15 Million Degrees

by Lucie Green

  This is what happens inside the Sun. Strictly speaking, the Sun is not a ball of gas as Lord Kelvin and Lane thought, but rather a ball of plasma. It is a common mistake. In 1993 the band They Might be Giants released a record called Why Does the Sun Shine?, featuring a song of the same name (which was their cover version of a 1959 song). The strap-line for the song, and part of the lyrics, is the line ‘the Sun is a mass of incandescent gas’, an almost exact quote from Lane. I was prepared to overlook this persistent inaccuracy because I like any songs about the Sun, but then They Might be Giants put it right when in 2009 they released a corrected song: ‘Why Does the Sun Really Shine? The Sun is a Miasma of Incandescent Plasma’.

  The extreme temperature in the centre of the Sun means that the atoms within it are torn apart into a plasma. The hydrogen atoms have lost their single electron, the helium atoms have lost both their electrons, lithium has lost its three, and so on through the heavier elements. Once an atom has been stripped of its electrons, only a naked atomic nucleus is left, and since hydrogen is the most abundant element in the Sun, the plasma is made mostly of electrons and single protons. This is the environment that the gamma ray photons shine into. So what happens to the gamma ray photons?

  It’s a useful analogy now to think of the photons as waves on an ocean. If you place a buoy on the ocean’s surface, you can watch it rise and fall as the waves ripple underneath it. If a wave with a short wavelength moves the buoy, it will bob rapidly up and down. Another wave, moving at the same speed as the first but having a longer wavelength, will move the buoy up and down less frequently.

  If you have an electromagnetic buoy – a device to measure the ripples in the magnetic and electric fields passing any one point – you would see that the strength of those fields moves continuously from high to low and back again. In fact, you do have such a device in the form of your TV aerial. The electromagnetic waves passing through it make the free-drifting electrons in metal bob around. This generates an electric current that is then converted into images and sound. The important point here is that the electrons act like a buoy for electromagnetic waves. With this in mind, let’s head back into the Sun.

  As the electromagnetic wave of the gamma rays ripples out from the core it encounters a fleet of liberated electrons. And, just like a buoy on the ocean, the electrons start to bob up and down. Each time this happens, energy has been transferred from an electromagnetic wave to an electron. The photon is actually ‘absorbed’ by the electron during this process, disappearing and leaving behind only a very excited electron. But that electron cannot contain its excitement. As we have seen, an accelerating charged particle emits radiation, so once the electron starts moving it sends out radiation of its own and emits another gamma ray photon. Crucially, though, the direction of that new flash of gamma ray light is completely random.

  Standing back and watching this you’d see a photon hit an electron and almost immediately go flying off in a random direction. Officially, though, it is a new photon that is produced, but what we care about is the energy, and the quantity of energy is the same even if the actual photon isn’t. Imagine that I lend you a £50 note and that you pay me back in a few days. I won’t get the same £50 note back. But that doesn’t matter – I’ll get the same amount of money and will still be in an excited state. It’s the same for photons. Photons are fungible.

  The collective effect is as if all the photons were being constantly scattered in random directions by the electrons. This scattering is known as ‘Thomson scattering’ and is named after J. J. Thomson, the British physicist who discovered the electron in 1897, during his research to understand the workings of the atom. Each photon is being scattered, time after time.

  In between each encounter with an electron, any one photon will be moving at the speed of light, but on average each photon only manages to travel about 1 millimetre in the radiation zone before hitting an electron and being scattered again. Not only is that 1 millimetre almost inconsequential compared to the overall thickness of the radiation zone it has to traverse (which stretches for over 400,000 kilometres above the core), but also it may not even be a millimetre in the correct direction. Each scattering event is as likely to send the photon back towards the centre of the Sun as it is to send it up towards the surface. The photon is on a random walk and this is why it takes so long for it to reach the surface. Each photon can expect to make around ten million billion billion steps before it randomly happens to reach the surface and get out. And this number of steps takes 170,000 years.

  Photons find the Sun’s plasma, with all its electrons, very difficult to get through. Their plight reminds me of one childhood memory that for some reason is still overwhelmingly vivid. It’s night and I am in the car with my mother, who is driving, and the night is so foggy that we are practically hanging out of the car windows, straining our eyes to see what lies ahead. Even though the headlights are on, the photons barely penetrate into the haze. Instead, the car lights and the fog create a bright glaring wall of white immediately in front of us, as much of the light is scattered right back at us. It is a memory that flashes back to me whenever I feel claustrophobic. And this is what an anthropomorphized photon would be feeling: the sense of being boxed in, of its near-futile progress.

