Testing the Hypothesis of Nuclear Burning

Science progresses as a result of the clash between theory and experiment, between speculation and measurement. Eddington, in the same lecture in which he first discussed the burning of hydrogen nuclei in stars, remarked:

I suppose that the applied mathematician whose theory has just passed one still more stringent test by observation ought not to feel satisfaction, but rather disappointment — “Foiled again! This time I had hoped to find a discordance which would throw light on the points where my model could be improved.”

Is there any way to test the theory that the sun shines because very deep in its interior hydrogen is burned into helium? At first thought, it would seem impossible to make a direct test of the nuclear burning hypothesis. Light takes about ten million years to leak out from the center of the sun to the surface and when it finally emerges in the outermost regions, light mainly tells us about the conditions in those outer regions. Nevertheless, there is a way of “seeing” into the solar interior with neutrinos, exotic particles discovered while trying to understand a different mystery.4

Discovery, Confirmation, and Surprise

A neutrino is a sub-atomic particle that interacts weakly with matter and travels at a speed that is essentially the speed of light. Neutrinos are produced in stars when hydrogen nuclei are burned to helium nuclei; neutrinos are also produced on earth in particle accelerators, in nuclear reactors, and in natural radioactivity. Based upon the work of Hans Bethe and his colleagues, we believe that the process by which stars like the sun generate energy can be symbolized by the relation,


in which four hydrogen nuclei (1H, protons) are burned into a single helium nucleus (4He, particle) plus two positive electrons ( ) and two neutrinos ( ) plus energy. This process releases energy to the star since, as Aston showed, four hydrogen atoms are heavier than one helium atom. The same set of nuclear reactions that supply the energy of the sun’s radiation also produce neutrinos that can be searched for in the laboratory.

This figure is a cross section of the sun. The features that are usually studied by astronomers with normal telescopes that detect light are labeled on the outside, e. g., sunspot and prominences. Neutrinos enable us to look deep inside the sun, into the solar core where nuclear burning occurs.

Because of their weak interactions, neutrinos are difficult to detect. How difficult? A solar neutrino passing through the entire earth has less than one chance in a thousand billion of being stopped by terrestrial matter. According to standard theory, about a hundred billion solar neutrinos pass through your thumbnail every second and you don’t notice them. Neutrinos can travel unaffected through iron as far as light can travel in a hundred years through empty space.

In 1964, Raymond Davis Jr. and I proposed that an experiment with 100,000 gallons of cleaning fluid (perchloroethylene, which is mostly composed of chlorine) could provide a critical test of the idea that nuclear fusion reactions are the ultimate source of solar radiation. We argued that, if our understanding of nuclear processes in the interior of the sun was correct, then solar neutrinos would be captured at a rate Davis could measure with a large tank filled with cleaning fluid. When neutrinos interact with chlorine, they occasionally produce a radioactive isotope of argon. Davis had shown previously that he could extract tiny amounts of neutrino-produced argon from large quantities of perchloroethylene. To do the solar neutrino experiment, he had to be spectacularly clever since according to my calculations only, a few atoms would be produced per week in a huge Olympic-sized swimming pool of cleaning fluid.

Our sole motivation for urging this experiment was to use neutrinos to:

enable us to see into the interior of a star and thus verify directly the hypothesis of nuclear energy generation in stars.

As we shall see, Davis and I did not anticipate some of the most interesting aspects of this proposal.

Davis performed the experiment and in 1968 announced the first results. He measured fewer neutrinos than I predicted. As the experiment and the theory were refined, the disagreement appeared more robust. Scientists rejoiced that solar neutrinos were detected but worried why there were fewer neutrinos than predicted.

What was wrong? Was our understanding of how the sun shines incorrect? Had I made an error in calculating the rate at which solar neutrinos would be captured in Davis’s tank? Was the experiment wrong? Or, did something happen to the neutrinos after they were created in the sun?

Over the next twenty years, many different possibilities were examined by hundreds, and perhaps thousands, of physicists, chemists, and astronomers5. Both the experiment and the theoretical calculation appeared to be correct.

Once again experiment rescued pure thought. In 1986, Japanese physicists led by Masatoshi Koshiba and Yoji Totsuka, together with their American colleagues, Eugene Beier and Alfred Mann, reinstrumented a huge tank of water designed to measure the stability of matter. The experimentalists increased the sensitivity of their detector so that it could also serve as a large underground observatory of solar neutrinos. Their goal was to explore the reason for the quantitative disagreement between the predicted and the measured rates in the chlorine experiment.

The new experiment (called Kamiokande) in the Japanese Alps also detected solar neutrinos. Moreover, the Kamiokande experiment confirmed that the neutrino rate was less than predicted by standard physics and standard models of the sun and demonstrated that the detected neutrinos came from the sun. Subsequently, experiments in Russia (called SAGE, led by V. Gavrin), in Italy (GALLEX and later GNO led by T. Kirsten and E. Belotti, respectively), and again in Japan (Super-Kamiokande, led by Y. Totsuka and Y. Suzuki), each with different characteristics, all observed neutrinos from the solar interior. In each detector, the number of neutrinos observed was somewhat lower than standard theory predicted.

What do all of these experimental results mean?

