No Escape: The Truth About Black Holes

Teacher Page: Science Background



Index:

Science background

1. What is a black hole?
2. How is a stellar black hole created?
3. How can light be trapped by the gravitational pull of a black hole if light has no mass?
4. How does a black hole appear?
5. Is a black hole a giant cosmic vacuum cleaner?
6. Do all stars become black holes?
7. How many kinds of black holes are there?
8. When was the existence of black holes first theorized?
9. What evidence do we have for the existence of black holes?

A few words from the scientist
Selected references


Science background:

The following information is provided to give the teacher some additional knowledge about the effect of gravity and black holes. This material can be used to inspire research topics for students or to encourage class discussion.

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1. What is a black hole?

A black hole is defined by the escape velocity that would have to be attained to escape from the gravitational pull exerted upon an object. For example, the escape velocity of earth is equal to 11 km/s. Anything that wants to escape earth's gravitational pull must go at least 11 km/s, no matter what the thing is — a rocket ship or a baseball. The escape velocity of an object depends on how compact it is; that is, the ratio of its mass to radius. A black hole is an object so compact that, within a certain distance of it, even the speed of light is not fast enough to escape.

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2. How is a stellar black hole created?

A common type of black hole is the type produced by some dying stars. A star with a mass greater than 20 times the mass of our Sun may produce a black hole at the end of its life. In the normal life of a star there is a constant tug of war between gravity pulling in and pressure pushing out. Nuclear reactions in the core of the star produce enough energy to push outward. For most of a star's life, gravity and pressure balance each other exactly, and so the star is stable. However, when a star runs out of nuclear fuel, gravity gets the upper hand and the material in the core is compressed even further. The more massive the core of the star, the greater the force of gravity that compresses the material, collapsing it under its own weight. For small stars, when the nuclear fuel is exhausted and there are no more nuclear reactions to fight gravity, the repulsive forces among electrons within the star eventually create enough pressure to halt further gravitational collapse. The star then cools and dies peacefully. This type of star is called the "white dwarf." When a very massive star exhausts its nuclear fuel it explodes as a supernova. The outer parts of the star are expelled violently into space, while the core completely collapses under its own weight.

To create a massive core a progenitor (ancestral) star would need to be at least 20 times more massive than our Sun. If the core is very massive (approximately 2.5 times more massive than the Sun), no known repulsive force inside a star can push back hard enough to prevent gravity from completely collapsing the core into a black hole. Then the core compacts into a mathematical point with virtually zero volume, where it is said to have infinite density. This is referred to as a singularity. When this happens, escape would require a velocity greater than the speed of light. No object can reach the speed of light. The distance from the black hole at which the escape velocity is just equal to the speed of light is called the event horizon. Anything, including light, that passes across the event horizon toward the black hole is forever trapped.

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3. Since light has no mass how can it be trapped by the gravitational pull of a black hole?

Newton thought that only objects with mass could produce a gravitational force on each other. Applying Newton's theory of gravity, one would conclude that since light has no mass, the force of gravity couldn't affect it. Einstein discovered that the situation is a bit more complicated than that. First he discovered that gravity is produced by a curved space-time. Then Einstein theorized that the mass and radius of an object (its compactness) actually curves space-time. Mass is linked to space in a way that physicists today still do not completely understand. However, we know that the stronger the gravitational field of an object, the more the space around the object is curved. In other words, straight lines are no longer straight if exposed to a strong gravitational field; instead, they are curved. Since light ordinarily travels on a straight-line path, light follows a curved path if it passes through a strong gravitational field. This is what is meant by "curved space," and this is why light becomes trapped in a black hole. In the 1920's Sir Arthur Eddington proved Einstein's theory when he observed starlight curve when it traveled close to the Sun. This was the first successful prediction of Einstein's General Theory of Relativity.

One way to picture this effect of gravity is to imagine a piece of rubber sheeting stretched out. Imagine that you put a heavy ball in the center of the sheet. The weight of the ball will bend the surface of the sheet close to it. This is a two-dimensional picture of what gravity does to space in three dimensions. Now take a little marble and send it rolling from one side of the rubber sheet to the other. Instead of the marble taking a straight path to the other side of the sheet, it will follow the contour of the sheet that is curved by the weight of the ball in the center. This is similar to how the gravitation field created by an object (the ball) affects light (the marble).