  To make things even worse, the photons have to put up with the other by-product of the fusion occurring at the Sun’s core: neutrinos. Each set of reactions that produces one helium nucleus releases two neutrinos as well as the two photons. But the neutrinos do not care about plasma. They race through it as it if weren’t there, like car headlights through still, empty air on a summer’s night. The neutrinos go from the core to the surface of the Sun in just two seconds! Imagine an exhausted photon, bounced around a millimetre at a time for hundreds of thousands of years, near the surface and probably only a few tens of thousands of years of random scattering away from making it out, when suddenly a neutrino less than two seconds old races by and doesn’t even acknowledge its existence!

  Even passing the surface is a non-event for a neutrino. It carries on at the speed of light regardless of what is going on around it. Eight minutes and 20 seconds later it reaches the Earth and pays us equally little heed. Hold up a finger right now and look at your fingernail – around 100 billion neutrinos are flying straight through your fingertip every second as if it weren’t there. Only on very rare occasions will a neutrino interact with an atom, which is our only way to glimpse them. Physicists monitor thousands of tonnes of water in vast underground tanks just to spot a handful of neutrino–water interactions.

  HITCHING A RIDE

  Things actually get slightly better for the photons when they reach the final 18 per cent of the distance out of the Sun and hit the convection zone. The pressure and temperature of the plasma have gradually been decreasing as the photons move further out. The centre of the Sun is a blistering 15 million Kelvin, but not all of the Sun is at that temperature: energy is constantly being lost from the surface of the Sun out into space. This means there is a temperature gradient from the centre of the Sun outwards: in the radiation zone the temperature drops to 7.5 million Kelvin and at the beginning of the convection zone it is a mere 2 million Kelvin – just as the further you sit away from a campfire in the cool night air, the more your temperature drops.

  It’s not just the relatively low temperature that is important in the convection zone though: it is the rate at which the plasma continues to cool as you go outwards towards the visible surface of the Sun. The steady drop-off in temperature in the radiation zone now becomes much more rapid, and this has an important consequence for both the plasma and the photons. />
  Very importantly, the photons have a much harder time getting through and the plasma starts convecting. Any rising bubbles of plasma that are hotter than their surroundings start to rise. But as they move higher, the rapid temperature drop in the plasma around them means that they have a good chance of still being hotter than their surroundings and they continue to rise. This is the cause of the thin convection zone which gives the boiling, mottled appearance to the Sun’s surface. But what happens to the photons in this zone?

  The temperature of the plasma has dropped enough for some of the particles, like carbon and nitrogen, to hold on to some of their electrons. Once this happens, the photons encounter not a plasma of just electrons and naked nuclei, but a plasma that also contains ions: ‘ion’ is simply the word for an atom that is electrically charged because it has managed to gain or lose some electrons, and doesn’t have the right amount to be electrically balanced. Because the nuclei are only just able to start holding on to some electrons, they are still a long way off having all the electrons they need.

  The problem for the photons here is that, unlike a free-floating electron, an electron attached to a nucleus has the ability to absorb a photon and it doesn’t necessarily have to re-emit it. These are electrons with an eye on the future. If you loan money to these electrons you won’t necessarily get it back. They have a very negative outlook on life. The reason why they can hold on to a photon comes down to their relationship with the nucleus.

  As a solar physicist, I find the image of an atom being like a miniature Solar System, with the electrons racing around the nucleus as the planets orbit the Sun, very appealing. This model of atoms was developed by a Danish physicist, Niels Bohr, and a scientist from New Zealand called Ernest Rutherford, and is very sadly not correct. An Austrian scientist, Erwin Schrödinger, showed that the electrons move in much more complicated ways: they don’t sit in a neat circular orbits but rather spread across more than one location, actually more like a wave than a discrete particle. In fact, it becomes impossible to say where the electron actually is. Schrödinger’s description was of a cloud around the nucleus in which he could assign the probability of the electron’s position. This cloud has become known as an ‘orbital’ – a nod to the naming in the old Solar System-like model.

  Thankfully, the Solar System analogy works perfectly if you replace the word ‘orbitals’ with ‘orbits’. In the Solar System, not all orbits are equal and it takes different amounts of energy for planets and other bodies to remain orbiting at different distances. At this moment the Moon is losing energy because of its gravitational interaction with the Earth, so its orbit is changing: the Moon drifts away from the Earth by about 3.7 centimetres per year. Likewise, different orbitals around the nucleus require the electron to have different amounts of energy.

  Crucially, unlike gravitational orbits that can have any amount of energy, the electrostatic orbitals can only take on set amounts of energy and nothing in between. It is as if, instead of gradually drifting away, the Moon suddenly jumped a few metres each time its energy matched an allowed orbit. And different kinds of nuclei, made of different combinations of protons and neutrons, allow for different energy levels that an electron can be in.

  There are very specific energy levels associated with each type of nucleus and this means that the electron isn’t free to choose the energy it can have. It must occupy one of the predetermined energy levels. So a photon will only be absorbed if its energy exactly matches the amount required to shift the electron between energy levels or if it can eject an electron completely. If there is no match the photon will simply pass by.

