## Info

Magnetic Field (polar)

0.001 T = 10G

" Mass density is given in kilograms per cubic meter, denoted kg m~3; the density of water is 1,000 kg m~3. The unit of pressure is bars, where 1.013 bar is the pressure of the Earth's atmosphere at sea level. The unit of luminosity is joule per second, power is often expressed in watts, where 1.0 watt = 1.0 Joule per second.

by astronomers, tte unit for this scale is written kelvin, without a capital K, or just denoted by a capital K. Water freezes at 273 K and boils at 373 K, and to convert to degrees Celsius, abbreviated by C, just subtract 273, or C = K—273. tte conversion to degrees Fahrenheit, denoted by F, is more complicated, with F = (9K/5) —459.4.

During the ensuing decades, radioactivity was discovered, leading to the realization that the Earth's rocks are older than ttomson's value for the age of the Sun's heat. Ms paradox was resolved when scientists discovered that nuclear fusion powers the Sun, providing the ultimate source of stellar energy.

Most of the matter on Earth is completely stable, but some atoms are unstable. Such radioactive atoms, like uranium, spontaneously change form when their nucleus hurls out energetic particles, radiates energy and relaxes to a less energetic state, forming a lighter, stable atom, like lead, in the process. Ms nuclear transformation can be used to determine the age of the rocks on the Earth's surface.

tte radioactive dating method is something like determining how long a log has been burning by measuring the amount of ash and waiting a while to determine how rapidly the ash is being produced. Except you do not need to know the total amount of radioactive ash. tte abundance ratio of stable decay atoms to their unstable parents, such as the relative amounts of lead and uranium, can be used with the known rate of radioactive decay to determine the time that has elapsed since the rocks were formed. Ms technique indicates that the oldest known rocks in the Solar System, from the Moon and meteorites, were formed 4.6 billion years ago when we think the Sun originated together with the planets and their moons.

Fossils of primitive creatures are found etched in rocks more than 3.5 billion years old, so the Sun was apparently warm enough to sustain life back then. Unusual powers must be at work to make the Sun shine so hotly for so long. Indeed, the only known process that can fuel the Sun's fire at the presently observed rates for billions of years involves nuclear fusion in the Sun's hot, dense core.

2.2 THE SUN'S CENTRAL PRESSURE COOKER

Most of the Earth is solid, and we can therefore walk on its surface. By contrast, all of the Sun is a gas, and it has no surface.

Under the extreme conditions within the Sun, the gaseous atoms lose their identity! tte atoms move rapidly here and there, colliding with each other at high speeds; the violent force of these collisions is enough to fragment the atoms into their constituent pieces, tte interior of the Sun therefore consists mainly of the nuclei of hydrogen atoms, called protons, and unattached electrons that have been torn off the atoms by innumerable collisions and set free to move throughout the Sun.

Negatively charged electrons neutralize the positively charged protons, so the mixture of electrons and protons, called plasma, has no net charge. But every particle in the Sun's plasma is charged, and therefore electrically conducting. And like any electrically charged object, the solar material generates magnetic fields when it moves.

tte entire Sun is nothing but a giant, hot ball of plasma. Plasma has been called the fourth state of matter to distinguish it from the gaseous, liquid, and solid ones. A candle flame is plasma, as are all the stars in the Universe.

With their electrons gone, the hydrogen nuclei, or protons, can be packed together much more tightly than normal atoms, ttis is because nuclei are about 100,000 times smaller than the atoms they normally occupy, tte bare nuclei can be squeezed together within the empty space of former atoms.

To understand the Sun's interior, imagine a hundred mattresses stacked into a pile, tte mattresses at the bottom must support those above, so they will be squeezed thin, ttose at the top have little weight to carry, and they retain their original thickness, tte nuclei at the center of the Sun are similarly squeezed into a smaller volume by the overlying material, so theybecome hotter and more densely concentrated.

