by Lucie Green
To provide the 4 × 1026 joules of energy that the nineteenth-century astronomers had calculated as being emitted in sunlight every second, the Sun would need to lose a few million tonnes of mass. But given the Sun has over a billion billion billion tonnes of mass to start with, it can certainly handle that. This line of reasoning is very appealing and gives another avenue to study now that our terrestrial fuel has hit a dead end. Is the Sun able to convert its own material into pure energy?
Perhaps. It’s one thing to show there is theoretically enough mass in the Sun to provide this energy. It is much harder to show a plausible mechanism for actually getting that energy out. For the coal hypothesis this was relatively straightforward: you burn it and the energy is released during a chemical reaction. To release the full amount of energy that Einstein proposed was in the material would require its complete annihilation. The various inanimate objects around you right now may all contain billions of joules’ worth of energy in their mass, but it (thankfully!) stays safely locked away.
The first elements of practical support for Einstein’s theory came at the start of the 1920s, when experiments to find the mass of atomic nuclei were being carried out. These experiments weren’t being done to test Einstein’s ideas, but to characterize the nuclei of different elements and understand what they were made from, but it was quickly realized that they provided some real-world support for what Einstein had proposed. The experiments showed that the mass of a helium nucleus was very slightly less than the mass of (what were thought at the time to be) its constituent particles. One helium atom somehow had less mass than the four constituent particles weighed separately. The mass of the whole nucleus was less than the sum of its parts and this mass difference could be explained and understood as energy liberated when a helium nucleus was formed.
Thanks to a British astronomer, Cecilia Payne-Gaposchkin, we know the Sun has plenty of hydrogen and helium. We’ll be finding out about her work, and the challenge she faced in having this discovery accepted, in the next chapter. So in theory, then, perhaps a helium nucleus could be built from a hydrogen nucleus by a process of ‘nuclear fusion’ – joining together small nuclei of atoms to build bigger ones – and could release the energy everyone was looking for. This led to great excitement, but with one major stumbling block: protons are electrically charged particles that repel each other. Even at the high temperatures inside the Sun, where protons would be moving fast and colliding with each other at great speeds, there still wasn’t enough energy to overcome the powerful electric repulsion of the two positively charged protons – at least, according to our old understanding of sub-atomic particles.
In 1928, though, the Russian theoretical physicist George Gamow came up with a description of sub-atomic particles that showed it was possible for charged particles to undergo a reaction at energies (that is, temperatures) lower than previously thought. Gamow’s formula showed that on rare occasions charged particles would ‘tunnel through’ the repulsive barrier created by their having the same electric charge and be able to fuse together. This brought helium fusion back into the race as a legitimate candidate to power the Sun.
The final piece of the puzzle was provided by a German nuclear physicist, Hans Bethe, who started his career in Germany but ended up working in America, having moved first to Britain and then to Cornell University in 1934. His mother’s family were Jewish, and in 1930s Germany that made him unemployable. When Hitler came to power, the Nazi government actually introduced a law that forbade anyone with a Jewish family from having a government-funded job. Bethe’s research contract was terminated as a result, but this had the benefit of causing him to leave the country while he still could.
This was a significant move not just for Bethe’s career, but for the course of the Second World War. His new home of America had no problem putting Bethe’s genius to work and he ended up being recruited in 1943 to lead the theoretical division of the Manhattan Project at the Los Alamos Laboratory. Nuclear physics was the ‘new’ science that looked like it would be able to reveal the structure of matter. And with that would come a mastery of the material around us so that its energy could be released in the most catastrophic way. This led to a perceived race to produce the first nuclear bomb, and Los Alamos’s single purpose was to do just that.
The list of people who worked on the Manhattan Project reads like a who’s who of scientists whose names are well known today: J. Robert Oppenheimer, Richard Feynman, Niels Bohr, Leo Szilard and Enrico Fermi. It was a joint letter by Szilard and Einstein to the President of the United States at that time, Franklin D. Roosevelt, which led to the creation of the Manhattan Project in the first place. They were concerned that developments in nuclear physics in Germany and German access to the necessary materials might mean that an atomic bomb was being built. Bohr had been awarded the Nobel Prize for Physics in 1927; Fermi had received the same award in 1938 – the Manhattan Project brought together the very best.
Despite the Earth-changing use for nuclear physics, Bethe’s interest in fission and fusion started with his theoretical studies of atomic nuclei. In the late 1930s a conference that brought together nuclear physicists and astrophysicists turned his attention to the Sun. He set out to calculate whether it was theoretically possible for hydrogen to be fusing into helium at the heart of the Sun at a rate that would explain the Sun’s radiated energy. The work of a British astrophysicist, Arthur Eddington, on stars as spherical balls of gas meant a temperature of around 40 million Kelvin in the centre of the Sun. This temperature came from Eddington’s erroneous assumption that the Sun is mostly made of iron. Using hydrogen as the dominant element gives a central temperature of 12 million Kelvin. This was the temperature that Bethe used. Today we have upgraded this temperature to 15.6 million Kelvin. Rounding down gives this book its title. This is perhaps the most important temperature in the Universe.
