Unravelling Stellar Fusion

Trying to unravel many things in modern science is painstaking, as will be seen from the following example, which makes looking for a needle in a haystack relatively easy. Here, the requirement for careful work and analysis can be seen, although less obvious is the need for assumptions during the calculations, and these are not always obviously correct. The example involves how our sun works. The problem is, how do we form the neutrons needed for fusion in the star’s interior? 

In the main process, the immense pressures force two protons form the incredibly unstable 2He (a helium isotope). Besides giving off a lot of heat there are two options: a proton can absorb an electron and give off a neutrino (to conserve leptons) or a proton can give off a positron and a neutrino. The positron would react with an electron to give two gamma ray photons, which would be absorbed by the star and converted to energy. Either way, energy is conserved and we get the same result, except the neutrinos may have different energies. 

The dihydrogen starts to operate at about 4 million degrees C. Gravitational collapse of a star starts to reach this sort of temperature if the star has a mass at least 80 times that of Jupiter. These are the smaller of the red dwarfs. If it has a mass of approximately 16 – 20 times that of Jupiter, it can react deuterium with protons, and this supplies the heat to brown dwarfs. In this case, the deuterium had to come from the Big Bang, and hence is somewhat limited in supply, but again it only reacts in the centre where the pressure is high enough, so the system will continue for a very long time, even if not very strongly.

If the temperatures reach about 17 million degrees C, another reaction is possible, which is called the CNO cycle. What this does is start with 12C (standard carbon, which has to come from accretion dust). It then adds a proton to make 13N, which loses a positron and a neutrino to make 13C. Then come a sequence of proton additions to make 14N (most stable nitrogen), then 15O, which loses a positron and a neutrino to make 15N, and when this is struck by a proton, it spits out 4He and returns to 12C. We have gone around in a circle, BUT converted four hydrogen nuclei to 4helium, and produced 25 MeV of energy. So there are two ways of burning hydrogen, so can the sun do both? Is it hot enough at the centre? How do we tell?

Obviously we cannot see the centre of the star, but we know for the heat generated it will be close to the second cycle. However, we can, in principle, tell by observing the neutrinos. Neutrinos from the 2He positron route can have any energy but not more than a little over 0.4 MeV. The electron capture neutrinos are up to approximately 1.1 MeV, while the neutrinos from 15O are from anywhere up to about 0.3 MeV more energetic, and those from 13N are anywhere up to 0.3 MeV less energetic than electron capture. Since these should be of the same intensity, the energy difference allows a count. The sun puts out a flux where the last three are about the same intensity, while the 2He neutrino intensity is at least 100 times higher. (The use of “at least” and similar terms is because such determinations are very error prone, and you will see in the literature some relatively different values.) So all we have to do is detect the neutrinos. That is easier said than done if they can pass through a star unimpeded. The way it is done is if a neutrino accidentally hits certain substances capable of scintillation it may give off a momentary flash of light.

The first problem then is, anything hitting those substances with enough energy will do it. Cosmic rays or nuclear decay are particularly annoying. So in Italy they built a neutrino detector under1400 meters of rock (to block cosmic rays). The detector is a sphere containing 300 t of suitable liquid and the flashes are detected by photomultiplier tubes. While there is a huge flux of neutrinos from the star, very few actually collide. The signals from spurious sources had to be eliminated, and a “neutrino spectrum” was collected for the standard process. Spurious sources included radioactivity from the rocks and liquid. These are rare, but so are the CNO neutrinos. Apparently only a few counts per day were recorded. However, the Italians ran the experiment for 1000 hours, and claimed to show that the sun does use this CNO cycle, which contributes about 1% of the energy. For bigger stars, this CNO cycle becomes more important. This is quite an incredible effort, right at the very edge of detection capability. Just think of the patience required, and the care needed to be sure spurious signals were not counted.

An Example of How Science Works: Where Does Gold Come From?

Most people seem to think that science marches on inexorably, gradually uncovering more and more knowledge, going in a straight line towards “the final truth”. Actually, it is far from that, and it is really a lurch from one point to another. It is true science continues to make a lot of measurements, and these fill our banks of data. Thus in organic chemistry, over the odd century or so we have collected an enormous number of melting points. These were obtained so someone else could check whether something else he had could be the same material, so it was not pointless. However, our attempts to understand what is going on have been littered with arguments, false leads, wrong turns, debates, etc. Up until the mid twentieth century, such debates were common, but now much less so. The system has coalesced in acceptance of the major paradigms, until awkward information comes to light that is sufficiently important that it cannot be ignored.

