Astronomy 162: Professor Barbara Ryden

Thursday, March 13

THE FIRST THREE MINUTES


``I am sufficiently proud of my knowing something to be modest about my not knowing everything.'' - Vladimir Nabokov

Key Concepts


(1) During the first four seconds of the universe, matter formed by pair production.

A Cautionary Note: It is sometimes said, paraphrasing Will Rogers, that all we know about the universe outside the Solar System comes from gathering photons. Aside from a few stray neutrinos that we've managed to capture, this is true. Thus, we can directly observe the universe only where it is transparent (that is, after the time of recombination, when the universe was about 300,000 years old). Knowledge of the earlier universe comes from indirect deductions. For instance, the theory of inflation is taken seriously because Speculations about the early universe which cannot be checked by comparison to observed properties of the universe are basically a waste of time.
The first three minutes of the universe are when light elements, such as hydrogen and helium, formed. We can check our theories about nucleosynthesis during the first 3 minutes by comparing the predicted abundances of H and He with the abundances which are actually observed. The very oldest stars known have the following proportion of elements:
75% H, 25% He, <0.01% heavier elements.

The elements heavier than helium are made in stars, but where did all that helium in the oldest generation of stars come from? It must have formed prior to the first stars. For that matter, where did hydrogen come from? Why doesn't the universe contain nothing but photons?


Two photons can collide to form a particle-antiparticle pair if the energy of each photon is greater than the energy equivalent (E = mc2) of the particle or antiparticle. For instance, a proton has mc2 of 10-10 joules. Two photons, each an energy greater than this value, can collide to form a proton-antiproton pair. This process is known as pair production.

Conversely, a particle and antiparticle can collide to form a pair of photons. For instance, a proton and antiproton colliding at a low relative velocity will produce a pair of photons, each with an energy of 10-10 joules. (This is a high energy for a photon, corresponding to an extremely energetic gamma-ray.) The process of converting a particle-antiparticle pair to photons is known as annihilation.

When the universe was less than 0.0001 second old, the photons of the cosmic background were so energetic, proton-antiproton pairs were continuously being formed by pair production. However, the proton-antiproton pairs were also continuously being destroyed by annihilation.

At an age of 0.0001 seconds, the temperature of the universe dropped below 10 trillion degrees Kelvin. At this temperature, the average photon energy is 10-10 joules, the energy equivalent of a proton or antiproton. Pair production of protons stops (the photons have dropped below the necessary energy), but the annihilation of protons continues.

Thanks to a subtle bias in the laws of physics, however, the production of protons is very slightly favored over the production of antiprotons. For every billion antiprotons, there will be a billion and one protons. So here's the situation after pair production stops:
1 billion and 1 protons + 1 billion antiprotons -> 2 billion photons + 1 proton
We now have a situation in which the universe contains lots of photons, a few protons, and no antiprotons. We state that the protons have ``frozen out'', since they are no longer being produced or annihilated.


Neutrons are about as massive as protons, so they freeze out at the same time as protons. Electrons and positrons, however, since they are only 1/2000 as massive as a proton, are produced and annihilated continuously until the universe drops to a much lower temperature.

At an age of 4 seconds, the temperature of the universe dropped below 6 billion degrees Kelvin. At this temperature, the average photon energy is 8 x 10-14 joules, the energy equivalent of an electron or positron. Pair production of electrons stops, but the annihilation of electrons continues.

The production of electrons is very slightly favored over the production of positrons (just as the production of protons is favored over that of antiprotons, and the production of neutrons is favored over that of antineutrons). Here's the situation after the pair production of electrons stops:
1 billion & 1 electrons + 1 billion positrons -> 2 billion photons + 1 electron.

The universe now contains protons, neutrons, electrons, and photons. The photons outnumber the massive particles by billions to one.


(2) After two minutes, deuterium formed by the fusion of protons and neutrons.

