Gamow, Alpher and Herman proposed the hot Big Bang as a means to produceall of the elements. However, the lack of stable nuclei with atomicweights of 5 or 8 limited the Big Bang to producing hydrogen and helium.Burbidge, Burbidge, Fowler and Hoyle worked out the nucleosynthesisprocesses that go on in stars, where the much greater density and longertime 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 processesoccur: most helium is produced in the Big Bang but carbon and everything heavier is produced in stars. Most lithium and beryllium is produced by cosmicray 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 rightmaintain the neutron:proton ratio in thermal equilibrium. About 1second after the Big Bang, the temperature is slightly less than theneutron-proton mass difference, these weak reactions become slower thanthe expansion rate of the Universe, and the neutron:proton ratiofreezes out at about 1:6. |  |
| After 1 second, the only reaction that appreciably changes the number ofneutrons is neutron decay, shown at right. The half-life of the neutron is 615 seconds.Without further reactions topreserve 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 theheavy form of hydrogen (H2).This reaction is exothermic with an energy difference of 2.2 MeV, but sincephotons are a billion times more numerous than protons, the reaction doesnot proceed until the temperature of the Universe falls to 1 billion Kor 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 makehelium 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, thesereactions only go one way. |  |
| The reactions at right also produce helium and usually go faster sincethey 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 repulsionof the deuterons causes the reaction to stop. The deuteron:protonratio when the reactions stop is quite small,and essentially inversely proportionalto 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 rapidlyswept up into helium nuclei.A very few helium nuclei combine into heavier nuclei giving a small abundanceof Li7 coming from the Big Bang.This graph is a corrected version of one from thisLBLpage.Note that H3 decays into He3 with a 12 year half-lifeso no H3 survives to the present, and Be7 decays intoLi7 with a 53 day half-life and also does not survive.
The graph above shows the time evolution of the abundances of the lightelements for a slightly higher baryon density. This figure is basedon data fromBurles, Nollett & Turner (1999).The asymptotic D/H ratio [by number] for this calculationis 1.78*10-5which corresponds to OmegaBh2 = 0.029.The bestcurrentestimate is OmegaBh2 = 0.0214 +/- 0.002 fromthe D/H ratio measured in quasar absorption line systems, andOmegaBh2 = 0.0224 +/- 0.001 from the amplitudesof the acoustic peaks in the angular power spectrum of theCMB anisotropy.
The deuterium, He3, He4 and Li7 abundancesdepend on the single parameter of the current density of ordinary mattermade out of protons and neutrons: baryonic matter. The graph above showsthe predicted abundance vs. baryon density for these light isotopes ascurves, the observed abundances as horizontal stripes, and the derivedbaryon 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 adispute about the actualprimordial helium abundance in the Universe: either 23.4 or 24.4 percentby mass, with both broups claiming 0.2 percent accuracy so this is 5 sigmadiscrepancy between the different observational camps.And a new measurement of the free neutron lifetime is 6 sigma smaller thatthe previous world average, giving anew predictionof the helium abundance of 24.6 percent.The observed lithium abundance in stars is less than the predicted lithiumabundance, by a factor of about 2. But stars destroy lithium so it is hard to assess thesignificance of this difference.
Other Big Bang Nucleosynthesis pages:LBL,MartinWhite.
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© 2002-2011Edward L.Wright. Last modified 26 Sep 2012