  And if the photon is absorbed when its energy matches, the ion may not release it again straight away. On top of that, the ion is also in motion: it is riding the convection currents up and down the convection layer. A photon can be absorbed by an ion, ride along with it up the convection zone and then be re-emitted closer to the surface. With an average speed of 1 kilometre per second, hot pockets of plasma move across the 125,000 kilometres of the convection zone in a couple of days. It takes far less time for photons to cross the convection zone than to cross the radiation zone, as they are able to hitch a ride for the final stages of this journey. Convection takes over from radiation as the main way to transport energy.

  The very last step of the journey is the photosphere – the sphere of light – where the plasma finally breaks its hold on the photons and they escape into the Solar System. It’s an incredible layer and is only 500 kilometres thick – less than one thousandth of the solar radius. Over a distance of 500 kilometres the plasma goes from being an opaque barrier to the photons to being transparent. Such a rapid transition gives an otherwise tenuous ball of gas, which has no surface, a very sharp edge indeed when we view it. No wonder that over the scientific generations there have been some who were convinced that the Sun is a solid object. And without this sharp visible edge, we wouldn’t be able to ascribe a particular size or shape to the Sun at all. It would look like a hazy amorphous blob.

  The clear and sharp edge, which looks so solid, belies the true density of the plasma, which is astonishingly thin. At the base of the photosphere, the plasma is 10,000 times less dense than the air around us. The temperature has also plummeted; the photosphere goes from only 6500 Kelvin to an almost chilly (relatively speaking) 4900 Kelvin at the outermost edge. Even though the plasma continues to extend well beyond this – more on this later – these are the temperatures and densities at which the photons can suddenly pass through the material unimpeded, finally make some distance and go streaming out into the Solar System.

  But they have not survived the journey unscarred. Each of those ten million billion billion scattering events had a slight impact on the photons. Unperceivable individually, only across so many collisions can the slight amount of energy that is lost each time start to accumulate. During the long radiation zone journey the gamma ray photons lose a little energy and become X-ray photons instead, and then, by the time they encounter the convection zone, they have lost enough energy to be ultraviolet photons. During the convection-zone journey the gradual leaking of energy brings the photons down into the range, by the time they escape the photosphere, visible to our eyes, giving us the sunlight we all know and love – with two slight problems. All through their journey, the photons have been pinged around by individual electrons and eventually individual ions. This means they should form a spectrum with thin discrete spectral lines – which is not what we see coming from the Sun. And the extremely low plasma density at the bottom of the photosphere should mean that the photons can easily fly through it – which is not what is happening. Photons are absorbed and emitted across a broad range of wavelengths covering the visible part of the spectrum and this is a puzzle when set against the description of the thin photosphere that we have developed. There is one last character-changing adventure that the photons experience in the thin photosphere.

  THE NEGATIVE HYDROGEN PARTICLE

  Firstly, the behaviour of electrons in orbits explains the emission spectra we saw in Chapter 3. When the electrons in an ion (or atom) lose energy and emit a photon, they can only move between certain set energy levels, and so the released energy can only have specific values. The energy of the photon determines its wavelength/frequency and this is why different elements release light of very specific colours. It is also why they can absorb only specific colours of light.

  To come back to our financial analogy, consider bank A, which only accepts deposits or withdrawals of £4.10, £4.34, £4.86 and £6.56,* and bank B, which only accepts £5.16, £5.17 and £5.18. † Just knowing these numbers allows u
s to recognize which bank money is going to or coming from by looking at the amounts being transferred.

  The problem is that we do not see an emission spectrum coming from the Sun, but instead a continuous spectrum that has an absorption spectrum removed from it. Half of this makes sense. The Sun’s atmosphere continues out past the photosphere and there are hydrogen, helium, lithium, iron and whatnot floating about in it. If a continuous spectrum were somehow produced by the plasma in the photosphere, it would have to pass out through these elements in the overlying plasma, which explains the absorption lines.

  It turns out that the continuous spectrum was coming from a very shadowy figure, a particle no one expected: a strange and exotic variation of hydrogen – the so-called ‘negative hydrogen ion’.

  A hydrogen ion with no electrons is a lone proton floating about by itself. This is the case at the base of the photosphere, where the temperature of 6500 Kelvin is enough to stop any of these loose protons from hanging on to an electron. But 500 kilometres later, the temperature has dropped sharply to around 4900 K. Now the temperature becomes cool enough for the hydrogen nuclei to capture their electron and form a neutral hydrogen atom again. Meanwhile, the electrons orphaned by much larger atoms are still present, as they find it even harder to hold on to their outermost electrons. As these orphaned electrons move around, they collide with the newly formed hydrogen atoms around them and something new is formed.