supernova explosion can absorb energy and break apart nuclei into helium nuclei.  This is all a consequence of the high temperature generated as carbon and oxygen undergo their fusion reactions—several billion degrees Kelvin, which is equivalent to about 0.5 MeV.  This high temperature means that many atomic nuclei have kinetic energies of several MeV, which enable them to undergo thermonuclear reactions that remove energy from the exploding star, particularly through reactions that create helium nuclei from carbon or oxygen.  In effect, some of the reactions that occurred during the star's main-sequence phase are reversed during a supernova explosion.

The first reactions to take place in the explosion are between carbon nuclei.  They do not directly follow the most energetic path, forming magnesium-24 (24Mg) in a single reaction that releases 14.0 MeV of energy; instead, they create smaller nuclei that each have a larger mass per nucleon than 24Mg.  The preferred reactions are the following:

12C + 12C → 20Ne + 4He + 4.6 MeV (66%)

12C + 12C → 23Na + p + 2.2 MeV (32%)

12C + 12C → 23Mg + n − 2.6 MeV (2%)

The preferred products are therefore neon-20 (20Ne), sodium-23 (23Na), and magnesium-23 (23Mg).  In these reactions, p is a proton, and n is a neutron.  The amount of energy released (positive sign) or absorbed (negative sign) in the reaction is given in units of MeV.  The percentages in parenthesis gives the percentage of times the reaction produces the given products.

The products of these reaction do not survive long.  Usually, 23Mg combines with a free neutron to create 23Na and a proton, and 23Na combines with a free proton to create 20Ne and a 4He nucleus.  The 20Ne can then combine with 4He to form 24Mg.  So carbon does eventually evolve into magnesium, but it involves many small drops in energy rather than one big drop.

Two additional reactions work along with the carbon-carbon creation of neon to liberate a total of three helium nuclei in a cycle that converts carbon to neon, neon to oxygen, and oxygen back to carbon.  These two reactions involve the absorption of a gamma-ray (γ), so each is called a photodisintegration.

12C + 12C → 20Ne + 4He

20Ne + γ → 16O + 4He

16O + γ → 12C + 4He

The gamma-rays are part of the thermal radiation within the hot material of the white dwarf, and they carry enough energy to break helium nuclei away from neon and oxygen nuclei.  This loop creates much of the helium that enable nuclei to gain mass in four-nucleon increments.

Reactions involving oxygen are similarly weighted to reactions that throw out protons, neutrons, and helium nuclei in preference to directly creating sulfur-32 (32S).

16O + 16O → 31P + p + 7.7 MeV (56%)

16O + 16O → 28Si + 4He + 9.6 MeV (34%)

16O + 16O → 31S + n + 1.5 MeV (5%)

16O + 16O → 30P + 2H - 2.4 MeV (5%)

The principal products when oxygen combines with oxygen are therefore phosphorus-31 (31P), silicon-28 (28Si), sulfur-31 (31S), and phosphorus-30 (30P).  In these reactions, 2H is deuterium, a hydrogen isotope.  The nuclei created in these reactions tend to combine with the particle thrown out at their creation to form 32S, so 32S is ultimately formed from the oxygen thermonuclear reactions.

The freeing of protons, neutrons, and helium nuclei from carbon and oxygen nuclei is a characteristic that persists in the reactions that build up and tear down heavier nuclei.  These reactions form a network that causes an atomic nucleus to change its mass by small amounts as it interacts with protons, neutrons, helium nuclei, and gamma-rays.  These reactions populate the white dwarf with nuclei that are not multiples of 4He in composition.  An example of how the network does this is the reaction of 24Mg with 4He, which, through the release of a proton, can generate 27Al, the only stable aluminum isotope.  A second example is provided by 32S; it can combine with a free neutron to create 33S, which can then combine with a neutron and release a 4He nucleus to create 30Si, the rarest of the stable silicon isotopes found on Earth.  In this way, every stable isotope and many unstable isotopes lighter than nickel-56 can be created as a white dwarf turns itself into nickel-56.  So, while the white dwarf is predominately composed of nuclei that are multiples of 4He, many other elements and isotopes are also present.

 The material in the white dwarf is composed only of 56Ni and 4He if thermonuclear fusion can run to completion throughout the star.  In general, however, only part of a white dwarf burns to nickel-56.  The energy released in the thermonuclear burning causes the star to expand, which causes the temperature to drop, halting the thermonuclear fusion in the outer parts of the star before burning is complete.  This can freeze the composition of the star early in the burning process, so that the star is composed of many elements and isotopes.  These elements are dispersed in the interstellar medium, and, along with elements created in core-collapse supernovae and in red giant stars, they constitute the diverse mixture of chemicals found in the universe.  The relative abundance of elements such as silicon, sulfur, and calcium, over elements such as phosphorus, potassium, and chlorine is a direct consequence of the common isotopes of silicon, sulfur, and calcium being multiples of 4He, while no isotope of phosphorus, potassium, and chlorine is a multiple of 4He.  The complexity of the thermonuclear burning of carbon and oxygen is therefore directly responsible for the diverse chemical composition found here on Earth.

[1]Woosley, S.E., Arnett, W. David, Clayton, Donald D.  “The Explosive Burning of Oxygen and Silicon.”  The Astrophysical Journal Supplement 26 (1973): 231–312.

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