How the sun shines

March 18, 2021

Above: A close-up view of one of the flares from AR 11944 emitted on January 7th, 2014. This flare may be how the Solar Energetic Particles, or SEPs, detected by Wind spacecraft were released from the Sun.

The Sun is a yellow dwarf star, a hot ball of glowing gases at the heart of our solar system. Its gravity holds everything from the biggest planets to tiny debris in its orbit.

Sunshine makes life possible on earth.

In this First Part, we shall review from an historical perspective the development of our understanding of how the sun (the nearest star) shines, beginning in the following section with the nineteenth-century controversy over the age of the sun. In later sections, we shall see how seemingly unrelated discoveries in fundamental physics led to a theory of nuclear energy generation in stars that resolved the controversy over the age of the sun and explained the origin of solar radiation.

The age of the sun

How old is the sun? How does the sun shine? These questions are two sides of the same coin, as we shall see.

The rate at which the sun is radiating energy is easily computed by using the measured rate at which energy reaches the earth’s surface and the distance between the earth and the sun. The total energy that the sun has radiated away over its lifetime is approximately the product of the current rate at which energy is being emitted, which is called the solar luminosity, times the age of the sun.

The older the sun is, the greater the total amount of radiated solar energy. The greater the radiated energy, or the larger the age of the sun, the more difficult it is to find an explanation of the source of solar energy.

To better appreciate how difficult it is to find an explanation, let us consider a specific illustration of the enormous rate at which the sun radiates energy. Suppose we put a cubic centimeter of ice outside on a summer day in such a way that all of the sunshine is absorbed by the ice. Even at the great distance between the earth and the sun, sunshine will melt the ice cube in about 40 minutes. Since this would happen anywhere in space at the earth’s distance from the sun, a huge spherical shell of ice centered on the sun and 300 million km (200 million miles) in diameter would be melted at the same time. Or, shrinking the same amount of ice down to the surface of the sun, we can calculate that an area ten thousand times the area of the earth’s surface and about half a kilometer (0.3 mile) thick would also be melted in 40 minutes by the energy pouring out of the sun.

X-rays stream off the sun in this image showing observations from by NASA's Nuclear Spectroscopic Telescope Array, or NuSTAR, overlaid on a picture taken by NASA's Solar Dynamics Observatory (SDO). Image credit: NASA/JPL-Caltech/GSFC

Conflicting estimates of the solar age

The energy source for solar radiation was believed by nineteenth-century physicists to be gravitation. In an influential lecture in 1854, Hermann von Helmholtz, a German professor of physiology who became a distinguished researcher and physics professor, proposed that the origin of the sun’s enormous radiated energy is the gravitational contraction of a large mass. Somewhat earlier, in the 1840s, J.R. Mayer (another German physician) and J.J. Waterson had also suggested that the origin of solar radiation is the conversion of gravitational energy into heat.not1

Biologists and geologists considered the effects of solar radiation, while physicists concentrated on the origin of the radiated energy. In 1859, Charles Darwin, in the first edition of On The Origin of the Species by Natural Selection, made a crude calculation of the age of the earth by estimating how long it would take erosion occurring at the current observed rate to wash away the Weald, a great valley that stretches between the North and South Downs across the south of England. He obtained a number for the “denudation of the Weald” in the range of 300 million years, apparently long enough for natural selection to have produced the astounding range of species that exist on earth.

As Herschel stressed, the sun’s heat is responsible for life and for most geological evolution on earth. Hence, Darwin’s estimate of a minimum age for geological activity on the earth implied a minimum estimate for the amount of energy that the sun has radiated.

Firmly opposed to Darwinian natural selection, William Thompson, later Lord Kelvin, was a professor at the University of Glasgow and one of the great physicists of the nineteenth century. In addition to his many contributions to applied science and to engineering, Thompson formulated the second law of thermodynamics and set up the absolute temperature scale, which was subsequently named the Kelvin scale in his honor. The second law of thermodynamics states that heat naturally flows from a hotter to a colder body, not the opposite. Thompson therefore realized that the sun and the earth must get colder unless there is an external energy source and that eventually the earth will become too cold to support life.

Kelvin, like Helmholtz, was convinced that the sun’s luminosity was produced by the conversion of gravitational energy into heat. In an early (1854) version of this idea, Kelvin suggested that the sun’s heat might be produced continually by the impact of meteors falling onto its surface. Kelvin was forced by astronomical evidence to modify his hypothesis and he then argued that the primary source of the energy available to the sun was the gravitational energy of the primordial meteors from which it was formed.

Thus, with great authority and eloquence Lord Kelvin declared in 1862:

That some form of the meteoric theory is certainly the true and complete explanation of solar heat can scarcely be doubted, when the following reasons are considered: (1) No other natural explanation, except by chemical action, can be conceived. (2) The chemical theory is quite insufficient, because the most energetic chemical action we know, taking place between substances amounting to the whole sun’s mass, would only generate about 3,000 years’ heat. (3) There is no difficulty in accounting for 20,000,000 years’ heat by the meteoric theory.

