How Does the Sun Shine?

For millennia peoples all over the world have taken sunshine very seriously, and well they should. The sun supplies the energy necessary to sustain all life on earth. Photosynthesis, which sustains plant life, requires sunlight, while animal life, in turn, is sustained by the consumption of plants. Thus, the food chain in its simplest form: No sun, no plants; no plants no animals. Given the importance of the sun, it is not surprising that it was often deified in past ages. Most early cultures saw the sun as the very epitome of the supernatural, and the Egyptians, among others, saw the source of the sun’s energy as God (Ra) himself. The earliest known naturalistic interpretation of the sun’s power is credited to the Greek philosopher Anaxagoras who around 500 B.C. proclaimed that the sun was a red-hot stone. This did not set well with the local religious authorities who had Anaxagoras promptly thrown in jail for blasphemy. Throughout the following centuries, well into the age of science, the energy source of the sun remained a complete mystery.

Energy from the Sun

It is easy to determine the total energy output (the luminosity) of the sun. First you measure the solar constant, the amount of energy per square meter reaching the Earth each second. A simple way to determine this is to measure how much the temperature of a known quantity of water in direct sunlight rises in a given amount of time. Of course, you have to take into account a number of variables such as the angle of the sun and the climatic conditions to arrive at a realistic number. Using modern precision measurement techniques the solar constant has been determined to be 1.37 kw/m². The luminosity (total solar output) is obtained by multiplying the solar constant (energy passing through 1 square meter) times the total number of square meters on the surface of a sphere with a radius of 1 A.U centered on the sun. This yields a total energy output of about 4 x 10²⁶ joules/sec (watts). That is a big number, but what does it mean? Consider that the total worldwide energy consumption in one year is around 4 x 10²² joules. Therefore, each second the sun emits as much energy as the world will consume in the next 10,000 years! From geological considerations this amount of energy has been produced without interruption for about 5 billion years.

Nineteenth Century Theories

No energy source known before the 20^th century could have produced energy at this rate for this length of time. Two explanations of the sun’s energy were popular in the 19^th century, the meteoric impact theory and the contraction theory. The meteoric theory postulated the continual bombardment of the sun by small bodies such as meteors and comets. Upon impact the kinetic energy of the speeding meteors would be converted into heat. The principle here is sound: any mass falling through a gravitational field acquires energy due to its increasing speed. Drop a wine glass to a concrete floor, and, upon impact, the energy acquired during the fall will be transferred to the glass’ constituent atoms, agitating them so vigorously that the wine glass will shatter. Now drop a bowling ball to the same floor. The ball does not shatter, but its atoms will still be agitated by the acquired energy, and this shows up as increased temperature – both ball and floor get hotter at the point of contact. Despite having a firm physical basis and a number of adherents, it soon became clear that this theory had a very obvious problem. Although heat would certainly be generated by such impacts, the number of meteors required to sustain the sun’s output would be enormous. And, if such vast amounts of meteoric material in interplanetary space really existed, then the Earth, too, would be similarly bombarded. According to one calculation made around 1900, to generate the observed output of the sun by meteoric impact alone, the required meteor swarm would each day rain 50 tons of material on every square mile of the Earth!

The second explanation, the contraction theory, became the most widely accepted theory of the sun’s energy in the latter part of the nineteenth century. It was particularly respected because it was proposed by two of the most eminent physicists of the day: Lord Kelvin and Hermann von Helmholtz, and it is often referred to as the Kelvin-Helmholtz contraction theory. Like the meteoric theory it involves mass falling through a gravitational field. Here, however, the falling mass does not arrive from an external source but is the material already in the sun, falling as the sun shrinks in diameter. That a mass falling through a gravitational field can generate heat even with no impact is illustrated in the figure below taken from an astronomy textbook published in 1897 (Elements of Descriptive Astronomy by Herbert A. Howe). As the weights fall under the influence of gravity, the paddles agitate the water molecules, generating heat and causing the water temperature to rise (have you ever stirred hard ice cream to make it melt?). Thus, if we can imagine that the sun is slowing getting smaller, every atom in the sun is falling through a gravitational field, acquiring energy and generating heat. But if the sun is getting smaller, why don’t we notice it? Well, according to Helmholtz’s calculations the rate of contraction would have to be only ten inches per day. Such a small contraction could not have been detected with 19^th century instruments, and the total shrinkage (about 7,000 miles) during the 10,000 years of recorded history would have been so gradual that it surely would not have been noticed. Finally, Kelvin and Helmholtz estimated the sun could have been radiating its present output via the contraction process for about 18 million years. Generally speaking, physicists were satisfied with the contraction theory. It was consistent with all observations and Robert S. Ball, professor of astronomy at Cambridge University, could write in 1910 that “It is to Helmholtz that we are indebted for the true solution of the long-vexed problem [the sun’s energy source]. He has demonstrated in the clearest manner where the source of the sun’s heat lies”(In the High Heavens, 1910). However, geologists and especially evolutionary biologists were not at all satisfied. The long pageant of biological evolution required a more or less constant illumination from the sun for billions, not millions of years. Opponents of Darwinian evolution were quick to seize on this discrepancy in timescales, hoping to discredit evolutionary theory once and for all. In fact this argument is still occasionally made today by people who apparently do not realize that physics has changed over last 100 years!