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4. What does a black hole look like?

A black hole itself is invisible because no light can escape from it. In fact, when black holes were first hypothesized they were called "invisible stars." If black holes are invisible, how do we know they exist? This is exactly why it is so difficult to find a black hole in space! However, a black hole can be found indirectly by observing its effect on the stars and gas close to it. For example, consider a double-star system in which the stars are very close. If one of the stars explodes as a supernova and creates a black hole, gas and dust from the companion star might be pulled toward the black hole if the companion wanders too close. In that case, the gas and dust are pulled toward the black hole and begin to orbit around the event horizon and then orbit the black hole. The gas becomes heavily compressed and the friction that develops among the atoms converts the kinetic energy of the gas and dust into heat, and x-rays are emitted. Using the radiation coming from the orbiting material, scientists can measure its heat and speed. From the motion and heat of the circulating matter, we can infer the presence of a black hole. The hot matter swirling near the event horizon of a black hole is called an accretion disk.

John Wheeler, a prominent theorist, compared observing these double-star systems to watching women in white dresses dancing with men in black tuxedos within a dimly lit ballroom. You see only the women, but you could predict the existence of their invisible partners because of the women's' spinning and whirling motions around a central axis. Searching for stars whose motions are influenced by invisible partners is one way in which astronomers search for possible black holes.

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5. Is a black hole a giant cosmic vacuum cleaner?

The answer to this question is "not really." To understand this, first consider why the force of gravity is so strong close to a black hole. The gravity of a black hole is not special. It does not attract matter at large distances differently than any other object does. At a long distance from the black hole the force of gravity falls off as the inverse square of the distance, just as it does for normal objects.

Mathematically, the gravity of any spherical object behaves as if all the mass were concentrated at one central point. Since most ordinary objects have surfaces, you will feel the strongest gravity of an object when you are on its surface. This is as close to its total mass as you can get. If you penetrated a spherical object with a constant mass density, getting closer to its core, you would feel the force of gravity get weaker, not stronger. The force of gravity you feel depends on the mass that is interior to you, because the gravity from the mass behind you is exactly canceled by the mass in the opposite direction. Therefore, you will feel the strongest force of gravity from an object, for example a planet, when you are standing on the planet's surface, because it is on the surface that you are closest to its total mass. Penetrating the surface of the planet does not expose you to more of the planet's total mass, but actually exposes you to less of its mass. Now remember the size of a black hole is infinitesimally small. Gravity near a black hole is very strong because objects can get extremely close to it and still be exposed to its total mass.

There is nothing special about the mass of a black hole. A black hole is different from our ordinary experience not because of its mass, but because its radius has vanished. Far away from the black hole, you would feel the same strength of gravity as if the black hole were a normal star. But the force of gravity close to a black hole is enormously strong because you can get so close to its total mass!

For example, the surface of the Earth where we are standing is 6378 km from the center of the Earth. The surface is as close as you can get and still be exposed to the total mass of the Earth. Thus, it is where you will feel the strongest gravity. If suddenly the Earth became a black hole (impossible!) and you remained at 6378 km from the new Earth-black hole, you would feel the same pull of gravity as you do today. For example, if you normally weigh 120 lbs, you would still weigh 120 lbs. The mass of the Earth hasn't changed, your distance from it hasn't changed, and therefore you would experience the same gravitational force as you feel on the surface of normal Earth. But with the Earth-black hole, it would be possible for you to get closer to the total mass of the Earth. Let's say that you weigh 120 lbs standing on the surface of normal Earth. As you venture closer toward the Earth-black hole you would feel a stronger and stronger force. If you went to within 3189 km (half the radius of normal Earth) of the Earth-black hole you would weigh 480 lbs! For the same exercise with the Earth as we normally experience it, if you dug your way to 3189 km of the center, you would weigh less than at the surface, a mere 60 lbs, because there would be less Earth mass interior relative to you!

As another example, consider the Sun. If the Sun suddenly became a black hole (equally impossible!), the Earth would continue on its normal orbit and would feel the same force of gravity from the Sun as usual!

Therefore, to be "sucked up" by a black hole, you have to get very close; otherwise, you experience the same force of gravity as if the black hole were the normal star it used to be. As you get close to a black hole, relativistic effects become important; for example, the escape velocity approximates and eventually reaches the speed of light and some very strange things like the "event horizon effect" begin to happen. For details, consult any popular book on black holes.

