University of Delaware


Quarks, Gluons, and the Big Bang

Maurice Barnhill

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Class Notes VI. Is the Sun Still Shining?

Class Notes on Solar Neutrinos

Last revised 1999/03/05


  1. The Problem
    1. Source of the energy of the sun
    2. Where do the Reactions Occur?
    3. Test by observing neutrinos
    4. Neutrino deficit
  2. A Possible Solution
    1. Neutrino states; superposition
    2. Long-distance neutrino oscillations

Technical Reference

I have used Paul Langacker's technical discussion of solar neutrinos (from the web, but no longer available) for information on the status of the problem as of about 1997.


The Problem

The sun puts out a lot of energy, and we are of course completely dependent on having this energy output continue at a steady rate. The energy is generated by nuclear reactions near the center of the sun. Heat is generated by the reactions and works its way gradually to the surface, where it is radiated as light of various frequencies, including infrared and ultravioledt. Because of the length of time that it takes the energy to reach the surface, it is not easy to monitor the actual production of energy. However, neutrinos can in principle allows us to do the direct monitoring.

The net effect of the reaction in the sun is the conversion of four protons into helium:

4 p --> He4 + energy (+ neutrinos)

[The notation we will use for nuclear reactions can be read in part from the line above. p = H1 = proton, N = neutron, e- = electron, e+ = positron, He4 = the isotope of Helium which has a total of 4 protons and neutrons. Other elements we will see are Ar = argon, B = Boron, Be = Beryllium, Cl = Chlorine, D = H2 = the isotope of hydrogen with one proton and one neutron in the nucleus, Ga = Gallium, Ge = Germanium, and Li = Lithium.]

It requires 1038 [1 followed by 38 zeros] such reactions per second to keep the sun shining at its present rate. If it were necessary for the reaction to occur exactly as written, with 4 protons in the same place instantaneously converted into 2 protons and 2 neutrons and bound together into a helium nucleus, there would be many fewer reactions than that number. Instead there is a chain of reactions, which I need to write down for reference but which you should not memorize in detail. The full process is

p + p --> D + e+ + electron-neutrino
D + p -->He3 + photon
He3 + He3 --> He4 + 2 p and He3 + He4 --> Be7 + photon

In practice 85% of the He3 made in the second reaction is used to make He4 and 15% is used in making Be7. The Be7 does not stay around forever. Most (99.9%) is converted to Li7 by a reaction

Be7 + e- --> Li7 + electron-neutrino

and the remainder becomes Be8 through the pair of reactions

Be7 + p --> B8 + photon
B8 --> Be8 + e+ + electron-neutrino

The reaction involving Be7 + p is very sensitive to temperature, occurring much more frequently as the temperature increases. A small error in the temperature at the center of the sun would make a big difference to predictions of the rate of the reaction. Since the number of neutrinos coming from the last reaction depends on the amount of B8 present in the sun, which depends on the frequency of the Be7 + p reaction, the number of neutrinos coming out of the last reaction is a somewhat unreliable measure of the total production of energy in the sun. Unfortunately, the neutrino from this reaction has higher energy than the other neutrinos generated by the set of reactions, and the higher energy makes it much easier to detect on earth.

The first experiment that attempted to detect these neutrinos is in fact still running. A group led by Ray Davis at Penn put a detector filled with 600 tons of perchloroethylene [dry-cleaning fluid, with 2 carbon atoms and 4 chlorine atoms per molecule] at the bottom of the Homestake Mine in South Dakota. Neutrinos entering the dry-cleaning fluid occasionally react with the chlorine in the fluid:

electron-neutrino + Cl37 --> e- + Ar37.

The resulting Argon dissolves in the cleaning fluid and is extracted monthly to measure the number of reactions. The experiment finds about 0.5 neutrino per day!

The problem is not that a normal sun produces very few neutrinos. At the position of the earth, approximately 6 x 1010 neutrinos should pass through every square-cm of surface every second. I am about 45 cm wide and 180 cm tall, not too untypical. When I am lying down my area is therefore about 8000 square cm. So roughly 5 x 1014 = 500,000,000,000,000 neutrinos pass through my body every second. Neutrinos do not react very readily, however, and all but a tiny, tiny fraction of the nutrinos pass right through me (or Davis's cleaning fluid) without having any effect at all. Absorbing much less than one neutrino a day doesn't do me much harm.

So we need to know how many neutrinos per day would be expected in Davis's detector given the amount of energy coming from the sun. Because only the neutrinos from B8 decay can be seen, the exact number is a bit uncertain. However, the detector should be seeing about 1.8 neutrinos per day and certainly more than 1.2 per day. The experiment sees 32-40% of the expected number of neutrinos. So where are the rest of the neutrinos? Is the sun currently producing enough energy to keep it shining at its current rate?

There are several possible solutions:

  1. The theory of the interior of the sun is not as good as astrophysicists think, and the interior of the sun is just a bit cooler than is now thought possible. This solution has appealled to particle physicists but has been considered very unlikely by astrophysicists, and the most recent data is in fact completely inconsistent with this solution.

  2. There is a subtle error in Davis's experiment that nobody has been able to find, and half or so of the Argon resulting from neutrino reactions are lost. This solution appeals to theoretical astrophysicists but is considered very unlikely by experimental particle physicists.

