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.

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