At an age of 2 minutes, the temperature of the universe dropped below 1.2 billion degrees Kelvin. At this temperature, the average photon energy is 1.8 x 10-14 joules. Why is this energy significant? Because it is the binding energy of a deuterium nucleus. A deuterium (alias ``heavy hydrogen'') nucleus consists of a proton and a neutron held together by the strong nuclear force. If a deuterium nucleus is struck by a photon with an energy of 1.8 x 10-14 joules or more, it is broken apart into its consituent parts.

Once the temperature of the universe drops below 1.2 billion degrees Kelvin, the photons of the cosmic background are no longer energetic enough to blast deuterium apart. Fusion proceeds:
p + n --> 2H + photon
That is, a proton (p) and neutron (n) fuse together to form deuterium (2H); since the mass of a deuterium nucleus is less than the mass of a proton and the mass of a neutron added together, the excess mass is converted to energy, and carried away by a photon.

For the first time, two minutes after the initial Big Bang, the universe contains nuclei more complicated than a single proton.


(3) After three minutes, helium formed by the fusion of deuterium, protons, and neutrons.

At an age of 3 minutes, the temperature of the universe dropped below 1 billion degrees Kelvin. At this temperature, the average photon energy is 1.5 x 10-14 joules. If a photon with this energy strikes a helium nucleus, it breaks it apart.

Once the temperature of the universe drops below 1 billion degrees Kelvin, the photons of the cosmic background are no longer energetic enough to blast deuterium apart. Fusion proceeds. The simplest way to form helium nuclei is to fuse a pair of deuterium nuclei together. (Deuterium contains 1 proton + 1 neutron; helium contains 2 protons + 2 neutrons.) However, deuterium never becomes very abundant in the early universe; after a minute of deuterium formation, there are still hundreds of protons & neutrons for every deuterium nucleus. The most common way of creating helium is a two-step process. You can add a proton, then add a neutron:
2H + p --> 3He + photon
3He + n --> 4He + photon
Or you can add a neutron first, then a proton:
2H + n --> 3H + photon
3H + p --> 4He + photon

Either way, the result is the same; a deuterium nucleus, a proton, and a neutron are converted to an ordinary helium nucleus, with the release of energy in the form of a pair of photons.

(Note that this method of creating helium differs from the proton-proton chain which takes place in the Sun. Free neutrons are unstable -- they decay into a proton plus an electron with a half-life of 15 minutes. Thus, in the Sun, there are no neutrons hanging around, as there were in the early universe, before neutrons had a chance to decay.)

What prevents additional protons and neutrons from fusing with helium nuclei to form yet heavier elements? There are no stable nuclei containing a total of 5 protons & neutrons. If you try to add a proton to a helium nucleus, it is spat right out again; if you try to add a neutron to a helium nucleus, it too is rejected. It is possible to make a nucleus of lithium by fusing helium and deuterium, but remember that deuterium is rare. Thus, only tiny quantities of lithium are made in the early universe. Tiny quantities of beryllium are also made, by fusing lithium and deuterium, but no heavier elements are created at all.

Nucleosynthesis in the early universe (unlike nucleosynthesis in stars) is unable to create elements heavier than the first four elements in the periodic table: hydrogen, helium, lithium, and beryllium. Nucleosynthesis in the early universe stops after a half-hour or so, when densities and temperatures drop too low for fusion to occur efficiently. The leftover neutrons decay into protons and electrons. For the next 2500 years or so, the universe remains in a rather boring state:

It isn't until matter started to dominate the density of the universe (after about 2500 years) and the universe become transparent (after about 300,000 years) that stars begin forming, and start up the process of nucleosynthesis again.

The study of nucleosynthesis during the first few minutes of the universe

Calculations of the fusion rates in the early universe predict that after nucleosynthesis is complete, the atomic matter in the universe should consist of 75% hydrogen by mass, with 25% helium, and only traces of other elements. This is in agreement with the observed chemical composition of the atmospheres of the oldest known stars.
Prof. Barbara Ryden (ryden@astronomy.ohio-state.edu)

Updated: 2003 Mar 12

Copyright 2003, Barbara Ryden