2. Energizing the Sun

Awesome power, enormous times

The Earth intercepts only a modest fraction of the energy being pumped out in all directions from the Sun. When we measure the total amount of sunlight that illuminates and warms our globe, and extrapolate back to the Sun, we find that it is emitting a power of 385.4 million, million, million, million, or 3.854 x 1026, watts. An enormous amount of energy is being expended. In just one second the energy output of the Sun equals the entire energy consumption of the United States for a million years.

The astonishing thing is the Sunís durability; the Sun has managed to last billions of years despite radiating such awesome amounts of energy. In looking back at Earthís history, we find that the Sun has been shining steadily and relentlessly for aeons, with a brilliance that could not be substantially less than it is now. The radioactive clocks in rock fossils indicate, for example, that the Sun was hot enough to sustain primitive creatures on Earth 3.5 billion years ago.

By the early 20th century, when your grandparents might have lived, no one had any clue as to why the Sun, or any other star, could shine so brightly for billions of years. That understanding had to await the discovery of the ingredients of the atom, observations that the Sun is mainly composed of hydrogen, and the realization that sub-atomic energy can be released within the extraordinary conditions inside stars.

A hot, dense core

Fig. .. 

Whole atoms are only found in the Sunís relatively cool, visible layers and they do not exist in most of the Sun. The solar atoms are stripped bare and lose their identity inside the Sun. The temperature is so high, and the particles are moving so fast, that innumerable collisions tear the atoms apart into their sub-atomic ingredients.

The most abundant atom in the Sun is hydrogen. Each hydrogen atom is made up of a nucleus that contains a positively charged proton, and a remote, negatively charged electron that orbits the nucleus. In the Sun, collisions rip the hydrogen atoms apart, and separate the electron from the nucleus. Both the electron and the proton are liberated from their atomic bonds, and are set free to move and wander throughout the solar interior unattached to each other.

At great depths inside the Sun, the pressure of overlying material is enormous, the protons are squeezed tightly together, and the material is very hot and extremely dense. To understand how this works, imagine a hundred mattresses stacked into a pile. The mattresses at the bottom must support those above, so they will be squeezed thin. Those at the top have little weight to carry, and they retain their original thickness. The gas at the center of the Sun is similarly squeezed into a smaller volume by the overlying material, so it becomes hotter and more densely concentrated.

Since we cannot see inside the Sun, or any other star, astronomers use mathematical models to determine the internal structure of stars. The crucial equations can be solved without any knowledge of properties of the star before arrival on the main sequence. They describe nuclear energy generation by hydrogen burning in the central core of the star, hydrostatic equilibrium that balances the outward force of gas pressure and the inward force of gravity, energy transport by radiative diffusion, and an opacity determined from atomic physics calculations.

These equations are integrated over 4.6 billion years, the age of the Sun, to obtain the present luminosity of the Sun, for a star of its mass and radius. This results in a Standard Solar Model that specifies the current mass density, temperature and pressure as a function of depth within the Sun (Fig. 3.1).

The model indicates just how hot and dense it is down at the core of the Sun (Fig. 3.1). At the Sunís center the temperature is 15.6 million degrees. The central density is 151,300 kilograms per cubic meter, or more than 13 times that of solid lead. Yet, the protons are so small that they can move about freely as a gas, even at this high density.

The visible solar disk is relatively cool, at 5780 degrees Kelvin, and extremely rarefied, about ten thousand times less dense than the air we breathe. The pressure of this tenuous gas is less than that beneath the foot of a spider. Just as the pressure on your body increases as you dive deeper and deeper in the sea, so does the pressure increase with greater depth into the Sun. The pressure at the center of the Sun is 233 billion times Earthís air pressure at sea level (Fig. 3.1); all that outward gas pressure is needed to support the mass of the Sun.

When the Sun arrived on the main sequence, at zero age, it was assumed to have a homogeneous chemical composition, with a hydrogen abundance of about 71 percent by mass and helium at about 27 percent by mass. Nuclear fusion reactions convert hydrogen into helium within the Sunís hot, dense core, providing the Sunís energy and explaining its luminosity. The amount of helium in the core of the Sun has therefore increased over the past 4.6 billion years, due to the ongoing synthesis of helium from hydrogen, and the amount of hydrogen in the core has decreased (Fig 3.1).

