During the 1800s, geologists and biologists found convincing evidence that Earth must have existed in more or less its present form for at least hundreds of millions of years. This fact posed severe problems for astrophysicists, because at that time it seemed impossible to explain how the Sun could continue to shine for so long, radiating immense amounts of energy into space as it does. If the Sun were shining by burning coal or hydrogen gas, it would be ablaze for only 5000 years before consuming all of its fuel.

Everyday experience tells us that the Sun is the source of an enormous amount of energy. We have just seen that observations reveal hot gas, intense magnetic fields, and a variety of continuous and transient features on the Sun’s surface. But the energy does not come from the surface gas or the magnetic fields—they have no mechanisms to create it. The origin of the Sun’s electromagnetic radiation is deep within it. To understand why the Sun shines, we must understand where its energy originates and how that energy is transported to its surface.

In 1905, Albert Einstein provided an important clue to the source of the Sun’s energy with his theory of special relativity. One of the implications of this theory is that matter and energy are related by the simple equation:

E = mc²

In other words, a mass (m) can be converted into an amount of energy (E) equivalent to mc², where c is the speed of light. Because c² (that is, c × c) is huge, namely, 9 × 10¹⁰ km²/s² (5.6 × 10¹⁰ mi²/s²), a small amount of matter can be converted into an awesome amount of energy.

Inspired by Einstein’s work, physicists discovered that the Sun’s energy output comes from the conversion of matter into energy. In the 1920s, the British astrophysicist Arthur Eddington proposed that the temperature at the center of the Sun, its core, is much greater than had ever been imagined. Calculations eventually revealed that the temperature there is about 15.5 × 10⁶ K. Physicists also showed that at temperatures above about 10 × 10⁶ K, hydrogen fuses into the element helium. In each such reaction, a tiny amount of mass is converted into energy in the form of gamma rays. Enough fusion occurs in its core to account for all of the energy emitted by the Sun.

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The process of fusing nuclei at such extreme temperatures is called thermonuclear fusion (see Discovery 9-1: Thermonuclear Fusion). In particular, conversion of hydrogen into helium is called hydrogen fusion. The same process provides the devastating energy released by a hydrogen bomb. (We will encounter the thermonuclear fusion of helium and other elements in later chapters.)

Hydrogen fusion is also called hydrogen burning, even though nothing is burned in the conventional sense. The ordinary burning of wood, coal, or any flammable substance is a chemical process involving only the electrons orbiting the nuclei of the atoms. Thermonuclear fusion is a far more energetic process that involves violent collisions that change the atomic nuclei themselves. Discovery 9-1 shows you just how energetic.

You may have heard statements like “matter is always conserved” or “energy is always conserved.” We know that both of these concepts are incorrect, because mass can be converted into energy, and vice versa. What is true, however, is that the total amount of energy plus mass (multiplied by c²) is conserved. So, the destruction of mass and the creation of energy by the Sun do not violate any laws of nature.

Now let us add up the energy emitted from the entire Sun. As noted earlier in this chapter, the Sun’s mass, usually designated 1 M_⊙, is equal to 333,000 Earth masses. Its total energy output per second, called the solar luminosity and denoted 1 L_⊙, is 3.9 × 10²⁶ watts. To produce this luminosity, the Sun converts 600 million metric tons of hydrogen into helium within its core each second. This value is twice the mass of the Empire State Building in New York City. This enormous rate is possible because the Sun contains a vast supply of hydrogen—enough to continue the present rate of energy output for another 5 billion years.

A scientific theory describing the Sun’s interior, called the solar model, explains how the energy from nuclear fusion in the Sun’s core gets to its photosphere. The model begins with the inward force due to the Sun’s gravity. This force increases the pressure and temperature in the Sun’s core, thereby causing hydrogen fusion to occur there. Because the Sun is not shrinking today, however, there must be an outward force throughout its interior that counters the inward force of gravity. That outward force is created by the gamma-ray photons generated during fusion.