Kelvin continued by attacking Darwin’s estimate directly, asking rhetorically:

What then are we to think of such geological estimates as [Darwin’s] 300,000,000 years for the “denudation of the Weald”?

Believing Darwin was wrong in his estimate of the age of the earth, Kelvin also believed that Darwin was wrong about the time available for natural selection to operate.

Lord Kelvin estimated the lifetime of the sun, and by implication the earth, as follows. He calculated the gravitational energy of an object with a mass equal to the sun’s mass and a radius equal to the sun’s radius and divided the result by the rate at which the sun radiates away energy. This calculation yielded a lifetime of only 30 million years. The corresponding estimate for the lifetime sustainable by chemical energy was much smaller because chemical processes release very little energy.

Darwin was so shaken by the power of Kelvin’s analysis and by the authority of his theoretical expertise that in the last editions of On The Origin of the Species he eliminated all mention of specific time scales. He wrote in 1869 to Alfred Russel Wallace, the codiscoverer of natural selection, complaining about Lord Kelvin:

Thompson’s views on the recent age of the world have been for some time one of my sorest troubles.

Today we know that Lord Kelvin was wrong and the geologists and evolutionary biologists were right. Radioactive dating of meteorites shows that the sun is 4.6 billion years old.

The Earth is superimposed on this image to give readers a sense of the scale. The length of the eruption extends about 160,000 miles out from the Sun. With Earth about 7,900 miles in diameter, this relatively minor eruption is about 20 times the diameter of our planet.

The direction established

The next fundamental advance came once again from an unexpected direction. In 1905, Albert Einstein derived his famous relation between mass and energy, as a consequence of the special theory of relativity. Einstein’s equation showed that a tiny amount of mass could, in principle, be converted into a tremendous amount of energy. His relation generalized and extended the nineteenth century law of conservation of energy of von Helmholtz and Mayer to include the conversion of mass into energy.

What was the connection between Einstein’s equation and the energy source of the sun? The answer was not obvious. Astronomers did their part by defining the constraints that observations of stars imposed on possible explanations of stellar energy generation. In 1919, Henry Norris Russell, the leading theoretical astronomer in the United States, summarized in a concise form the astronomical hints on the nature of the stellar energy source. Russell stressed that the most important clue was the high temperature in the interiors of stars.

F.W. Aston discovered in 1920 the key experimental element in the puzzle. He made precise measurements of the masses of many different atoms, among them hydrogen and helium. Aston found that four hydrogen nuclei were heavier than a helium nucleus. This was not the principal goal of the experiments he performed, which were motivated in large part by looking for isotopes of neon.

The importance of Aston’s measurements was immediately recognized by Sir Arthur Eddington, the brilliant English astrophysicist. Eddington argued in his 1920 presidential address to the British Association for the Advancement of Science that Aston’s measurement of the mass difference between hydrogen and helium meant that the sun could shine by converting hydrogen atoms to helium. This burning of hydrogen into helium would (according to Einstein’s relation between mass and energy) release about 0.7% of the mass equivalent of the energy. In principle, this could allow the sun to shine for about a 100 billion years.

On July 19, 2012, million-degree plasma in the sun's atmosphere began to cool and fall to the surface, resulting in a dazzling magnetic display known as coronal rain.

In 1938, C.F. von Weizsäcker came close to solving the problem of how some stars shine. He discovered a nuclear cycle, now known as the carbon-nitrogen-oxygen (CNO) cycle, in which hydrogen nuclei could be burned using carbon as a catalyst. However, von Weizsäcker did not investigate the rate at which energy would be produced in a star by the CNO cycle nor did he study the crucial dependence upon stellar temperature.

By April 1938, it was almost as if the scientific stage had been intentionally set for the entry of Hans Bethe, the acknowledged master of nuclear physics. Professor Bethe had just completed a classic set of three papers in which he reviewed and analyzed all that was then known about nuclear physics. These works were known among his colleagues as “Bethe’s bible.” Gamow assembled a small conference of physicists and astrophysicists in Washington, D.C. to discuss the state of knowledge, and the unsolved problems, concerning the internal constitution of the stars.

In the course of the next six months or so, Bethe worked out the basic nuclear processes by which hydrogen is burned (fused) into helium in stellar interiors. Hydrogen is the most abundant constituent of the sun and similar stars, and indeed the most abundant element in the universe.

Bethe described the results of his calculations in a paper entitled “Energy Production in Stars,” which is awesome to read. He authoritatively analyzed the different possibilities for reactions that burn nuclei and selected as most important the two processes that we now believe are responsible for sunshine. One process, the so-called p-p chain, builds helium out of hydrogen and is the dominant energy source in stars like the sun and less massive stars.

We will continue this subject in next Wisdom Wednesday.
Till then keep shining bright.

How the sun shines

The age of the sun

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How the sun shines

The age of the sun

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