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6. Do all stars become black holes?

Only stars with very large masses can become black holes. Our Sun, for example, is not massive enough to become a black hole. Four billion years from now when the Sun runs out of the available nuclear fuel in its core, our Sun will die a quiet death. Stars of this type end their history as white dwarf stars. More massive stars, such as those with masses of over 20 times our Sun's mass, may eventually create a black hole. When a massive star runs out of nuclear fuel it can no longer sustain its own weight and begins to collapse. When this occurs the star heats up and some fraction of its outer layer, which often still contains some fresh nuclear fuel, activates the nuclear reaction again and explodes in what is called a supernova. The remaining innermost fraction of the star, the core, continues to collapse. Depending on how massive the core is, it may become either a neutron star and stop the collapse or it may continue to collapse into a black hole. The dividing mass of the core, which determines its fate, is about 2.5 solar masses. It is thought that to produce a core of 2.5 solar masses the ancestral star should begin with over 20 solar masses. A black hole formed from a star is called a stellar black hole.

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7. How many types of black holes are there?

According to theory, there might be three types of black holes: stellar, supermassive, and miniature black holes — depending on their size. These black holes have also formed in different ways. Stellar black holes are described in Question 6. Supermassive black holes likely exist in the centers of most galaxies, including our own galaxy, the Milky Way. They can have a mass equivalent to billions of suns. In the outer parts of galaxies (where our solar system is located within the Milky Way) there are vast distances between stars. However, in the central region of galaxies, stars are packed very closely together. Because everything in the central region is tightly packed to start with, a black hole in the center of a galaxy can become more and more massive as stars orbiting the event horizon can ultimately be captured by gravitational attraction and add their mass to the black hole. By measuring the velocity of stars orbiting close to the center of a galaxy, we can infer the presence of a supermassive black hole and calculate its mass. Perpendicular to the accretion disk of a supermassive black hole, there are sometimes two jets of hot gas. These jets can be millions of light years in length. They are probably caused by the interaction of gas particles with strong, rotating magnetic fields surrounding the black hole. Observations with the Hubble Space Telescope have provided the best evidence to date that supermassive black holes exist.

The exact mechanisms that result in what are known as miniature black holes have not been precisely identified, but a number of hypotheses have been proposed. The basic idea is that miniature black holes might have been formed shortly after the "Big Bang," which is thought to have started the Universe about 15 billion years ago. Very early in the life of the Universe the rapid expansion of some matter might have compressed slower-moving matter enough to contract into black holes. Some scientists hypothesize that black holes can theoretically "evaporate" and explode. The time required for the "evaporation" would depend upon the mass of the black hole. Very massive black holes would need a time that is longer than the current accepted age of the universe. Only miniature black holes are thought to be capable of evaporation within the existing time of our universe. For a black hole formed at the time of the "Big Bang" to evaporate today its mass must be about 1015g (i.e., about 2 trillion pounds), a little more than twice the mass of the current Homo sapien population on planet Earth. During the final phase of the "evaporation," such a black hole would explode with a force of several trillion times that of our most powerful nuclear weapon. So far, however, there is no observational evidence for miniature black holes.

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8. When were black holes first theorized?

Using Newton's Laws in the late 1790s, John Michell of England and Pierre LaPlace of France independently suggested the existence of an "invisible star." Michell and LaPlace calculated the mass and size — which is now called the "event horizon" — that an object needs in order to have an escape velocity greater than the speed of light. In 1967 John Wheeler, an American theoretical physicist, applied the term "black hole" to these collapsed objects.

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9. What evidence do we have for the existence of black holes?

Astronomers have found convincing evidence for a supermassive black hole in the center of the giant elliptical galaxy M87, as well as in several other galaxies. The discovery is based on velocity measurements of a whirlpool of hot gas orbiting the black hole. In 1994, Hubble Space Telescope data produced an unprecedented measurement of the mass of an unseen object at the center of M87. Based on the kinetic energy of the material whirling about the center (as in Wheeler's dance, see Question 4 above), the object is about 3 billion times the mass of our Sun and appears to be concentrated into a space smaller than our solar system.

For many years x-ray emission from the double-star system Cygnus X-1 convinced many astronomers that the system contains a black hole. With more precise measurements available recently, the evidence for a black hole in Cygnus X-1 is very strong.