Consider an idealized journey of one gamma-ray photon created by fusion in the Sun’s core. The photon begins its journey outward, quickly slamming into a nearby ion. The photon then disappears, its energy being incorporated into the ion, which as a result moves upward at very high speed. Because the particles in the Sun are densely packed, the energized ion does not travel far before striking another particle above it. After the collision, the two particles involved rebound (think billiard balls here). As a result of the collision, a photon is emitted from the interacting particles. The emitted photon has less energy than the photon that was previously absorbed by the ion. The energy taken from the incoming photon in the collision goes into preventing the upper particle, into which the ion slammed, from descending deeper into the Sun. The lower-energy photon slams into another particle above it and the process repeats. For each photon created by fusion, this happens numerous times. Combining these collisions with bulk upward flow of gases (by convection, discussed shortly), the photon energy that did not go into preventing the Sun from collapsing finally gets to the photosphere and is radiated into space as part of sunlight. From fusion to sunlight typically takes about 170,000 years.

Over 10³⁸ fusion events occur every second in the Sun’s core, providing just the right amount of energy to prevent it from collapsing. The balance between the inward force of gravity and the outward force from the motion of the hot gas is called hydrostatic equilibrium (Figure 9-21).

The outward movement of energy by photons hitting particles, which then bounce off other particles and thereby reemit photons, is called radiative transport, because individual photons are responsible for carrying energy from collision to collision. Calculations show that radiative transport is the dominant means of outward energy flow in the radiative zone, extending from the core to about 70% of the way out to the photosphere.

Near the photosphere, energy is carried the remaining distance to the surface by the bulk motion of the hot gas, rather than by the flying, energetic photons. As we discussed in Section 7-1, this circulation of gas blobs is called convection. We thus say that the Sun has a convective zone. Hot gas travels up to the top of this zone by convection and from there it radiates photons into space. These photons are what we see as sunlight, and you can see that the photosphere, which is at the bottom of the solar atmosphere, is also at the top of the convective zone. Once the gases in the convective zone lose energy by emitting photons into space, they cool and settle back into the Sun. As noted earlier, this convective flow is also the origin of solar granules, and the departing energy is the visible light and other electromagnetic radiation that the Sun emits into space. Figure 9-22a is a sketch of our model of the internal structure of the Sun.

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Different gamma rays created in the Sun’s core lose different amounts of energy as they and their successors travel upward through the Sun. Therefore, the photons emitted from the photosphere have a wide range of energies and, hence, wavelengths. The most intense emission is in the visible part of the electromagnetic spectrum. This process of energy loss by photons traveling up from the Sun’s core is the origin of the blackbody nature of the photosphere’s spectrum.

Our model of the Sun’s interior can be expressed as a set of mathematical equations, called the equations of stellar structure. The model quantitatively describes the Sun’s internal characteristics, such as its pressure, temperature, and density at various depths. These equations also describe the conditions inside other stars as they evolve. Because the equations are so complex, astrophysicists today use computers to solve them. Figure 9-22b presents their results graphically. The four graphs show how the Sun’s luminosity, mass, temperature, and density vary from the Sun’s center to its photosphere. For example, the upper left graph gives the percentage of the Sun’s luminosity created within that radius. The luminosity increases to 100% at about one-quarter of the way from the Sun’s center to its photosphere. This trend tells us that all of the Sun’s energy is produced within a volume extending out to 0.25 R_⊙ where R_⊙ is the radius of the Sun.

The mass curve rises to nearly 100% at about 0.6 R_⊙ from the Sun’s center. Almost all of the Sun’s mass is therefore confined to a volume extending only 60% of the distance from the Sun’s center to its visible surface. This distribution of mass is consistent with the fact that the density of the gas in the photosphere is so low, 10⁴ times lower than the density of the air we breathe.

The Sun fuses hydrogen into helium in its core. Therefore, when the Sun first formed, it had less helium and more hydrogen in its core than it does today. Helium is a denser element than hydrogen and therefore the young Sun’s core was less dense than it is now. Recall that density is the measure of how much mass is packed into any volume. For example, a cubic meter of carbon (with each atom containing 6 protons and 6 neutrons) is less dense than a cubic meter of iron (with each atom containing 26 protons and 30 neutrons).