Deep down inside, within the dense, central core, the Sun's temperature has risen to 15.6 million kelvin, and the gas density is greater than 10 times that of solid lead. Such extreme central conditions were recognized as long ago as 1870 when Jonathan Homer Lane (1819-1880), an American astrophysicist at the U.S. Patent Office, assumed that gas pressure supports the weight of the Sun. As the result of such crowding, the nuclei in the Sun's center collide more frequently with higher speeds than elsewhere in the Sun, and push more vigorously outward, ttis pushing is called gas pressure, and it is the force that keeps the Sun from collapsing.

At the center of the Sun, the gas pressure needed to resist the weight of the overlying gas is 233 billion times the pressure of our atmosphere at sea level, tte high-speed motions and collisions of particles with temperatures of 15.6 million degrees provide the enormous central pressure.

At greater distances from the center, there is less overlying material to support and the compression is less, so the plasma gets thinner and cooler (Fig. 2.1). Halfway from the center of the Sun to the surface, the density is the same as that of water, and about nine tenths of the distance from the center to the Sun's apparent edge, we find material as tenuous as the transparent air that we breathe on Earth.

At the visible solar disk, the rarefied gas is about one thousand times less dense than our air, the pressure is less than that beneath the foot of a spider, and the temperature has fallen to 5,780 kelvin. Any hot gas with the radius of the Sun and a disk temperature of 5,780 kelvin will emit the Sun's luminosity.

2.3 NUCLEAR FUSION, ANTI-MATTER AND HYDROGEN BURNING

tte extraordinary conditions within the center of the Sun provided one clue to the mysterious process that keeps the Sun hot and makes it shine. Other important evidence was accumulated at the Cavendish Laboratory at Cambridge University in England, where the New Zealand-born British physicist Ernest Rutherford (1871-1937) showed, in 1920, that the massive nuclei of all atoms are composed of hydrogen nuclei, which he named protons. In the previous year the English chemist Francis W. Aston (1877-1945) invented the mass spectrograph and used it to show that the mass of the helium nucleus is slightly less than the sum of the masses of the four hydrogen nuclei, or protons, which enter into it.

At the same time that Rutherford and Astron were discovering the inner secrets of the atoms, the British astronomer, Arthur Stanley Eddington (1882-1944), also at Cambridge University, was trying to understand the internal workings of the Sun and other stars. Eddington, an avid reader of mystery novels, once likened the process to analyzing the clues in a crime. He knew that certain elements can be transformed into other ones in the terrestrial laboratory, and reasoned that stars are the crucibles in which the elements are made. He further realized that such stellar alchemy would release energy, arguing that hydrogen is transformed into helium inside stars, with the resultant mass difference released as energy to power the Sun.

Eddington could therefore lay the foundation for solving the Sun's energy crisis, concluding in a paper entitled "^e Internal Constitution of the Stars" written in 1920 that:

What is possible in the Cavendish Laboratory may not be too difficult in the Sun____^e reservoir [of a star's energy] can scarcely be other than the subatomic energy ^ere is sufficient subatomic energy in the Sun to maintain its output of heat for 15 billion years.6

FIG. 2.1 Internal compression The Sun's luminosity, temperature, and composition all vary with depth in its interior, from the Sun's visible disk (left) to the center of the Sun (right). The nuclei are squeezed into a smaller volume by the pressure of the material above, becoming hotter and more densely concentrated at greater depths. At the Sun's center, the temperature has reached 15.6 million kelvin, and the pressure is 233 billion times that of the Earth's atmosphere at sea level. Nuclear fusion in the Sun's energy-generating core synthesizes helium from hydrogen, so this region contains more helium and less hydrogen than the primordial amounts detected in the light of the visible Sun.

FIG. 2.1 Internal compression The Sun's luminosity, temperature, and composition all vary with depth in its interior, from the Sun's visible disk (left) to the center of the Sun (right). The nuclei are squeezed into a smaller volume by the pressure of the material above, becoming hotter and more densely concentrated at greater depths. At the Sun's center, the temperature has reached 15.6 million kelvin, and the pressure is 233 billion times that of the Earth's atmosphere at sea level. Nuclear fusion in the Sun's energy-generating core synthesizes helium from hydrogen, so this region contains more helium and less hydrogen than the primordial amounts detected in the light of the visible Sun.