The Twentieth Century Solution

What was needed was a new source of energy. The first hints of a new energy source came with the discovery of radioactivity by the French physicist A.H. Becquerel in 1895. Radioactivity is the term given to the process by which atoms with large unstable nuclei such as radium or uranium divide into smaller units, releasing energy in the form of electromagnetic radiation in the process. This way of obtaining energy from an atomic nucleus is known today as fission. Many physicists in the early years of the twentieth century reasoned that since these atoms could release energy spontaneously, perhaps such atoms were in the sun, fueling its heat output. The problem with fission as a solar energy source is that it requires atoms with massive nuclei, and this is not consistent with either the observed abundance of such atoms (they are quite rare) or the observed density of the sun (the density is low, suggesting light materials). But there is another nuclear energy process that has been proven to hold the key to the sun’s output. Scientists studying the nucleus noticed that the atomic weight of the helium nucleus (two protons and two neutrons) was slightly less than the sum of the individual masses of protons and neutrons comprising it. The implication is that when protons and neutrons are added together to make helium, some mass is lost. In accordance with Einstein’s E=mc² equation, the “lost” mass must be converted into energy. This process is known as nuclear fusion, and is today seen as the major source of the sun’s energy. It is known that the sun is mostly hydrogen (one proton in the nucleus), thus plenty of “fuel” is available. However, in order for two or more protons to come together, they have to overcome the coulomb barrier, the electromagnetic repulsion between like charges. This requires the protons to be tremendously energetic, which in turn requires that they be in a very high temperature environment.

In 1925 the English astrophysicist Arthur Eddington showed that the core of the sun was an environment with the necessary temperature. He did this by reasoning that the sun is neither getting smaller or larger. For a fluid substance such a condition is known as hydrostatic equilibrium. The force trying to collapse the sun is gravity. Since the sun’s dimensions are not changing, at each and every point in the sun’s interior the inward directed pressure (force per unit area) caused by gravity must be counter balanced by an equal but opposite outward directed pressure. The pressure opposing gravity is the kinetic gas pressure (pressure provided by the rapid motion of the sun’s constituent atoms). There is a simple equation that relates the pressure, P, exerted by a gas to its density, D, and its temperature, T: P =DT. In other words, the pressure at any point inside a volume of gas (P) is equal to the density of that gas (D) times its temperature (T). Knowing the mass and volume of the sun and the temperature at its surface, Eddington was able to proceed downward, calculating the temperature required at any point in the sun’s interior to produce the outward pressure necessary to counter balance the inward directed gravitational pressure. He found that at its core, the sun’s temperature would have to be around 10 million K. When Eddington first published his results it was felt that this was not hot enough to ignite the fusion process. However, further understanding of the behavior of matter at the quantum level showed that such a temperature is sufficient. Further, modern refinements of Eddington’s calculations have yielded a core temperature of 15 million K. Today we recognize that thermonuclear fusion, the conversion of hydrogen (one proton) into helium (two protons + two neutrons) plus energy, at the core of the sun is the basic process that makes the sun shine.

The Proton-proton Chain

The thermonuclear fusion process in the core of medium size stars like the sun is known as the proton-proton chain. Basically, four hydrogen nuclei (protons) are fused in to one helium nucleus (two protons and two neutrons). However, this does not happen all at once, and the steps involved in this process are shown in the diagram below. Note particularly the first step. When two protons collide two elementary particles, the positron and the neutrino, are created. The positron is exactly like the electron, but with a positive charge. Thus, it carries away the positive charge from one of the protons, leaving it a neutron. The positron immediately collides with one of the many electrons in core, and the two particles experience complete annihilation, creating energy in the form of a gamma ray (symbol: γ). Because of the extreme particle density in the sun’s core, the gamma rays immediately interact with the surrounding particles. The energy associated with a gamma ray will be absorbed and re-emitted many times as it journeys through the sun. This energy can take as long as a million years to reach the sun’s surface. By contrast, the other elementary particle created when the protons collide, the neutrino (symbol: ν) is particularly useful for analyzing the reactions in the core. This is so because it hardly interacts with matter at all, and it flies through the sun at the speed of light, arriving at the earth eight minutes after its creation.