Bethe knew that at its centre the material was incredibly dense too: 150,000 kilograms per cubic metre, which is 150 times the density of water and about ten times the density of lead. Eddington is central to our story here as, in fact, it was Eddington who immediately realized fusing hydrogen to helium might be the energy source of the Sun when it had been discovered that the mass of a helium atom is less than the sum of its parts.
At the huge temperature in the centre of the Sun, protons and electrons are so energetic that they break free of the electric charge that holds them together in the hydrogen atoms. Released from their bonds, the protons would be moving at over 500 kilometres per second. In turn, their motion would create a gas pressure at the centre of the Sun that is 2.5 billion times that of the air pressure around you. At such a high density and fast speeds, collisions between protons are very frequent. Armed with the knowledge of the extreme conditions inside the Sun, Bethe set about finding out how often Gamow’s tunnelling could be taking place to produce a nuclear reaction (how many collisions are successful) and whether collectively these reactions could produce enough energy to power the Sun.
Bethe’s work was show-stopping. He was able to demonstrate that the source of the Sun’s energy is dominated by a series of events at the Sun’s core that do indeed convert hydrogen to helium. But not in a straightforward manner. Known as ‘the proton–proton chain’, the path from hydrogen to helium is long and winding.
The first step takes place when two protons tunnel through the barrier they feel between them and a reaction takes place: one of the protons transforms into a neutron, which has no electric charge, and an antimatter particle called a ‘positron’ (essentially a positively charged electron) is formed along with a particle known as a ‘neutrino’. T
he neutron does not hang around though, and combines with the other proton to form a new particle called a ‘deuteron’ (which now contains one proton and one neutron). The positron is also short-lived and rapidly encounters an electron – its matter equivalent – and the two annihilate each other, releasing energy in the form of a gamma ray in the process.
What’s needed next is for the deuteron to fuse with another proton to form an almost-helium nucleus, which has two protons but only one neutron (whereas a fully formed helium nucleus has two neutrons). Another gamma ray is formed too. Only then can the third and final step take place, in which two* of these helium nuclei come together to form a complete helium nucleus with two protons and two neutrons, leaving the two extra protons to go their separate ways. This means that, overall, four hydrogen nuclei have gone in and one helium nucleus comes out. Crucially for our world (and this book), the mass of the helium nucleus is 0.7 per cent less than the mass of the four protons that went in, and along the way this mass has been transformed into energy. And part of that energy, released in step two of the chain and in the electron positron annihilation, takes the form of a photon.
2.1 Flowchart illustrating the three basic steps in the proton–proton chain. Steps 1 and 2 need to occur twice for step 3 to be possible.
In recognition of his calculation which showed that this journey from hydrogen to helium was powering the Sun, in 1967 Bethe received a phone call. It was 6.15 a.m. but it would have been a very welcome call, despite waking him at such an inconvenient hour. As he answered, a Swedish voice at the other end of the line announced that he had been awarded the Nobel Prize for Physics – for work which was so significant that this was the first time a Nobel Prize had been awarded for a discovery in astrophysics, despite the fact that Bethe was not an astrophysicist and had done the work twenty-eight years earlier.
IS THE SUN A NUCLEAR BOMB?
No. It’s not.
The processes that occur inside the Sun may sound very similar to what happens in a nuclear (hydrogen) bomb, and much of the science was developed by the same people, but there are some fundamental differences.
While the aim of a thermonuclear bomb is to release a vast amount of energy in a very short amount of time, the Sun releases its energy relatively slowly and constantly. In fact, each time a proton–proton chain reaction is completed, the amount of energy liberated is tiny: a mere 4000 billionths of a joule. It is the sheer number of fusion reactions that take place in the core every second to power the Sun that leads to the vast energy output. If you could scoop up a coffee cup’s worth of material at the centre of the Sun a billion reactions would be happening in the material every second. Combined together they would release just four thousandths of a joule. It would be like eating those 100 grams of corn chips slowly over sixteen years. Gram for gram the sailors studied by Mayer are able to create more energy from their food than the Sun does from its nuclear reactions.