In the same article, he continued with the prescient statement that:

If indeed, the subatomic energy in the stars is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfillment our dream of controlling this latent power for the well-being of the human race - or for its suicide.7

Great ideas have a curious way of surfacing in different places at about the same time. In an essay entitled "Atomes et Lumière, or Atoms and Light", the French physicist Jean Baptiste Perrin (1870-1942) argued that "radioactive" transformation of the elements could maintain the Sun's luminous output at its present rate for several billion years, or perhaps several dozen billion years, and that the mass lost during the transformation of four hydrogen nuclei into one helium nucleus would supply energy.8

It was probably Eddington who convinced most astronomers that subatomic (that is, nuclear) energy must fuel the stars. During the ensuing decade it was realized that the lightest known element, hydrogen, is the most abundant element in the Sun, so hydrogen nuclei, or protons, must play the dominant role in nuclear reactions within our daytime star. Protons must somehow be fused together, forming helium nuclei, but the details were lacking. After all, Rutherford had only shown that atomic nuclei contain protons the same year as Eddington's historic article, and the neutron wasn't discovered until 1932.

Physicists were nevertheless convinced that protons could not react with each other inside the Sun. tte proton is positively charged and positive charges repel each other, tte force of repulsion between like charges becomes larger and larger as they are brought closer and closer. And even at the enormous central temperature of the Sun, the protons did not seem to have enough energy to overcome this electrical repulsion and merge together. In other words, the Sun's core did not seem hot enough to permit protons to fuse together.

But Eddington was certain that subatomic energy fueled the stars, and in the mid-1920s retorted defiantly that:

"tte helium that we handle must have been put together at some time and some place. We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotterplace.9

As it turned out, Eddington was right and the physicists were wrong.

tte paradox was resolved after the Russian physicist George Gamow (1904-1968) explained why the nuclei of radioactive substances are releasing energetic particles. He used the uncertain, probabilistic nature of the very small, adopting the quantum theory to show in 1928 how a subatomic particle could be anywhere, everywhere, and nowhere at all. According to quantum theory, a very small particle does not have a well-defined position, and instead acts like a spread-out thing, existing in a murky state of possibility with a set of probabilities ofbeing in a range of places.

As a result of this location uncertainty, a subatomic particle's sphere of influence is larger than was previously thought. It might be anywhere, although with decreasing probability at regions far from the most likely location. Ms explains the escape of fast-moving, energetic particles from the nuclei of radioactive atoms like uranium; these particles usually lack the energy to overcome the nuclear barrier, but some of them have a small probability of escaping to the outside world. In this surreal world of subatomic probability, one could relentlessly throw a ball against a wall, watching it bounce back countless times, until eventually the ball would tunnel under the wall, effectively passing through it. As Ahab said in Herman Melville's (1819-1891) Moby Dick,

How can the prisoner reach outside except by thrusting through the wall?10

A similar tunneling process, or barrier penetration, occurs the other way around at the center of stars like the Sun. It means that a proton has a very small but finite chance of occasionally moving close enough to another proton to overcome the barrier of repulsion and tunnel through it. Protons therefore sometimes get close enough to fuse together, even though their average energy is well below that required to overcome their electrical repulsion.

But this bizarre tunneling reaction doesn't occur all the time. For fusion to occur, the collision must still be almost exactly head-on, and between exceptionally fast protons. Nuclear reactions therefore proceed very slowly inside the Sun, and it is a good thing. If the temperature were high enough to permit frequent fusion, the Sun would blow up! After all, similar nuclear processes produce the explosive energy in hydrogen bombs.

