Deuterium, cosmic wunderkind!

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(Every now and again I get the urge to write a little essay on something that tickles me about astronomy/cosmology, mostly for my own (re-)education. I have it on the authority of my old English teacher that my prose-writing skills are complete rubbish, so apologies in advance).


Deuterium is a kind of cosmic wunderkind. It was created at the start of the universe, it dies in the process of giving birth to stars, is fleetingly recreated during a star's adulthood, and may well be the salvation of humanity.

Sounds intriguing? Let's start at the beginning. Hydrogen is the simplest atom that can exist. Almost all of it consists of a single proton (plus a single electron if it is a neutral atom). The remaining tiny fraction is deuterium, the only other stable isotope of hydrogen. It differs by having an additional neutron which doubles its mass but leaves it (mostly) chemically unchanged. Sometimes we call single-proton hydrogen protium to distinguish it from deuterium and tritium. The latter is radioactive with a half-life of twelve years, so doesn't persist in nature.


The isotopes of hydrogen: protium, deuterium, and tritium

All of the matter in the universe condensed from the hot dense fireball of the Big Bang, nearly 14 billion years ago. Initially it was too hot for even protons and neutrons to exist. We have to wait until a millionth of a second after the Big Bang for the universe to cool sufficiently to allow this. But it is still too hot for atoms. Any that try to form are immediately zapped by high energy gamma rays, a process called photodisintegration. We have to wait a relative age -- all of three minutes -- before the temperature falls to a billion degrees which is cool enough for the production of atomic nuclei to get going. In the meantime we are losing neutrons because free neutrons are unstable and turn into protons and electrons by beta decay. Finally, though, those neutrons start to stick to protons to make deuterium, the first atomic nucleus more complicated than a proton.

The deuterium doesn't hang around long. It's quite anxious to combine with more deuterium to make helium nuclei. This era of primordial nucleosynthesis lasts seventeen minutes. After that the rapidly expanding universe is no longer dense enough for chance energetic encounters between particles. At just twenty minutes old, the universe has made all the atoms that are going to exist for the next hundred million years. 75% of those atoms are still just single-proton hydrogen. 25% is helium. There are vanishingly small traces of deuterium which has been mostly destroyed, and even smaller traces of lithium and beryllium. Near the start of nucleosynthesis one in every thousand nuclei was a deuteron, by the end it is only three in a hundred thousand.

But deuterium is about to get even rarer. Over the next tens of millions of years matter starts to clump together under the force of gravity. The expansion of space has stretched the density out to nearly nothing, and the universe is icy cold and totally dark. Things are stirring though. Random density fluctuations occurred in the first billionth of a trillionth of a trillionth of a second, long before even the start of nucleosynthesis. The ghosts of those over-densities still persist. At a few atoms per cubic meter the universe is now a trillion trillion times more rarefied than air. Still, those individual atoms are starting to drift toward the slightly more massive regions of higher density. What starts as an imperceptible drift becomes a trickle, then a torrent. As more matter congregates into regions millions of light years across, giant rivers of gas begin to pour down into the hearts of these nascent proto-galaxies.

Soon we get clumps within clumps as the gas clouds start to fragment. The universe is on the way to making the first stars, and ending the Dark Ages which have lasted for tens of millions of years. But now deuterium is about to enter the stage again for Act 2. And it's going to play a vital role, without which we couldn't exist. Clumpy gas is hot gas. The increasingly frequent random collisions between atoms translate into higher pressure and temperature. Gravity can only do so much before particles are close enough to fuse into heavier nuclei. This releases energy which increases the pressure and pushes back on the gravitational collapse. A star is now born, but the crucial question for us is how large that star is. Big stars burn faster due to the higher gravitational pressure, and they die violent deaths which scatter the heavy atoms that our planet -- and we ourselves -- are made of. We depend on past generations of giant stars. Carl Sagan famously said "we are star stuff". But we are also BIG star stuff.