On top of this, despite the enormous number of nuclear reactions that do take place in the core of the Sun, they are still only a minute fraction of the total number of particle collisions that occur. (Really, it’s incredible that the Sun generates energy at all.) What counts is, again, the vast number of collisions that take place. What allows the Sun to produce the energy it does is its size: the Sun’s core, where the conditions make nuclear fusion possible, occupies the inner 25 per cent of the Sun – a sphere 350,000 kilometres across, around thirty times the Earth’s diameter. This is so large that, despite the low likelihood of a collision resulting in a fusion event, the huge number of proton collisions really add up: every second, 600 billion kilograms of hydrogen in the core are turned into 596 billion kilograms of helium, with the missing 4 billion kilograms being turned into other forms of energy. Luckily for us, mass is not something the Sun is short of and it has enough hydrogen in the core to keep it shining for some billions of years yet. In fact, the Sun is a middle-aged star – it has been fusing hydrogen to helium in its core for around 4.6 billion years but has enough supplies to live out another 4.6 billion years, meaning that it is only halfway through its life.
3. Suns and Daughters
Given the enormous number of nuclear reactions that take place in the core of the Sun, why doesn’t it explode now? There is a vital difference between the Sun and a nuclear bomb: there are 522,000 kilometres of gas lying between the core and the surface of the Sun and this gas tames the thermonuclear bomb within it, turning it into a clean energy source with a power output and longevity that we currently can only dream of re-creating on Earth.
All that extra material around the Sun’s core does throw up two new mysteries though. Firstly: what is it? Is it the same material as that fusing in the Sun’s core? To answer this question we have to look at how the Sun was formed.
That the Sun does not explode like a thermonuclear bomb is because of a delicate balancing act, one that keeps the Sun exploding enough to stay hot, but not so much that it blows apart. We now know this equilibrium was established when the Sun was young and that fusion proceeded at a steady rate, and has remained safely stable ever since. For centuries scientists have been trying to discover how the Sun formed, with no idea they were also working towards a theory of how it keeps its thermonuclear reactor in check.
What we see now when we look up at the Solar System around us is just one snapshot in its life cycle. The Solar System has been here for almost 5 billion years and has about that long left to go. As a family, the Sun and the planets have been through a lot together already, and they have plenty of ups and downs still ahead of them.
If the Solar System were an actual family, the Sun would undoubtedly be the boss, but I’m not just saying this because I have made a career out of studying the Sun. It is the dominant member of our cosmic gang. It is a single parent trying to raise its offspring planets in a modern galaxy. It is the head of the family.
But even though the Sun rules the roost and makes up over 99 per cent of all matter in the Solar System, that 99 per cent may be the most difficult to study. Historically it has been easier to track the movement of the planets in the sky and to try to understand them. But studying all family members, even looking at planetary motions, can help us to understand the Sun. The first realistic family portrait of the Solar System was formed in 1755, by a German philosopher, Immanuel Kant.
As well as being a hugely influential philosopher, largely responsible for the Western philosophy of the past three centuries, Kant also dabbled in science. This was at a time before academics had the clear-cut roles we do today. In a modern university you would not expect to see a solar physicist striding into the philosophy department! Actually, to be more accurate, the era that Kant worked in was a time when modern science was gradually breaking away from its philosophical roots – though the connection lingers today: I have a Ph.D., which is the abbreviation for Doctor of Philosophy, in solar physics.
In Kant’s time, the Solar System was thought of as a small family. Only five planets other than the Earth were known – Mercury, Venus, Mars, Jupiter and Saturn, as they can be seen without the aid of a telescope. The complete family portrait actually includes Uranus, Neptune, Pluto and friends, the Kuiper belt objects, asteroids and comets. But that picture was still to be painted. And we can’t be smug even now as we are still working on the portrait: new members of the family are still being discovered. The information that Kant needed was all there, though.
Kant used not only the movements of those five planets but also the way they spin to create his picture. The Earth rotates once every twenty-four hours, giving us our day, but it is not unique in that: all of its si
blings spin as well. What struck Kant were the striking similarities in how all of the planets spun and moved: they all orbited the Sun in the same direction and they all spun in that same direction. If you were to look ‘down’ on the Solar System (from a northern-hemisphere-centric point of view) all of the planets went around the Sun anti-clockwise and they all spun anti-clockwise. Not only that: they didn’t orbit the Sun in a haphazard fashion, but all moved on one plane, as if they were all rolling around on the same flat surface.
It should be said, though, that today we know things aren’t quite as simple as this. Two planets spin in the opposite direction to the rule Kant stated: it was not until the 1960s that radar measurements discovered that Venus, which is shrouded by thick clouds, spins the opposite way; as too does Uranus, a planet not visible to the naked eye and not known about by Kant. But these are exceptions that still fit within Kant’s theories with some modern tweaks.
Because all the planets share the same family traits, Kant knew they must have all formed together – the planets were not created individually and then later adopted by the Sun but must have all originated via the same process. Kant wound the clock backwards and concluded that the Solar System must have started as the one nebulous cloud of gas that then gave birth to the planets and Sun we see today. The sticking point with this is that his theory predicts that the Sun and the Earth are made of the same stuff. But it is hard to think of two more dissimilar objects: the water-soaked Earth and a raging ball of super-heated gas. To test Kant’s theory requires us to know more about what the Sun is composed of.