Nuclear fusion reactions in the Sun

The ultimate source of the Sunís energy is nuclear fusion in its core. The intense pressures and searing temperatures at the Sunís core are fusing together the nuclei of the most abundant element in the Universe, hydrogen, to form nuclei of the second most abundant element, helium. The mass lost in the nuclear fusion reactions supplies the energy that makes the Sun shine. The nuclear fusion begins when two of the fastest moving protons collide head on, and very occasionally tunnel through the electrical barrier that almost always keeps them apart. When two protons merge and come into each other, they initiate a chain of reactions that ends when four protons have joined together to make one helium nucleus consisting of two protons and two neutrons. This sequence of nuclear fusion reactions is called the proton-proton chain. Outside the solar core, where the overlying weight and compression are less, the gas is cooler and thinner and nuclear fusion cannot occur. In main-sequence stars more massive than the Sun, carbon acts as a catalyst in hydrogen burning by the CNO cycle; less massive main-sequence stars burn hydrogen by the proton-proton chain.

Mass Lost is Energy Gained

Energy can only be derived from energy, and the source of energy in nuclear fusion is mass loss. The foundation was provided by Albert Einsteinís special theory of relativity, which included the famous formula E = mc2 for the equivalence of mass, m, and energy, E. Because the velocity of light c = 299,792,458 meters per second is a very large number, only a tiny amount of mass is needed to produce a huge amount of energy. Even the smallest grain of sand holds an enormous quantity of energy locked up inside its atoms.

The next clue to explaining the Sunís awesome energy came from measurements in the laboratory on Earth. They showed that the helium nucleus is slightly less massive (by a mere 0.7 percent) than the sum of the mass of the four hydrogen nuclei, or four protons, that combine to make it. So, what you get out in making helium is less than what you put into it, like the usual outcome of a slot machine or other type of gambling. The part that disappears goes into energizing the Sun and other stars. The mass difference, ?m, is converted into energy, ?E, to power the Sun, all in accordance with Einsteinís equation ?E = ?m c2.

Hydrogen Burning

The Sun and most other stars are mainly composed of hydrogen, and that is the material that must energize them. If these stars were only made of heavy elements, instead of hydrogen, they could not shine. To understand how hydrogen is burned within the central furnace of stars, we need to know about the sub-atomic constituents of matter. The most familiar sub-atomic particles, the particles that make up atoms, are protons, neutrons and electrons. The nucleus of a hydrogen atom consists of a single proton, and the nucleus of any other atom contains protons and neutrons, collectively called nucleons. The nucleus of the helium atom, for example, has four nucleons - two neutrons and two protons.

Our understanding of nuclear reactions additionally required knowledge of the positron and the neutrino. The positron is the positive electron, or the anti-matter version of the electron, with the same mass and a reversed charge. The insubstantial neutrino has no charge and very little mass; it moves very fast at nearly the velocity of light. There are three types of neutrinos, and the kind of neutrino that is made inside the Sun is called an electron neutrino.

Fig. .. 

It wasnít until the late 1930s that Hans A. Bethe and Charles L. Critchfield demonstrated how a sequence of nuclear reactions makes the Sun shine. Bethe was awarded the Nobel Prize in Physics in 1967 for this and other discoveries concerning energy production in stars. The hydrogen fusion reactions that fuel the Sun are collectively called the proton-proton chain (Fig. 2.2). They are also known as hydrogen-burning reactions, for it is hydrogen nuclei, the protons, that are being consumed to make helium; but it is a chain of nuclear reactions and not combustion in the ordinary chemical sense.

How the energy gets out

All of the Sunís energy is produced by nuclear fusion reactions deep down inside a dense, high-temperature core, which extends from the Sunís center to about one quarter of its radius, or 1.74 x 108 meters out. It thus accounts for only 1.6 percent of the Sunís volume Ė but about half its mass since the gas is so compacted down there.

Fig. .. 

Energy moves from the core to the rest of the Sun through two spherical shells that surround the core like nested Russian dolls (Fig. 2.3). The inner shell is called the radiative zone, and the outer one is called the convective zone. Radiation and convection are the two ways that energy can travel from one place to another inside a star.

Although light is the fastest thing around, radiation does not move quickly through the radiative zone. Instead, it diffuses slowly outward in a haphazard zig-zag pattern, called a random walk, that resembles a drunk staggering through a crowd of people. An insulating shroud of charged particles in the radiative zone controls the flow, reducing the energy content of the radiation by repeatedly absorbing, re-radiating and deflecting it. Each time the energy is re-emitted, it comes on the average from a layer at a slightly lower temperature, so the energy of the radiation is degraded as it works its way out.