When the Sun was young, the larger number of hydrogen atoms (that is, the larger number of protons) in its core created more repulsion than the core experiences today, with its larger number of neutron-rich helium atoms. (Recall that neutrons are neutral and hence do not repel other particles.) The greater repulsion in the young core prevented it from heating up as much as the denser core of today. Therefore, the young Sun, with its cooler core, had less fusion occurring because the cooler a star’s core is, the lower the rate of fusion it experiences. Using the equations of stellar structure on the younger Sun, with its cooler core, reveals that the gamma rays created by fusion back then did not push the outer layers out as much as they do today; hence, the Sun was smaller. But the equations also reveal that the surface of the smaller, younger Sun was about the same temperature as it is today. Because it had less surface from which to radiate, the younger Sun emitted less energy than it does is today—it was dimmer.

Even though its surface temperature has remained roughly constant, the increase in surface area means that the Sun today is giving off more energy than it formerly emitted. In other words, its luminosity has increased. As more helium accumulated in the core, it became denser and was compressed more by the surrounding mass. This increased compression heated the core to higher temperatures, enabling more fusion to occur. The increased numbers of gamma rays thereby generated were able to push outward more and thereby enlarge the Sun to its present size. The Sun has become brighter, meaning that it is emitting more energy than when it was younger. Calculations indicate that the Sun has gotten about 30% more luminous over the past 4.6 billion years.

The fact that the Sun was cooler when the Earth first formed raises the question of whether the Sun always provided enough heat to allow water to be liquid on Earth’s surface. There is overwhelming geological evidence for liquid water back at least 4.2 billion years ago. However, if everything on Earth was then as it is today, the young Sun did not heat Earth sufficiently for its surface water to be liquid. This is called the faint young sun paradox. The paradox is resolved by noting, as we discussed in Section 6-2, that the greenhouse effect created by the Earth’s early CO₂-rich atmosphere kept the Earth sufficiently warm so that surface water was liquid back then.

As explained in Discovery 9-1, for every proton that changes into a neutron during thermonuclear fusion, a neutrino is released. Neutrinos have no electric charge, and they are extraordinarily difficult to detect because they rarely interact with ordinary matter. The Sun is largely transparent to neutrinos, allowing these particles to stream outward, unimpeded, from its core. Likewise, most of the neutrinos from the Sun that arrive at Earth pass right through it.

According to our model of fusion in the Sun, nearly 10³⁸ solar neutrinos per second are produced in the Sun’s core. This output is so huge that here on Earth roughly 100 billion solar neutrinos pass through every square centimeter of your body each second!

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Occasionally, however, solar neutrinos strike neutrons and convert them into protons. If astronomers could detect even a few of these converted protons, it might be possible to build a “neutrino telescope” that could be used to detect the thermonuclear inferno in the Sun’s core that is hidden from the view of telescopes that collect photons.

Inspired by such possibilities, the American chemist Raymond Davis designed and built a large neutrino detector. This device consisted of a huge tank that contained 100,000 gallons of perchloroethylene (C₂Cl₄, the fluid your local dry cleaner uses) located deep in the Homestake gold mine in Lead, South Dakota. All neutrino experiments are performed underground to help prevent them from being contaminated by other sources of energy, like high-energy protons from space. Because matter is virtually transparent to neutrinos, most of the solar neutrinos passed right through Davis’s tank. On rare occasions, however, a solar neutrino hit the nucleus of one of the chlorine atoms in the cleaning fluid and converted one of its neutrons into a proton, creating a radioactive atom of argon. The rate at which argon was produced was therefore correlated with the number of solar neutrinos arriving at Earth.

On average, solar neutrinos created one radioactive argon atom every 3 days in Davis’s tank. To the consternation of physicists and astronomers, this rate corresponds to only one-third of the neutrinos predicted to be created by the fusion in the Sun’s core. There were three possible explanations for this unexpected result: The experiment could be faulty; the Sun might not be fusing at the expected rate; or our understanding of the properties of neutrinos could be in error. This experiment, which began in the mid-1960s, was repeated with extreme care by other researchers around the world who got the same results, suggesting that the experiment was not at fault. Calculations of how much energy the Sun must generate to shine as it does confirmed the number of neutrinos created per second. The problem had to lie in our understanding of the neutrino.