If you have time for a small diversion, Michelle Thaller is very enthusiastic about the "star stuff" theme:

The initial size of a star depends on how much matter managed to congregate before hydrogen fusion got underway. Once the star reaches a stable hydrogen-burning equilibrium it produces stellar winds which blow away any remaining gas from the proto-stellar cloud. Its size is essentially fixed for the next millions to billions of years. So the longer the initial period of collapse continues the larger the star, as more gas continues to rain down onto the contracting blob. This is where deuterium plays a blinder. The star must reach 10 million degrees before hydrogen fusion begins. But remember how deuterium was so anxious to fuse to helium shortly after the Big Bang? It is now about to meet its few remaining long lost neighbours again. Deuterium fusion takes place during proto-stellar collapse at a temperature of a mere one million degrees. The energy released delays the star's collapse for as much as a million years. This extends the period of matter aggregation, creating large stars which otherwise would never have existed. Without the traces of deuterium left over from the Big Bang, no star would be more than a couple of times as massive as our Sun.

Still, most stars are much less massive than the Sun. The smallest are less than a tenth its mass, or less than the mass of a hundred Jupiters. That's the minimum mass for hydrogen burning. But even the mass of a dozen Jupiters is enough to get deuterium burning going. And so we have a population of sub-stellar objects that we call brown dwarfs. They burn for a million years and then go out leaving a hot, but cooling, remnant. They are disparagingly called "failed stars". Whether they are failed stars or super-planets, they are very common. There may be as many of them as "successful" stars. It's hard to tell as they are faint so we can only see nearby ones, and there is currently quite a large gap between theory and observation.

Our story isn't over yet. What about the hydrogen burning in successful stars? The reaction that fuses hydrogen to helium progresses in several stages. Here's a picture:



Taking it from the top, initially we have a pair of protons (i.e. hydrogen nuclei). If they can be persuaded to get close enough, one of them can transmute into a neutron by a process called inverse beta decay. The neutron and proton combine to form ... deuterium! Now the deuterium nucleus can meet another proton to form helium-3, and two helium-3 nuclei can combine to form the more common helium-4. So even hydrogen burning turns out to depend on deuterium. And this is brought home even more when we realise the timescales and energies involved. The inverse beta decay process is extremely rare and depends on 10m+ degree temperatures to smash protons sufficiently close together. Even at the monstrous temperatures and pressures in the core of the Sun, the average proton takes a billion years before it happens. After this billion year wait, the resulting deuterium nucleus lasts just one second before fusing to helium!



We can also look at it from an energy perspective. On these small scales we use the electron-volt as our unit of energy, with MeV denoting a million electron volts. The complete fusion of four protons to helium-4 releases 27 MeV of energy. But the creation of deuterium from each pair of protons only releases 1.4 MeV. Thus, 90% of the energy output of the Sun actually results from deuterium fusion, with the glacially slow initial hydrogen fusion mainly acting to prevent the whole thing going up in one cataclysmic flash!

And this brings us to some very good news for humans. I mentioned that when our Sun got going, the stellar wind blew away the remaining gas from the stellar nebula. Not quite all of it, of course ... we are made from the leftovers. Deuterium is twice as heavy as hydrogen, so a bit less of it got blown away. This served to concentrate deuterium from the primordial 30 parts per million to about 150 ppm in our vicinity. Hydrogen is too light to be retained in our atmosphere but we've got lots of it combined with oxygen in our oceans. Of every million molecules of H₂O, 150 of them are actually D₂O. There's an awful lot of water, and so when we manage to build a fusion reactor the extraction of deuterium fuel from seawater will be cheap and easy. A litre of seawater will provide fusion energy equivalent to burning 300 litres of petrol. The Sun is forced to start with protons as all its free deuterium was burned up five billion years ago. But we can skip that difficult step and start with the deuterium fuel that nature has provided. It's gonna be awesome! (Actually, it's gonna be very difficult. We'll probably have to start with deuterium-tritium fusion which is 10,000 times easier, but the fuel cycle is more complicated. But that's another day's story).