Because of this continuing ricocheting in the radiative zone, it takes about 170,000 years, on average, for radiation to work its way out from the Sunís core to the bottom of the convection zone.

The cool, opaque material at the bottom of the convective zone absorbs great quantities of radiation without re-emitting it. This causes the material to become hotter than it would otherwise be. The heated material expands and becomes less dense than the gas in the overlying layers. Due to its low density, the hot gas rises, just as a balloon does. On Earth you can see hot air rising when watching the smoke above a fire or hawks riding on upward currents of heated air.

The heated material carries energy through the convection zone, from bottom to top, in about 10 days. The hot material then cools by radiating sunlight into space, and sinks back down to become reheated and rise again. Such wheeling convective motions occur in a kettle of boiling water, with hot rising bubbles and cooler sinking material.

Fig. .. 

High-resolution images of the Sun taken in white light, or in all the visible colors of the Sun combined, show a granular pattern that marks the top of the convective zone (Fig. 2.4). This solar granulation exhibits a non-stationary, overturning motion, a visible manifestation of convection. The bright center of each granule, or convection cell, is the highest point of a rising column of hot gas. The dark edges of each grain are the cooled gas beginning its descent to be heated once again.

Fig. .. 

A larger cellular pattern, called the supergranulation, has typical sizes of 10 to 30 million meters, but it is not visible in white light. The supergranulation is instead observed as the difference of two monochromatic images at closely spaced wavelengths (Fig. 2.5). About 2,500 supergranules are seen on the visible solar disk, each persisting for one or two days. Like the ordinary granulation, the supergranulation is generally accepted as convection. Whereas the small granules form and disperse within minutes, supergranules last, on average, about a day before they are replaced by other supergranules. The material in these large-scale convection cells rises in the center at about 100 meters per second, moves away from the centers with horizontal velocities of about 400 meters per second, and sinks down again at about 200 meters per second.

The Sun's remote past and distant future

Nothing in the cosmos is fixed and unchanging, and nothing escapes the ravages of time. Everything moves and evolves, and that includes the seemingly constant and unchanging star of our solar system. The Sun and planets in our solar system formed 4.5 billions of years ago when a spinning cloud of dust and gas in space fell in on itself. The center got denser and denser, until it became so packed, so tight and so hot that protons came together and fused into helium, making the Sun glow. Ever since then, the Sun has slowly grown in luminous intensity with age, a steady, inexorable brightening that is a consequence of the increasing about of helium accumulating in the Sunís core.

Fig. .. 

The luminosity, effective temperature and radius of the Sun have all slowly increased with time (Fig. 3.9). The Sun is now 30 percent brighter than it was 4.5 billion years ago. The brightening is enough to make the visible solar disk 300 degrees Kelvin hotter and its radius 6 percent greater than when the Sun first shone. The luminosity has only increased by a miniscule 0.0000023 (2.3 x 10-6) percent during the past 350 years, and there is no way that this small change will ever be directly measured. Yet, it has profound implications over cosmic periods of time.

In the end, our prospects are not all that great anyway. The Earthís self-regulating thermostat will eventually go out of control, and the Sun will eventually consume the life it once nurtured. We can anticipate an additional 7 billion years of slow luminosity increase (Fig. 3.9), but terrestrial life will be wiped out well before then. In just 1 billion years the Sun will have brightened by another 10 percent. Calculations suggest that the Earthís oceans could then evaporate at a rapid rate, resulting in a hot, dry uninhabitable Earth. And if that doesnít do us in, any Earthly life is doomed to fry in about 3 billion years from now. The Sun will then be hot enough to boil the Earthís oceans away, leaving the planet a burned-out cinder, a dead and sterile place.

The Sun cannot shine forever, because it will eventually use up the hydrogen fuel in its core. Although it has converted only a trivial part of its original mass into energy, the Sun has processed a substantial 37 percent of its core hydrogen into helium during the past 4.5 billion years. There will be no hydrogen left at the very center of the Sun 4.8 billion years form now. Slow evolution will continue burning hydrogen near the center, but it is too cool and tenuous for nuclear fusion outside the hot, dense core. The Sun will have used up all its available core hydrogen in about 7 billion years, and will then balloon into a red giant star with a dramatic increase in size and a powerful rise in luminosity (Fig. 3.9).