Neutrinos, like the planet Neptune, were discovered because, according to theory, they had to exist. Back in the first few decades of the twentieth century, physicists observed neutrons in nuclei spontaneously transforming into protons and electrons. The transformation is a result of the weak nuclear force, briefly introduced in Section 3-16. When these scientists calculated the energy and momenta of the neutron and the particles into which it changed, the numbers didn’t match—conservation of mass/energy and momentum (see Appendix P: Energy and Momentum) appeared to be violated. If this were indeed the case, it would have required a fundamental reworking of many of the laws of nature. A simpler solution was proposed in 1930 by the physicist Wolfgang Pauli, who posited the existence of a hard-to-detect particle that carried away the “lost” energy and momentum (this particle was named the neutrino in 1931 by physicist Enrico Fermi). Ray Davis shared the Nobel Prize in 2002 for his work in observing solar neutrinos.

Among the properties neutrinos had to have are very small masses compared to any other types of particles that have mass and very little interaction with other matter, as we have just discussed. Because electrons or positrons (identical to electrons, except with opposite electric charge) always accompany the formation of the neutrinos created in the Sun, they are often called electron neutrinos.

Two other kinds of neutrinos were subsequently proposed. One, the muon neutrino, is emitted in reactions in which elementary particles, called muons (or antimuons), are released, while the other, the tau neutrino, accompanies the formation of other elementary particles, the tau and antitau particles. The Sun emits neither muon nor tau neutrinos, and the first generation of detectors could only detect electron neutrinos. The solution to the neutrino rate dilemma lay in the existence of muon and tau neutrinos.

Initially, the three “flavors” of neutrinos (electron, muon, and tau) were thought to be massless, and, if so, the equations revealed that they could not change from one flavor into another. But if neutrinos have even the slightest mass, then they can transform from one to another. The transformation of massive neutrinos would occur spontaneously, meaning that if an electron neutrino left the Sun’s core and sped toward Earth, there would be a finite probability (about 65%, actually) that by the time it got here, it would have become a tau or muon neutrino. So, if neutrinos have mass, we should observe only one-third of them (which we do), because the rest would have changed flavor before they got to us.

In 1998, the super Kamiokande neutrino detector in Japan observed the other two types of neutrinos coming from the direction of the Sun. The observations were repeated in 2002 at the Sudbury Neutrino Observatory (Figure 9-23a) in Ontario, Canada. At least a dozen other neutrino detectors have begun operations or are being built to further study solar neutrinos.

To understand how the present generation of neutrino detectors works, let us consider one of the several interactions that occur between neutrinos and other matter. The Sudbury Neutrino Observatory is filled with water that contains a rare type of hydrogen nucleus, called deuterium, which consists of a proton and a neutron. When a solar neutrino is absorbed by a deuterium nucleus, the nucleus breaks apart into two protons and an electron. As this electron rushes through the water, it emits a flash of light, called Cerenkov radiation (Figure 9-23b).

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As the Russian physicist Pavel A. Cerenkov (pronounced Che-REN-kov) first observed, the flash occurs whenever a particle moves through a medium, such as water, faster than light can. Such motion does not violate the tenet that the speed of light in a vacuum (3 × 10⁵ km/s or 186,000 mi/s) is the ultimate speed limit in the universe. Light is slowed considerably as it passes through water, and high-energy particles can exceed this reduced speed of light in a medium without violating the laws of nature.

Thus, scientists detect neutrinos by observing Cerenkov radiation flashes with light-sensitive devices, called photomultipliers, mounted in the water (see Figure 9-23a). The three flavors of neutrinos have different interactions with water, all of which have been detected. This evidence that neutrinos can change requires that they have mass, and it explains the earlier low rate of solar neutrino observations. The fact that neutrinos have mass was confirmed in 1998, although the amount of mass each has is still under investigation.