Gamow, Alpher and Herman proposed the hot Big Bang as a means to produce all of the elements. However, the lack of stable nuclei with atomic weights of 5 or 8 limited the Big Bang to producing hydrogen and helium. Burbidge, Burbidge, Fowler and Hoyle worked out the nucleosynthesis processes that go on in stars, where the much greater density and longer time scales allow the triple-alpha process (He+He+He -> C) to proceed and make the elements heavier than helium. But BBFH could not produce enough helium. Now we know that both processes occur: most helium is produced in the Big Bang but carbon and everything heavier is produced in stars. Most lithium and beryllium is produced by cosmic ray collisions breaking up some of the carbon produced in stars.
The following stages occur during the first few minutes of the Universe:
|Less than 1 second after the Big Bang, the reactions shown at right maintain the neutron:proton ratio in thermal equilibrium. About 1 second after the Big Bang, the temperature is slightly less than the neutron-proton mass difference, these weak reactions become slower than the expansion rate of the Universe, and the neutron:proton ratio freezes out at about 1:6.|
|After 1 second, the only reaction that appreciably changes the number of neutrons is neutron decay, shown at right. The half-life of the neutron is 615 seconds. Without further reactions to preserve neutrons within stable nuclei, the Universe would be pure hydrogen.|
|The reaction that preserves the neutrons is deuteron formation. The deuteron is the nucleus of deuterium, which is the heavy form of hydrogen (H2). This reaction is exothermic with an energy difference of 2.2 MeV, but since photons are a billion times more numerous than protons, the reaction does not proceed until the temperature of the Universe falls to 1 billion K or kT = 0.1 MeV, about 100 seconds after the Big Bang. At this time, the neutron:proton ratio is about 1:7.|
|Once deuteron formation has occurred, further reactions proceed to make helium nuclei. Both light helium (He3) and normal helium (He4) are made, along with the radioactive form of hydrogen (H3). These reactions can be photoreactions as shown here. Because the helium nucleus is 28 MeV more bound than the deuterons, and the temperature has already fallen so far that kT = 0.1 MeV, these reactions only go one way.|
|The reactions at right also produce helium and usually go faster since they do not involve the relatively slow process of photon emission.|
|The net effect is shown at right. Eventually the temperature gets so low that the electrostatic repulsion of the deuterons causes the reaction to stop. The deuteron:proton ratio when the reactions stop is quite small, and essentially inversely proportional to the total density in protons and neutrons. Almost all the neutrons in the Universe end up in normal helium nuclei. For a neutron:proton ratio of 1:7 at the time of deuteron formation, 25% of the mass ends up in helium.|
The mass fraction in various isotopes vs time is shown at right.
Deuterium peaks around 100 seconds after the Big Bang, and is then rapidly
swept up into helium nuclei.
A very few helium nuclei combine into heavier nuclei giving a small abundance
of Li7 coming from the Big Bang.
This graph is a corrected version of one from this
Note that H3 decays into He3 with a 12 year half-life
so no H3 survives to the present, and Be7 decays into
Li7 with a 53 day half-life and also does not survive.
The graph above shows the time evolution of the abundances of the light elements for a slightly higher baryon density. This figure is based on data from Burles, Nollett & Turner (1999). The asymptotic D/H ratio [by number] for this calculation is 1.78*10-5 which corresponds to OmegaBh2 = 0.029. The best current estimate is OmegaBh2 = 0.0214 +/- 0.002 from the D/H ratio measured in quasar absorption line systems, and OmegaBh2 = 0.0224 +/- 0.001 from the amplitudes of the acoustic peaks in the angular power spectrum of the CMB anisotropy.
The deuterium, He3, He4 and Li7 abundances
depend on the single parameter of the current density of ordinary matter
made out of protons and neutrons: baryonic matter. The graph above shows
the predicted abundance vs. baryon density for these light isotopes as
curves, the observed abundances as horizontal stripes, and the derived
baryon density as the vertical stripe.
A single value of the baryon density fits 4 abundances simultaneously.
The fit is good but not perfect. There has been a
dispute about the actual
primordial helium abundance in the Universe: either 23.4 or 24.4 percent
by mass, with both broups claiming 0.2 percent accuracy so this is 5 sigma
discrepancy between the different observational camps.
And a new measurement of the free neutron lifetime is 6 sigma smaller that
the previous world average, giving a
of the helium abundance of 24.6 percent.
The observed lithium abundance in stars is less than the predicted lithium
abundance, by a factor of about 2.
But stars destroy lithium so it is hard to assess the
significance of this difference.
Other Big Bang Nucleosynthesis pages: LBL, Martin White.
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© 2002-2011 Edward L. Wright. Last modified 26 Sep 2012