Neutrinos produced in the center of the sun have been detected in five experiments. Their detection shows directly that the source of the energy that the sun radiates is the fusion of hydrogen nuclei in the solar interior. The nineteenth century debate between theoretical physicists, geologists, and biologists has been settled empirically.

From an astrophysical perspective, the agreement between neutrino observations and theory is good. The observed energies of the solar neutrinos match the values predicted by theory. The rates at which neutrinos are detected are less than predicted but not by a large factor. The predicted neutrino arrival rate at the earth depends approximately upon the 25th power of the central temperature of the sun, T x T x…T (25 factors of the temperature T). The agreement that has been achieved (agreement within a factor of three) shows that we have empirically measured the central temperature of the sun to an accuracy of a few percent. Incidentally, if someone had told me in 1964 that the number of neutrinos observed from the sun would be within a factor of three of the predicted value, I would have been astonished and delighted.

In fact, the agreement between normal astronomical observations (using light rather than neutrinos) and theoretical calculations of solar characteristics is much more precise. Studies of the internal structure of the sun using the solar equivalent of terrestrial seismology (i. e., observations of solar vibrations) show that the predictions of the standard solar model for the temperatures in the central regions of the sun are consistent with the observations to an accuracy of at least 0.1%. In this standard model, the current age of the sun is five billion years, which is consistent with the minimum estimate of the sun’s age made by nineteenth-century geologists and biologists (a few hundred million years).

Given that the theoretical models of the sun describe astronomical observations accurately, what can explain the disagreement by a factor of two or three between the measured and the predicted solar neutrino rates?

New Physics

Physicists and astronomers were once again forced to reexamine their theories. This time, the discrepancy was not between different estimates of the sun’s age, but rather between predictions based upon a widely accepted theory and direct measurements of particles produced by nuclear burning in the sun’s interior. This situation was sometimes referred to as the Mystery of the Missing Neutrinos or, in language that sounded more scientific, the Solar Neutrino Problem.

As early as 1969, two scientists working in Russia, Bruno Pontecorvo and Vladimir Gribov, proposed that the discrepancy between standard theory and the first solar neutrino experiment could be due to an inadequacy in the textbook description of particle physics, rather than in the standard solar model. (Incidentally, Pontecorvo was the first person to propose using a chlorine detector to study neutrinos.) Gribov and Pontecorvo suggested that neutrinos suffer from a multiple personality disorder, that they oscillate back and forth between different states or types.

According to the suggestion of Gribov and Pontecorvo, neutrinos are produced in the sun in a mixture of individual states, a sort of split personality. The individual states have different, small masses, rather than the zero masses attributed to them by standard particle theory. As they travel to the earth from the sun, neutrinos oscillate between the easier-to-detect neutrino state and the more difficult-to-detect neutrino state. The chlorine experiment only detects neutrinos in the easier-to-observe state. If many of the neutrinos arrive at earth in the state that is difficult to observe, then they are not counted. It is as if some or many of the neutrinos have vanished, which can explain the apparent mystery of the missing neutrinos.

Building upon this idea, Lincoln Wolfenstein in 1978 and Stanislav Mikheyev and Alexei Smirnov in 1985 showed that the effects of matter on neutrinos moving through the sun might increase the oscillation probability of the neutrinos if Nature has chosen to give them masses in a particular range.

Neutrinos are also produced by the collisions of cosmic ray particles with other particles in the earth’s atmosphere. In 1998, the Super-Kamiokande team of experimentalists announced that they had observed oscillations among atmospheric neutrinos. This finding provided indirect support for the theoretical suggestion that solar neutrinos oscillate among different states. Many scientists working in the field of solar neutrinos believe that, in retrospect, we have had evidence for oscillations of solar neutrinos since 1968.

But, we do not yet know what causes the multiple personality disorder of solar neutrinos. The answer to this question may provide a clue to physics beyond the current standard models of sub-atomic particles. Does the change of identity occur while the neutrinos are traveling to the earth from the sun, as originally proposed by Gribov and Pontecorvo? Or does matter cause solar neutrinos to “flip out”? Experiments are underway in Canada, Italy (three experiments), Japan (two experiments), Russia, and the United States that are attempting to determine the cause of the oscillations of solar neutrinos, by finding out how much they weigh and how they transform from one type to another. Non-zero neutrino masses may provide a clue to a still undiscovered realm of physical theory.

4 The existence of neutrinos was first proposed by Wolfgang Pauli in a 1930 letter to his physics colleagues as a “desperate way out” of the apparent non-conservation of energy in certain radioactive decays (called -decays) in which electrons were emitted. According to Pauli’s hypothesis, which he put forward very hesitantly, neutrinos are elusive particles which escape with the missing energy in -decays. The mathematical theory of  -decay was formulated by Enrico Fermi in 1934 in a paper which was rejected by the journal Nature because “it contained speculations too remote from reality to be of interest to the reader.” Neutrinos from a nuclear reactor were first detected by Clyde Cowan and Fred Reines in 1956.

5 Perhaps the most imaginative proposal was made by Stephen Hawking, who suggested that the central region of the sun might contain a small black hole and that this could be the reason why the number of neutrinos observed is less than the predicted number.

Nature: A Wonderful Mystery