By Gabriel Ferrero

It is widely known that the sun, our closest star, is the main source of energy for our planet. We receive around 10¹⁷ watts from it, which is approximately the power that 10 thousand billion electric irons would consume. However, this is only a tiny fraction of the energy that the sun emits, since most of it is simply dispersed in space¹.

How the sun can be so powerful was a big question for many centuries. The answer was only found in the 1920s and 30s and is also the explanation for the brightness of every star. Several brilliant physicists and astronomers contributed to its comprehension, including Arthur Eddington, George Gamow, Hans Bethe, Fred Hoyle, the spouses Margaret and Geoffrey Burbidge, William A. Fowler and others.

This was their central idea: the source of the stars’ energy is nuclear fusion. Nuclear fusion occurs when two atomic nuclei unite to become one new, heavier, atomic nucleus. For nuclei lighter than those of iron and nickel, this process releases energy.

However, for nuclear fusion to occur inside a star, several strange things have to happen.

The first one: remember that electric charges of the same sign repel each other? Well, all nuclei have a positive charge because they contain protons. So they do repel each other, which tends to becoming infinite if they are too close to each other. But, for two nuclei to unite, they need to come to within a distance of approximately 10^-15 meters. At that distance a different force appears (called strong nuclear force) that can bond them together. To arrive there, each nucleus has to overcome something like a very high and hard barrier, which is almost an impossible task for them.

However, nature has an amazing trick to help them. At such small distances, matter fully exhibits its quantum properties. One of them, is that there is an intrinsic uncertainty in the position of a nucleus. So, there is a very little, but non–zero, probability that a nucleus can arrive so close to the other one as to bond with it after all. This is called the tunnel effect. It is as if there was a hole in the barrier.

The second one: even with the help of the tunnel effect, the nucleus has to have an important amount of kinetic energy so that the probability of crossing the barrier becomes significant. But, in the case of two hydrogen nuclei (i.e., two protons) in the center of the sun, the most common energy of nuclei is ten times smaller than the energy needed for bonding to become probable.

Fortunately, as in every gas at a given temperature, not all of the protons have the same kinetic energy. In fact, there is always a very small number of nuclei with a kinetic energy high enough to take advantage of the tunnel effect².

At the very end, the probability of: finding a nucleus with high enough energy, and that this nucleus crosses the barrier, is very small, but it is not zero! In the case of two protons in the center of the sun, only 1 nucleus in a million can make it.

However, close to the center of the sun there are 10²⁶ protons per cubic centimetre! So the phenomenon happens: a lot of nuclei fuse every second, a huge power is released, the star shines brightly and here we are … living thanks to this scarcely probable process and enjoying another astonishing sunny day.

As Sting already said … there’s “nothing like the sun”!

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¹ The total power of solar emission, a quantity called solar luminosity, is almost 4 x 10²⁶ watts, which means a 4 followed by 26 zeros of watts.

² In a gas at a given temperature, there will always be a certain probability of finding particles with every energy. But the higher the energy of the particles we look for, the lower the probability of finding them. These probabilities are determined by a law called Maxwell distribution.

References

Clayton, Donald D., Principles of stellar evolution and nucleosynthesis, 1968, New York, McGraw-Hill.

Gamow, G., Zur Quantentheorie des Atomkernes, 1928, Zeitschrift für Physik, Volume 51, Issue 3-4, pp. 204-212. English translation available at http://www.physics.utah.edu/~lebohec/P5110/Material/Gamow_Geiger_Nuttal_law_1928.pdf

Gabriel Ferrero is an Uruguayan astronomer and physicist. He works at the University of La Plata as professor, researcher and head of the Argentinian office of the Gemini Observatory.