Unlike a bomb, the temperature-sensitive reactions inside the Sun act like a thermostat, releasing energy in a steady, controlled fashion at exactly the rate needed to keep the Sun in equilibrium. If a star shrinks a little and gets hotter inside, more nuclear energy is generated, making the star expand and restoring it to the original temperature. If the Sun expanded slightly, and became cooler inside, subatomic energy would be released at a slower rate, making the Sun shrink again and restoring equilibrium.

So, we now know that the Sun shines by nuclear fusion, whereby hydrogen nuclei, or protons, fuse together into helium nuclei, also known as alpha particles, tte detailed sequence of nuclear reactions is known as the proton-proton chain (Fig. 2.2), since it begins by the fusion of two protons.

FIG. 2.2 The proton-proton chain The Sun gets its energy when hydrogen nuclei are fused together to form helium nuclei within the solar core. This hydrogen burning is described by a sequence of nuclear fusion reactions called the protonproton chain. It begins when two protons, here designated by the symbol !H, combine to form the nucleus of a deuterium atom, the deuteron that is denoted by D, together with the emission of a positron, e+, and an electron neutrino, v.. Another proton collides with the deuteron to make a light nuclear isotope of helium, 3He, and then a nucleus of normal heavy helium, 4He, is formed by the fusion of two light 3He nuclei, returning two protons to the gas. Overall, this chain successively fuses four protons together to make one helium nucleus. Even in the hot, dense core of the Sun, only rare, fast-moving particles are able to take advantage of the tunnel effect and fuse in this way.

At the suggestion of the German physicist Carl Friedrich von Weizsäcker (1912- ), the German-born American physicist Hans A. Bethe (1906-2005) investigated the fusion of two protons. And then Gamow, who had defected to the United States, suggested to one of his graduate students, Charles Critchfield (1910-1994), that he calculate the details of the proton-proton reaction, ttese results were sent to Bethe, who found them correct, and in 1938 the two published a joint paper entitled "tte Formation of Deuterons by Proton Combination."

Later that year, Gamow organized a conference in Washington, D.C. to bring astronomers and physicists together to discuss the problem of stellar energy generation. tte Swedish astronomer Bengt Strömgren (1908-1987) reported that since the Sun was predominantly hydrogen it would have a central temperature of about 15 million kelvin, rather than 40 million as estimated by Eddington under the assumption that the Sun had about the same chemical composition as the Earth, tte lower temperature meant that the calculations of Bethe and Critchfiled correctly predicted the Sun's luminosity, and Bethe, who attended the conference, was able to explain just how the Sun shines by the proton-proton chain (Focus 2.1), while also showing how more massive stars could use carbon as a catalyst in burning hydrogen into helium. In 1967 Bethe was awarded the Nobel Prize in Physics for his discoveries concerning energy production in stars.

Also in 1938, Weizsäcker (1912- ) independently investigated the proton-proton chain, and showed how other nuclear reactions could fuel stars that are more massive than the Sun using carbon as a catalyst in the synthesis of helium from hydrogen. Bethe soon went to Los Alamos, New Mexico, to use his knowledge of nuclear physics in support of the construction of the first atomic bomb, and at about the same time Weizsäcker helped the Germans investigate the feasibility of constructing nuclear weapons, tte Americans developed the bomb first, bringing an end to World War II (1939-1945).

In the burning of hydrogen, four protons are united, but two of them have to be changed into neutrons, ttis is because the helium nucleus consists of two protons and two neutrons. Something must be carrying away the charge of the proton, leaving behind a neutron with little change of mass; that mysterious agent is the anti-particle of the electron.

In 1931, Paul Adrien Maurice "P. A. M." Dirac (1902-1984), then at Cambridge University, predicted the existence of anti-matter. For Dirac, mathematical beauty was the most important aspect of any physical law describing nature. He noticed that the equations that describe the electron have two solutions. Only one of them was needed to characterize the electron; the other solution specified a sort of mirror image of the electron - an anti-particle, now called the positron for "positive-electron."