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A few words from the scientist:

When we got together last summer it was a particularly exciting time to be creating a lesson about black holes. A new instrument on HST had just become the ideal science instrument to find and study supermassive black holes that reside in the center of galaxies. Among the remarkable things HST can accomplish with this instrument, the Imaging Spectrograph (STIS), will be a black hole survey. STIS is something like a "Cosmic Speed Gun" - when Hubble is pointed at a galaxy it can determine the speed of material that circulates the galactic center. The faster stuff moves around the center, the more massive that center must be. With high-school-level physics we can determine the mass of these supermassive black holes. Just as we know the mass of our Sun by observing the planets in their orbits about the Sun, we will know the mass of the black holes that reside in the center of each and every galaxy in which we point the STIS "speedgun." The real STIS image of the central region of galaxy M84 is used in the "Amazing Space Black Hole Activity." As more STIS results accumulate, it seems that many, if not most, galaxies have supermassive black holes at their center.

In my research I have studied gravity on a much smaller scale. I use the circulation of our oceans and atmosphere to test how this motion affects the gravitational field of the earth. For example, satellites orbiting the Earth exhibit measurable changes in their orbits as a result of El Niņo. In fact, when you get up and leave the computer terminal you will be changing the Earth's gravitational field by a very small amount. Of course, your walking across the room is not measurable from space. However, it would be an interesting experiment to see how many teachers would have to get up and walk across their rooms to cause a measurable change in the Earth's gravitational field. The gravitational phenomena that occur on Earth and in our solar system are many times smaller in magnitude and scale and not nearly as bizarre as those that occur in and around a black hole. I hope that the activities developed in this lesson plan will capture students' imagination, provide them with a better understanding of our universe, and let them have fun all at the same time.

Daniel Steinberg

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Selected reference sources

Books

Begelman, Mitchell and Rees, Martin J. Gravity's Fatal Attraction: Black Holes in the Universe. Paperback, 246 pages, Scientific American Library, 1998. ISBN: 0716760290.

Boslough, John. Stephen Hawking's Universe. Morrow Publishing, 1985.

Ferguson, Kitty. Prisons of Light: Black Holes. Hardcover, Cambridge Univ. Press, 1996. ISBN: 0521495180.

Hawking, Stephen. A Brief History of Time. Bantam Publishing, 1996.

Hawking, Stephen W. Black Holes and Baby Universes and Other Essays. Paperback reprint edition, Bantam Books, 1994. ISBN: 0553374117.

Hazen, Robert M. and Singer, Maxine. Why Aren't Black Holes Black? The Unanswered Questions at the Frontiers of Science. Paperback, 304 pages, Anchor, 1997. ISBN: 0385480148.

Kaufmann, William J. III. Black Holes and Warped Spacetime. W.H. Freeman & Co., San Francisco, 1979.

Kaufmann, William J. III. Universe. W.H. Freeman & Co., San Francisco, 1998.

Novikov, Igor. Black Holes and the Universe. Cambridge University Press, 1995.

Pickover, Clifford A. Black Holes: A Traveler's Guide. Hardcover, 352 pages, John Wiley & Sons, 1996. ISBN: 0471125806.

Strathern, Paul. Hawking and Black Holes. Paperback, 112 pages, 1 Anchor edition, Doubleday, 1998. ISBN: 0385492421.

Thorne, Kip S. Black Holes and Time Warps. W.W. Norton & Co., 1994.

Magazines

Buckley, Richard. "Black Holes." Astronomy News, Vol. 13, No. 2, February 1999, p. 47.

Charles, Phil. "Black holes: Do they exist?" Astronomy News, Vol. 13, No. 2, February 1999, p. 53.

Freedman, David H. "The Mysterious Middle of the Milky Way." Discover, Vol.19, No. 11, November 1998, p. 66.

Nicolson, Iain. "The Nature of Black Holes Explained." Astronomy News, Vol. 13, No. 2, February 1999, p. 49.

Schilling, Govert. "Starving Black Holes Sound an SOS." Science, Vol. 284, No. 5414, April 23, 1999, p. 567.

Sincell, Mark. "Black Holes Enter the Middleweights." Science, Vol. 284, No. 5414, April 23, 1999, p. 566.

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