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Although most massive stars end their lives as neutron stars, a topic we started in the last lesson and finish here, a select few leave behind a remnant so massive that it collapses for eternity. Gravity is the force that stars fight their whole lives, and gravity is what wins in the end. To understand black holes (one of the reasons students take an astronomy course), we must find a way to describe gravity under such extreme conditions. This lesson introduces you to the theory of general relativity as proposed by Albert Einstein. Don't panic! The text goes through the theory in a logical, comprehensible way. You will marvel at yourself as you find you actually understand this whole new way of thinking about gravity.
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After completing this lesson, you should be able to
In this lesson we complete our discussion of the lives and times of the most massive stars, and delve more deeply into the exotic objects known as black holes. Reread Section 14.2 and 14.3 that discuss the supernova event and the formation of a neutron star. Many things occur in an extremely short period of time when a massive star reaches the level of fusion where iron is the end result. It is theorized that the last stages of fusion may take only a few hours, and the collapse of the iron core into a ball of neutrons takes less time than it does to read the two sections in the text that describe it.
The end result for most massive stars is to leave behind a neutron star having between 1.4 and 3 solar masses and to spill the rest of its material back to the interstellar medium. Since these stars started out with over 6 solar masses, a whole lot of material gets recycled. Our models of neutron stars are solid on both observational and theoretical grounds, even though we rightfully think of them as weird—a ball the size of a large city that would weigh 1014 times as much as a marble if we could scoop up a marble-sized chunk of it. Now set this dense ball spinning at thousands of times a second, about as fast as it could possibly spin without breaking up, and we have a neutron star.
A few stars are so massive to start with that their cores end up with more than 3 solar masses during the fusion-to-iron stage. During the collapse to a neutron star, the core finds that even the pressure created by neutrons packed extremely close together is not enough to battle the force of gravity. Gravity always wins in the end. The core collapses forever. The phrase "mind boggling" probably has popped into your head about now. Some of discussion here and your reading probably will make you dizzy!
To understand black holes, we must bring in Dr. Albert Einstein's theory of general relativity—what happens around extremely massive objects. This is where you cover in just a few hours what Einstein took a lifetime to develop. You should find that it brings in a whole new perspective to our universe.
In Lesson Two, you reviewed a number of experiments using toys to demonstrate the physics of the Universe. Go back to that activity and look at the list of 13 demonstrations once again. Think about how such simple examples of everyday life also apply to the way stars evolve and to the most violent explosion in the Universe, that of a supernova. Conservation of energy and momentum, conservation of angular momentum, and Newton's Third Law are applicable in the most fundamental of stellar theory. When do our physics break down? Our physics breaks down (or rather our ability to understand the physics or come up with new theories) when we finally get to the black hole, where nature cannot provide an "equal and opposite force" to counteract gravity.
All pulsars are neutron stars, but not all neutron stars are pulsars. How could that be? If you were able to go any where in the Galaxy, would you see more pulsars or less? You would see more. A pulsar is a neutron star that happens to be beaming its radiation towards Earth. Think of the "Spinning Lighthouse Model," as described in chapter 14 your text. If you are on the water, you will have the beam of light sweep by you. If you are in a hot-air balloon overhead, the beam will not sweep by you, but the lighthouse is still a lighthouse. In the boat in pitch dark, you see a flashing beam of light; overhead you see the dark shape of a tower.
How do these neutron stars end up spinning so fast? Conservation of angular momentum. The angular momentum of an object depends on the product of the mass of the object, its angular velocity, and its radius from the center to the edge (roughly speaking). If our Sun were to shrink to 1/100 of its current radius, it would have to spin 100 times as fast (assuming no mass is gained or lost). Going to the size of a neutron star (which the Sun won't do, but let's imagine), the radius of the Sun would go from around 700,000 km to 7 km! It currently takes about 25 days, or 2,160,000 seconds to rotate once. Going to the size of a neutron star, it would take only 21.6 seconds to rotate once. More massive stars get spun up much, much more.
Your text explains the process whereby the core of the massive star gets crushed into a ball of neutrons. Read through that section and the next on the production of neutrinos carefully. When SN 1987A exploded in the Large Magellenic Cloud, the flux of neutrinos passing through the Earth was a confirmation of much of our theory about supernovae, and how neutron stars form.
We will complete our study of supernovae and neutron stars and pulsars during the activity for this lesson, where we take a much closer look at the Crab Nebula and its pulsar.
Before we can fully understand the concept of a black hole and the bending of spacetime, we must take a look at what is known as the principle of equivalence of gravitation and inertia. Einstein, when formulating his theories of general relativity—his theory of gravitation—connected the theory with the geometry. Under Newton's Second Law, we remember that the force exerted on an object is proportional to the mass of that object. We view this as the inertial mass, the property that anything that has mass resists a change in its current state unless acted upon by an outside force:
F = ma
In his law of gravity, Newton showed that the force of gravity on an object is proportional to the mass of that object that the gravity acts on:
F = G [M1M2/D2]
and by Newton's Third Law, that the force is also proportional to the mass of the source. Is the "inertial mass" precisely the same as the "gravitational mass"? Newton could not find any difference. Additional tests have shown that these two masses are the same to at least one part in one billion. "Einstein was very impressed with the observed equality of gravitational and inertial mass. . . ." (Weinberg, Steven, 1972, Gravitation and Cosmology, John Wiley & Sons)
What this means is that in an isolated system, within small regions of space, the effects of gravity are exactly equivalent to the effects of acceleration. For us Earthlings, we could not tell the difference between being on a solid surface feeling 1 g of gravity (Earth) or being accelerated in outer space at 1 g (10 m/sec/sec).