As an example, currently, there is a debate going on relating to how elements like gold were formed. All elements heavier than helium, apart from traces of lithium, were formed in stars. The standard theory says we start with hydrogen, and in the centre of a star, where the temperatures and pressures are sufficient two hydrogen atoms combine to form, for a very brief instant, helium 2 (two protons). An electron is absorbed, and we get deuterium, which is a proton and a neutron combined. The formation of a neutron from a proton and an electron is difficult because it needs about 1.3 MeV of energy to force it in, which is about a third of a million times bigger than the energy of any chemical bond. The diproton is a bit easier because the doubling of the positive field provides some supplementary energy. Once we get deuterium, we can do more and eventually get to helium 4 (two protons, two neutrons) and then it stops because the energy produced prevents the pressure from rising. The inside of the sun is an equilibrium, and in any given volume, a surprisingly few fusion reactions take place. The huge amount of energy is simply because of size. However, when the centre starts to run out of hydrogen, the star collapses further, and if it is big enough, it can start burning helium to make carbon and oxygen. Once the supply of helium becomes insufficient, if the star is large enough, a greater collapse happens, but this refuses to form an equilibrium. Atoms fuse at a great rate and produce the enormous amount of energy in a supernova.

What has happened in the scientific community is that once the initial theory was made, it was noticed that iron is at an energy minimum, and making elements heavier than iron absorb energy, nevertheless we know there are elements like uranium, gold, etc, because we use them. So how did they form? The real short answer is, we don’t know, but scientists with computers like to form models and publish lots of papers. The obvious way was that in stars, we could add a sequence of helium nuclei, or protons, or even, maybe, neutrons, but these would be rare events. However, in the aftermath of a supernova, huge amounts of energy are released, and, it is calculated, a huge flux of neutrons. That 1.3 MeV is a bit of a squib to what is available in a supernova, and so the flux of neutrons could gradually add to nuclei, and when it contained too many neutrons it would decay by turning a neutron into a proton, and the next element up, and hence this would be available form further neutrons. The problem though, is there are only so many steps that can be carried out before the rapidly expanding neutron flux itself decays. At first sight, this does not produce enough elements like gold or uranium, but since we see them, it must have.

Or must it? In 2017, we detected gravitational wave from an event that we could observe and had to be attributed to the collision of two neutron stars. The problem for heavy elements from supernovae is, how do you get enough time to add all the protons and neutrons, more or less one at a time. That problem does not arise for a neutron star. Once it starts ejecting stuff into space, there is no shortage of neutrons, and these are in huge assemblies that simply decay and explode into fragments, which could be a shower of heavy elements. While fusion reactions favour forming lighter elements, this source will favour heavier ones. According to the scientific community, problem solved.

There is a problem: where did all the neutron stars come from? If the elements come from supernovae, all we need is big enough stars. However, neutron stars are a slightly different matter because to get the elements, the stars have to collide. Space is a rather big place. Let over all time the space density of supernovae be x, the density of neutron stars y, and the density of stars as z. All these are very small, but z is very much bigger than x and x is almost certainly bigger than y. The probability of two neutron stars colliding is proportional to y squared, while the probability of a collision of a neutron stars another star would be correspondingly proportional to yz. Given that y is extremely small, and z much bigger, but still small, most neutron stars will not collide with anything in a billion years, some will collide with a different star, while very few will collide with another neutron star. There have been not enough neutron stars to make our gold, or so the claims go.So what is it? I don’t know, but my feeling is that the most likely outcome is that both mechanisms will have occurred, together with possible mechanisms we have yet to consider. In this last respect, we have made elements by smashing nuclei together. These take a lot of energy and momentum, but anything we can make on Earth is fairly trivial compared with the heart of a supernova. Some supernovae are calculated to produce enormous pressure waves, and these could fuse any nuclei together, to subsequently decay, because the heavy ones would be too proton rich.  This is a story that is unfolding. In twenty years, it may be quite different again.