Dirac's trust in the beauty and symmetry ofhis equations led him to predict:

A new kind of particle, unknown to experimental physics, having the same mass and opposite charge to an electron.11

tte American physicist Carl D. Anderson (1905-1991) discovered the then-unknown positron in 1932, when studying high-energy particles from space called cosmic rays; they create positrons and many other subatomic particles when colliding with nuclei in

### FOCUS 2.1 Proton-Proton Chain

"tte Sun shines by a sequence of nuclear reactions, called the proton-proton chain, in which four protons are fused together to form a helium nucleus that contains two protons and two neutrons. Each nuclear transformation releases 25 MeV, or 0.000 000 000 004, or 4 X 10~12, Joules of energy, "ttis is due to the fact that the mass of the resulting helium nucleus is slightly less (a mere 0.007 or 0.7 percent) than the mass of the four protons that formed it, and the missing mass appears as energy.

"tte energy content of the lost mass is given by E = Amc2. Because the velocity of light, c, is a very large number, the annihilation of relatively small amounts of mass, Am, produces large quantities of energy, E. Moreover, that energy is multiplied by the huge number of reactions that occur inside the Sun every second. Roughly 100 trillion trillion trillion, orlO38, helium nuclei are created every second, resulting in a total mass loss of 5 million tons, or 5 billion kilograms, per second, which is enough to keep the Sun shining with its present luminous output of 385.4 million billion billion, or 3.854 x 1026, watts, where a power of one watt is equal to an energy loss of one Joule every second.

"tte details of this proton-proton chain were first described by Han A. Bethe (1906-2005) in a paper entitled "Energy Production in Stars," published in 1939. In the first step of the protonproton chain, two protons, each designated by either 'H orp, are united to form a deuteron, D, the nucleus of a heavy form of hydrogen known as deuterium. Since a deuteron consists of one proton and one neutron, one of the protons entering the reaction must be transformed into a neutron, emitting a positron, e+, to carry away the proton's charge, together with a low-energy electron neutrino, v, to balance the energy in the reaction. A positron is the anti-matter particle of the electron, "ttis initiating protonproton reaction is written:

Each proton inside the Sun is involved in a collision with other protons millions of times in every second, but only exceptionally hot ones are able to tunnel through their electrical repulsion and fuse together. Just one collision in every ten trillion trillion initiates the proton-proton chain.

"tte electron neutrinos escape from the Sun without reacting with matter, carrying energy away. And every positron is immediately annihilated when colliding with an electron, e~, producing energetic radiation at short gamma-ray wavelengths, 7. "ttis energy-producing interaction can be written as:

"tte next step follows with little delay. In less than a second the deuteron collides with another proton to form a nucleus of light helium, He3, and releases yet another gamma ray.

"ttis reaction occurs so easily that deuterium cannot be synthesized inside stars; it is quickly consumed to make heavier elements.

In the final part of the proton-proton chain, two such light helium nuclei meet and fuse together to form a nucleus of normal heavy helium, He4, returning two protons to the solar gas; this step takes about a million years on average.

"ttis normal helium nucleus contains two protons and two neutrons.

A total of six protons are required to produce the two He3 nuclei that go into this last reaction. Since two protons and a helium nucleus are produced, the net result of the proton-proton chain is:

4p^H4 + gamma-ray radiation + 2 neutrinos.

our outer atmosphere. At the time of his discovery, Anderson was unaware of Dirac's theoretical prediction of the positron. In 1933 Dirac was awarded the Nobel Prize in Physics for his prediction; Anderson received the honor in 1936 for the discovery of the positron, in the same year as the Austrian physicist Victor Hess (1883-1964) who shared the prize for his discovery of cosmic rays.

Once created, anti-matter does not stay around for very long. And it is a good thing, for we occupy a material world, and any anti-matter will self-destruct when it encounters ordinary matter, tte singer Madonna expressed it with a different connotation:

We are living in a material world

### And I am a material girl.12

When an electron and positron meet, they annihilate each other and disappear in a puff of energetic radiation. Ms is how some of the Sun's nuclear energy is converted into radiation.