If you could not see outside your room, and acceleration were constant at 1 g, the equivalence principle states that you would not know whether you were studying on the Earth or heading into outer space.
If we take the equivalence principle one step further, we see that the warping of space and time around a massive object is capable of bending even light. Say we shine a flashlight at an accelerating rocket with the light entering through a teeny, tiny slit that we have put there along the length of the rocket. From our point of view, the beam of light travels in a straight line, while the rocket passes by it. From the perspective of the astronaut within the rocket, however, he sees the light beam coming in high on one side and leaving low on the other. He thinks that the beam has curved, not realizing that he is, in fact, accelerating at 1 g. (Note, however, that to get light to bend as much as is shown here, the acceleration would have to be enormously greater than 1 g.) Since being in a gravitational field and accelerating are equivalent, the conclusion is that light responds to the bending of spacetime.
What the Space Ship is Doing:
What the Astronaut Sees:
This whole "spacetime–thing" is not an easy thing to grasp by any means. It takes minds like those of Newton and Einstein to formulate the theories and carry them far beyond what normal minds might imagine. Thus, we have every reason to struggle a bit at this point, and maybe even feel a bit dizzy!
Under Einstein's theory of general relativity, one does not mention the "force of gravity." One talks about an object with mass bending spacetime. Theory is fine, but is there any observational evidence of the bending of spacetime and light responding by being "bent"? The answer is a resounding "Yes!" Numerous times!
The first observational test of general relativity was the orbit of Mercury. Mercury precesses in its orbit, meaning that its perhelion point gradually shifts around the Sun. Although Newton's Law of Gravity can account for most of this precession, it cannot account for all of it. Spacetime is more distorted on the part of Mercury's orbit that is the closest to the Sun. General relativity is needed for the complete explanation. See Fig. 15.7 in your text.
The second test, which also was passed with flying colors, came during a total eclipse of the Sun in 1919. Einstein had predicted that starlight would be bent by the Sun's warping of spacetime. Measurements of the separation of stars, see illustration below, before and during the eclipse confirmed the predictions.
The warping of spacetime around a blackhole is so severe that light cannot escape. Another way of stating this is to say that the gravitational redshift of the light is infinite. The gravitational "tug" is so strong that even light cannot break free.
One of the problems with trying to depict four dimensions in a three-dimensional world is that we cannot really portray how objects will look. You will see black holes usually displayed as rubber sheets with bowling balls laid on them, or like the funnels seen in retail stores where you roll a dime down a ramp and watch it spiral down. Perhaps you feel that if you came in at just the right angle, you'd be able to sneak up behind a black hole, or that when things fall into a black hole, it is much like going down a funnel. Find a marble, preferably black, and hold it up. Now, imagine all matter and energy in your house and neighborhood funneling into that marble from every direction right down to the center, never to return. Down to the singularity where we meet infinite density, zero volume, and a place our physics cannot explain. Black holes are truly mind boggling.
Review the sections in your text that talk about how black holes are formed. What are the effects of black holes on the matter and radiation in their vicinity? What would it be like if you were to unfortunately come too close to a black hole (an extremely unlikely event) and start to fall in? What would your friends observe as you were pulled in? There is a term for what happens to you, "spaghettification," at least momentarily until even your molecules, atoms, and subatomic particles are stretched and broken.
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Going Into the Black Hole: A Personal Point of View. |
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| Going Into the Black Hole: An Observer's Point of View. |
How do we detect black holes? "The problem with black holes is that they are black, and they are holes! We see a hole in the road because of the pavement around it, not because there is a hole." From Black Holes, the Ultimate Abyss Discovery Channel Education. We detect a black hole only if there is a star near it that is being dramatically affected by the presence of the black hole.
While you still have your marble in hand, take a look at the following table. The marble is proably about 1 cm in diameter. Here is what it would weigh if it had the densities of the following stellar objects.
| Stage | Object | Mass | Equivalent Object |
|---|---|---|---|
| MS | Fusing H | 100 gm | Hamburger |
| Subgiant | He core | 10 kg | Dachshound |
| Red Giant | He core | 100 kg | Defensive End |
| AGB Giant | C core | 1,000 kg | VW Bug |
| White Dwarf | Carbon | 10,000 kg | 10 VW Bugs |
| Neutron Star | Neutron | 500 billion kg | Mt Rainier |
| Passage of time | Colors of the watches | Physical changes |
|---|---|---|
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You start to see her watch
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You see her watch
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You see her
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Your friend sees your watch
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Your friend sees your watch
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Your friend sees you
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Your friend sees her watch
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Your friend sees her watch
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Approaching the black hole, your friend feels
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From the textbook:
For more information on the Crab Nebula, be sure to visit the following sites:
