Hyperspace (37 page)

To understand black holes and how difficult they are to find, we must first understand what makes the stars shine, how they grow, and how they eventually die. A star is born when a massive cloud of hydrogen gas many times the size of our solar system is slowly compressed by the force of gravity. The gravitational force compressing the gas gradually heats up the gas, as gravitational energy is converted into the kinetic energy of the hydrogen atoms. Normally, the repulsive charge of the protons within the hydrogen gas is sufficient to keep them apart. But at a certain point, when the temperature rises to 10 to 100 million°K, the kinetic
energy of the protons (which are hydrogen nuclei) overcomes their electrostatic repulsion, and they slam into one another. The nuclear force then takes over from the electromagnetic force, and the two hydrogen nuclei “fuse” into helium, releasing vast quantities of energy.

In other words, a star is a nuclear furnace, burning hydrogen fuel and creating nuclear “ash” in the form of waste helium. A star is also a delicate balancing act between the force of gravity, which tends to crush the star into oblivion, and the nuclear force, which tends to blow the star apart with the force of trillions of hydrogen bombs. A star then matures and ages as it exhausts its nuclear fuel.

To see how energy is extracted from the fusion process and to understand the stages in the life of a star leading to a black hole, we must analyze
Figure 10.1
, which shows one of the most important curves in modern science, sometimes called the
binding energy curve
. On the horizontal scale is the atomic weight of the various elements, from hydrogen to uranium. On the vertical scale, crudely speaking, is the approximate average “weight” of each proton in the nucleus. Notice that hydrogen and uranium have protons that weigh, on average, more than the protons of other elements in the center of the diagram.

Our sun is an ordinary yellow star, consisting mainly of hydrogen. Like the original Big Bang, it fuses hydrogen and forms helium. However, because the protons in hydrogen weigh more than the protons in helium, there is an excess of mass, which is converted into energy via Einstein’s
E = mc
²
formula. This energy is what binds the nuclei together. This is also the energy released when hydrogen is fused into helium. This is why the sun shines.

However, as the hydrogen is slowly used up over several billion years, a yellow star eventually builds up too much waste helium, and its nuclear furnace shuts off. When that happens, gravity eventually takes over and crushes the star. As temperatures soar, the star soon becomes hot enough to burn waste helium and convert it into the other elements, like lithium and carbon. Notice that energy can still be released as we descend down the curve to the higher elements. In other words, it is still possible to burn waste helium (in the same way that ordinary ash can still be burned under certain conditions). Although the star has decreased enormously in size, its temperature is quite high, and its atmosphere expands greatly in size. In fact, when our own sun exhausts its hydrogen supply and starts to burn helium, its atmosphere may extend out to the orbit of Mars. This is what is called a
red giant
. This means, of course, that the earth will be vaporized in the process. Thus the curve also predicts the ultimate fate of the earth. Since our sun is a middle-aged
star about 5 billion years old, it still has another 5 billion years before it consumes the earth. (Ironically, the earth was originally born out of the same swirling gas cloud that created our sun. Physics now predicts that the earth, which was created with the sun, will return to the sun.)

Figure 10.1. The average “weight” of each proton of lighter elements, such as hydrogen and helium, is relatively large. Thus if we fuse hydrogen to form helium inside a star, we have excess mass, which is converted to energy via Einstein’s equation
E = mc
²
.
This is the energy that lights up the stars. But as stars fuse heavier and heavier elements, eventually we reach iron, and we cannot extract any more energy. The star then collapses, and the tremendous heat of collapse creates a supernova. This colossal explosion rips the star apart and seeds the interstellar space, in which new stars are formed. The process then starts all over again, like a pinball machine
.

Finally, when the helium is used up, the nuclear furnace again shuts down, and gravity takes over to crush the star. The red giant shrinks to become a
white dwarf
, a miniature star with the mass of an entire star squeezed down to about the size of the planet earth.
¹
White dwarfs are not very luminous because, after descending to the bottom of the curve, there is only a little excess energy one can squeeze from it through
E = mc
²
. The white dwarf burns what little there is left at the bottom of the curve.

Our sun will eventually turn into a white dwarf and, over billions of years, slowly die as it exhausts its nuclear fuel. It will eventually become a dark, burned-out dwarf star. However, it is believed that if a star is sufficiently massive (several times the mass of our sun), then most of the elements in the white dwarf will continue to be fused into increasingly heavier elements, eventually reaching iron. Once we reach iron, we are near the very bottom of the curve. We can no longer extract any more energy from the excess mass, so the nuclear furnace shuts off. Gravity once again takes over, crushing the star until temperatures rise explosively a thousandfold, reaching trillions of degrees. At this point, the iron core collapses and the outer layer of the white dwarf blows off, releasing the largest burst of energy known in the galaxy, an exploding star called a
supernova
. Just one supernova can temporarily outshine an entire galaxy of 100 billion stars.

In the aftermath of the supernova, we find a totally dead star, a
neutron star
about the size of Manhattan. The densities in a neutron star are so great that, crudely speaking, all the neutrons are “touching” one another. Although neutron stars are almost invisible, we can still detect them with our instruments. Because they emit some radiation while they are rotating, they act like a cosmic lighthouse in outer space. We see them as a blinking star, or
pulsar
. (Although this scenario sounds like science fiction, well over 400 pulsars have been observed since their initial discovery in 1967.)

Computer calculations have shown that most of the heavier elements beyond iron can be synthesized in the heat and pressure of a supernova. When the star explodes, it releases vast amounts of stellar debris, consisting of the higher elements, into the vacuum of space. This debris eventually mixes with other gases, until enough hydrogen gas is accumulated
to begin the gravitational contraction process once again. Second-generation stars that are born out of this stellar gas and dust contain an abundance of heavy elements. Some of these stars (like our sun) will have planets surrounding them that also contain these heavy elements.

This solves a long-standing mystery in cosmology. Our bodies are made of heavy elements beyond iron, but our sun is not hot enough to forge them. If the earth and the atoms of our bodies were originally from the same gas cloud, then where did the heavy elements of our bodies come from? The conclusion is inescapable: The heavy elements in our bodies were synthesized in a supernova that blew up
before
our sun was created. In other words, a nameless supernova exploded billions of years ago, seeding the original gas cloud that created our solar system.

The evolution of a star can be roughly pictured as a pinball machine, as in
Figure 10.1
, with the shape of the binding energy curve. The ball starts at the top and bounces from hydrogen, to helium, from the lighter elements to the heavier elements. Each time it bounces along the curve, it becomes a different type of star. Finally, the ball bounces to the bottom of the curve, where it lands on iron, and is ejected explosively in a supernova. Then as this stellar material is collected again into a new hydrogen-rich star, the process starts all over again on the pinball.

Notice, however, that there are two ways for the pinball to bounce down the curve. It can also start at the other side of the curve, at uranium, and go down the curve in a single bounce by fissioning the uranium nucleus into fragments. Since the average weight of the protons in fission products, like cesium and krypton, is smaller than the average weight of the protons in uranium, the excess mass has been converted into energy via
E
=
mc
²
. This is the source of energy behind the atomic bomb.

Thus the curve of binding energy not only explains the birth and death of stars and the creation of the elements, but also makes possible the existence of hydrogen and atomic bombs! (Scientists are often asked whether it would be possible to develop nuclear bombs other than atomic and hydrogen bombs. From the curve of binding energy, we can see that the answer is no. Notice that the curve excludes the possibility of bombs made of oxygen or iron. These elements are near the bottom of the curve, so there is not enough excess mass to create a bomb. The various bombs mentioned in the press, such as neutron bombs, are only variations on uranium and hydrogen bombs.)

When one first hears the life history of stars, one may be a bit skeptical. After all, no one has ever lived 10 billion years to witness their evolution. However, since there are uncountable stars in the heavens, it
is a simple matter to see stars at practically every stage in their evolution. (For example, the 1987 supernova, which was visible to the naked eye in the southern hemisphere, yielded a treasure trove of astronomical data that matched the theoretical predictions of a collapsing dwarf with an iron core. Also, the spectacular supernova observed by ancient Chinese astronomers on July 4, 1054, left behind a remnant, which has now been identified as a neutron star.)

In addition, our computer programs have become so accurate that we can essentially predict the sequence of stellar evolution numerically. I once had a roommate in graduate school who was an astronomy major. He would invariably disappear in the early morning and return late at night. Just before he would leave, he would say that he was putting a star in the oven to watch it grow. At first, I thought he said this in jest. However, when I pressed him on this point, he said with all seriousness that he was putting a star into the computer and watching it evolve during the day. Since the thermodynamic equations and the fusion equations were well known, it was just a matter of telling the computer to start with a certain mass of hydrogen gas and then letting it numerically solve for the evolution of this gas. In this way, we can check that our theory of stellar evolution can reproduce the known stages of star life that we see in the heavens with our telescopes.

If a star was ten to 50 times the size of our sun, then gravity will continue to squeeze it even after it becomes a neutron star. Without the force of fusion to repel the gravitational pull, there is nothing to oppose the final collapse of the star. At this point, it becomes the famous black hole.

In some sense, black holes must exist. A star, we recall, is the by-product of two cosmic forces: gravity, which tries to crush the star, and fusion, which tries to blow the star apart like in a hydrogen bomb. All the various phases in the life history of a star are a consequence of this delicate balancing act between gravity and fusion. Sooner or later, when all the nuclear fuel in a massive star is finally exhausted and the star is a mass of pure neutrons, there is nothing known that can then resist the powerful force of gravity. Eventually, the gravitational force will take over and crush the neutron star into nothingness. The star has come full circle: It was born when gravity first began to compress hydrogen gas in the heavens into a star, and it will die when the nuclear fuel is exhausted and gravity collapses it.

The density of a black hole is so large that light, like a rocket launched from the earth, will be forced to orbit around it. Since no light can escape from the enormous gravitational field, the collapsed star becomes black in color. In fact, that is the usual definition of a black hole, a collapsed star from which no light can escape.

To understand this, we note that all heavenly bodies have what is called an
escape velocity
. This is the velocity necessary to escape permanently the gravitational pull of that body. For example, a space probe must reach an escape velocity of 25,000 miles per hour in order to leave the gravitational pull of the earth and go into deep space. Our space probes like the
Voyager
that have ventured into deep space and have completely left the solar system (carrying good-will messages to any aliens who might pick them up) have reached the escape velocity of our sun. (The fact that we breathe oxygen is because the oxygen atoms do not have enough velocity to escape the earth’s gravitational field. The fact that Jupiter and the other gas giants are made mainly of hydrogen is because their escape velocity is large enough to capture the primordial hydrogen of the early solar system. Thus escape velocity helps to explain the planetary evolution of the planets of our solar system over the past 5 billion years.)