  3. Some of the neutrinos disappear on the way to the earth from the sun. Everybody could live with this one.

  4. The sun is a variable star on some time scale and is currently not producing as much energy as it is giving off. In this case the sun (and us) would be living off energy produced in the past. This solution is logically possible but everyone, especially those who have studied the past climates of the earth, find it extremely unlikely.

  5. There has been some kind of catastrophe in the interior of the sun so that the sun will get much fainter within 10,000 years or so. Nobody likes this one, and there is no sign of such events occurring on other stars. It makes a good "teaser" title but don't worry about it.

What we need is more data to distinguish between the possibilities. There are now three additional experiments running of two different types.

  1. Kamiokande experiment in Japan.
    This experiment looks for the scattering of neutrinos in 1000 tons of water. It is also sensitive primarily to neutrinos from B8 decay, although with a different neutrino-energy dependence. It is capable of directly determining whether the neutrinos it sees are coming from the sun, which Davis's experiment cannot, and it is not dependent on chemical extraction of reaction products. This experiment has in fact confirmed that the observed neutrinos are coming from the sun, but it sees only about 50-65% of the expected number of neutrinos. Thus it confirms Davis's result that too few neutrinos reach the earth and suggests that the size of the deficit depends on the energy of the neutrino. Our concern that the chemistry of Davis's experiment might be a problem is relieved. Our concern that there might not be enough neutrinos has therefore been heightened.

  2. Gallium experiments: Baksan in Russia and GALLEX in the Gran Sasso Tunnel in Italy.
    Gallium experiments use the reaction

    neutrino + Ga71 --> Ge71 + e-

    They use chemistry to extract the resulting Germanium atoms as their measure of the number of reactions. Physics Today (October 1990) said of these experiments that "Happily, the gallium-71 transmutation threshold ... [allows] such a detector to monitor much of the solar pp-neutrino spectrum. Unhappily, a ton of gallium costs a half-million dollars -- a lot more than cleaning fluid." The Baksan experiment uses 60 tons of the stuff; they got it from reserves kept by the Soviet army. Certain parts of the Russian government have tried to seize the Gallium by force to cure their budget problems; so far all such efforts have been prevented from being successful.

    The advantage of the gallium experiments is that the number of neutrinos that they should see is almost completely determined by the energy output of the sun without having to know the temperature of the central regions. The disadvantage, besides cost, is that they depend on difficult chemistry. However, great care has been taken to calibrate the experiments by putting known amounts of a different isotope of Germanium into the detector so as to verify the determination of the concentration of Germanium. Their results: they see about 60% of the expected number of neutrinos.

So it certainly looks like the problem is real and is not caused by a misunderstanding of the physics of the inner sun. Now what do we do?

A Likely Solution

The most likely solution for this problems makes use of quantum phenomena involving the three types of neutrino. This solution requires that at least one of the neutrinos have mass. The detailed predictions of this idea fit experiment rather well. Although only one neutrino would have to be massive, once one neutrino has mass there is no particular reason why the others shouldn't also, and I will assume for purposes of explanation that all of the neutrinos have smallish masses.

Neutrinos can exist in "states" in which they are combinations of electron, muon, and tau neutrinos. There is no particular reason why a neutrino should not be, for example, 90% electron-neutrino, 8% muon-neutrino, and 2% tau-neutrino. If the three types of neutrinos have different masses, then such a neutrino state would not have a definite mass, but would have a probability of having one mass, another probability of having a different mass, and a third probability of having a third mass. If it were in a state with indefinite mass then Quantum Mechanics predicts that the proportion of electron-neutrino, muon-neutrino, and tau-neutrino in the state would change with time.

Let's call the states with definite mass neutrino-1, neutrino-2, and neutrino-3. If the neutrino associated with each lepton is a different combination of neutrinos 1, 2, and 3, then an electron neutrino given off at the sun will not necessarily be exactly an electron neutrino when it gets to the earth. It is said to have oscillated into a combination of electron-, muon-, and tau-neutrino.

How does this oscillation help our problem? [It had better help. If we have to deal with something this weird we might as well get something out of it.] Well, all three types of neutrino-detection experiments detect electron-neutrinos only. Any muon- or tau-neutrinos present go right through the detector with no absorption or scattering at all. Moreover, the proportion of electron-neutrino left when the neutrino reaches the earth is energy-dependent. So the experiments must see fewer neutrinos than left the sun, and how many fewer depends on the energy of the neutrino. A failue to detect a few of the neutrinos is just what we need to understand why the experiment sees fewer neutrinos than expected.

There is now (March, 1999) also an experiment done at Super-Kamiokande in Japan that measures fairly directly the likelihood of oscillation of mu-neutrinos using the products of reactions of cosmic rays with upper-atmosphere atoms. This experiment sees the disappearance of mu-neutrinos into something, but that something is not electron-neutrinos. The mu-neutrinos might be oscillating into tau-neutrinos or into something entirely unexpected. It is possible to choose a set of parameters that would explain both the disappearance of solar neutrinos and the cosmic-ray oscillation experiment without having to assume a new particles for the mu-neutrinos to change into. A Los Alamos National Lab accelerator experiment also gives evidence for neutrino masses and oscillation and is consistent with the Kamiokande measurement. Unfortunately no single set of parameters will explain all three of the experiments, Kamiokande, Los Alamos, and solar neutrinos, without inventing a new particle. There is still work to be done before it is clear exactly what is going on.

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