l>Chapter 22, thing Review
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SUMMARY

A core-collapse supernova might leave behind a remnant, one ultracompressed sphere of material called a spirit star. The procedures that kind neutron stars ensure that these stars are swiftly rotating and strongly magnetized at birth.

Pulsars room objects that appear to emit consistent bursts that electromagnetic energy. The embraced explanation because that pulsars is the lighthouse model, in which a rotating ghost star sends a beam of power into space. If the beam sweeps previous Earth, we see a pulsar. The pulse duration is the rotation period of the ghost star.

A neutron star in a near binary device can attract matter indigenous its companion, forming an accretion disk. The material in the disk heats up even before it get the ghost star, and also the disk is generally a strong source of X-rays. Together gas build up ~ above the star"s surface ar it at some point becomes hot sufficient to fuse hydrogen. As with a nova explode on a white dwarf, when hydrogen burn starts top top a ghost star, it does for this reason explosively. One X-ray burster results. Even more energetic room gamma-ray bursts, which may an outcome from the violent mergers of spirit stars in far-off binary systems.

The fast rotation that the inner component of the accretion disk reasons the neutron star come spin much faster as brand-new gas come on that is surface. The eventual an outcome is a very rapidly rotating spirit star—a millisecond pulsar. Numerous millisecond pulsars are found in the hearts of old globular clusters. They can not have created recently, so they must have actually been be crazy up by interactions with other stars.

Careful evaluation of the radiation obtained has presented that part pulsars are orbited by planet-sized objects. The origin of these "pulsar planets" is still uncertain.

The top limit top top the fixed of a neutron star is around 3 solar masses. Past that massive the star can no much longer support itself versus its own gravity, and it should collapse. No known pressure can protect against the product from collapsing every the method to a pointlike singularity, a region of exceptionally high density where the recognized laws the physics rest down. Neighboring the singularity, in ~ a street of a few kilometers for a solar-mass object, is a an ar of room from which also light can not escape—a black hole. Astronomers believe that the most massive stars type black holes, rather than spirit stars, after lock explode in a supernova.

Conditions in and also near black holes can not be described by Newtonian mechanics. A proper description requires the theories the relativity arisen by Albert Einstein beforehand in the twenty century. Also relativity theory falls short right in ~ the singularity, however.

The "surface" of a black hole is the event horizon; its street from a singularity is referred to as the Schwarzschild radius. At the occasion horizon the escape speed equals the rate of light. Within this distance, nothing have the right to escape. Photons passing as well close to a black hole space deflected onto routes that cross the occasion horizon and also become trapped.

Relativity theory defines gravity in regards to a warping, or bending, of room by the visibility of mass. The more mass, the higher the warping. Every particles—including photons—respond to that warping by moving along bent paths. A black hole is a region where the warping is so great that space folds ago on itself, cutting turn off the internal of the feet from the rest of the universe.

To a far-off observer the clock on a spaceship falling into a black hole would present time dilation—it would show up to sluggish down together the ship approached the event horizon. The observer would never see the delivery reach the surface of the hole. In ~ the very same time, irradiate leaving the ship would certainly be topic to gravitational redshift as it climbed the end of the hole"s extreme gravitational field. Light emitted just at the occasion horizon would certainly be redshifted to infinite wavelength. Both phenomena are predictions of the theory of relativity. The gravitational redshifts because of both Earth and the Sun are very little but have actually been recognize experimentally.

Once matter drops into a black hole, it deserve to no longer interact with the outside. However, top top its means in, the can type an accretion disk and emit X-rays just as in the neutron-star case. The finest candidates for black holes room binary equipment in i m sorry one component is a compact X-ray source. Cygnus X-1, a well-studied X-ray resource in the constellation Cygnus, is a long-standing black-hole candidate. Researches of orbital motions suggest that the compact objects space too massive to be neutron stars, leaving black holes together the only alternative.

SELF-TEST: TRUE OR FALSE?

1.

You are watching: According to general relativity, space is warped, or curved, by matter.

The thickness of a spirit star is comparable to the thickness of an atom nucleus. (Hint)

2. as a an outcome of their high masses and little sizes, ghost stars have actually only weak gravitational pulls at your surfaces. (Hint)

3. Newly created neutron stars have actually extremely solid magnetic fields. (Hint)

4. A millisecond pulsar is in reality a very old neutron star that has been recently spun up by interaction with a neighbor. (Hint)

5. Millisecond pulsars are discovered only in globular clusters. (Hint)

6. Planet-sized body will never be found around a pulsar, since the supernova that created the pulsar would have destroyed any planets in the system. (Hint)

7. Nothing have the right to travel faster than the rate of light. (Hint)

8. all things, except light, room attracted by gravity. (Hint)

9. A black hole is an object whose to escape speed equals or above the rate of light. (Hint)

10. back visible light cannot escape indigenous a black color hole, high-energy radiation, like gamma rays, deserve to escape. (Hint)

11. that is feasible for a beam of irradiate to enter orbit around a black color hole. (Hint)

12. If you could touch it, the surface ar of a black color hole, the occasion horizon, would certainly be very hard. (Hint)

13. The regulations of physics break down near the center of a black color hole. (Hint)

14. X-rays are emitted by issue accreting ~ above a stellar-mass black hole. (Hint)

15. thousands of black holes have actually now been identified. (Hint)

SELF-TEST: to fill IN THE BLANK

1. No remnant continues to be after the explode of a _____ supernova. (Hint)

2. A usual neutron star is _____ kilometres in diameter. (Hint)

3. ghost stars might be defined as having actually _____ prices of rotation and also _____ magnetic fields. (Hint)

4. Pulsars were discovered through monitorings in the _____ component of the electromagnetic spectrum. (Hint)

5. typical pulsar periods variety from _____ come _____. (Give numbers and also units.) (Hint)

6. The pulse period of pulsar radiation tells united state the _____ of the ghost star emitting the radiation. (Hint)

7. all millisecond pulsars room now, or when were, members that _____ star systems. (Hint)

8. X-ray bursters an outcome from accretion of material from a binary companion top top a _____ star. (Hint)

9. according to general relativity, room is warped, or curved, through _____. (Hint)

10. If the sunlight were magically to turn right into a black hole the the very same mass, Earth"s orbit would _____. (Hint)

11. The radius that the event horizon of a black hole is called the _____. (Hint)

12. The region of exceptionally high density at the facility of a black color hole is dubbed a _____. (Hint)

13. Photons _____ energy as lock escape from a gravitational field. (Hint)

14. black color holes that stellar origin are thought to have actually been found in numerous _____ systems. (Hint)

15. researchers infer the the energy-emitting region in Cygnus X-1 need to be very little because the the fast _____ the the radiation received. (Hint)

REVIEW and also DISCUSSION

1. exactly how does the method in i beg your pardon a neutron star creates determine some of its most basic properties? (Hint)

2. What would take place to a human standing top top the surface ar of a spirit star? (Hint)

3. Why aren"t all neutron stars seen as pulsars? (Hint)

4. What room X-ray bursters? (Hint)

5. explain the line of thinking that led astronomers to conclude that gamma-ray bursts are an extremely distant and really energetic. (Hint)

6. What is the favored explanation for the quick spin rates of millisecond pulsars? (Hint)

7. Why did astronomers not intend to uncover a pulsar with a planetary system? (Hint)

8. What go it median to say that the measured speed of a light beam is elevation of the activity of the observer? (Hint)

9. use your understanding of escape rate to describe why black color holes are stated to it is in "black." (Hint)

10. Why is the so difficult to test the predictions of basic relativity? describe two test of the theory. (Hint)

11. What would occur to who falling right into a black hole? (Hint)

12. What is the rule of cosmic censorship? execute you think the is a sound scientific principle? (Hint)

13. What makes Cygnus X-1 a an excellent black-hole candidate? (Hint)

14. Imagine the you had the ability to take trip at will v the Galaxy. Describe why girlfriend would find many more neutron stars 보다 those known to observers ~ above Earth. Wherein would you it is in most likely to discover these objects? (Hint)

15. execute you think the planet-sized objects found in orbit around a pulsar should be dubbed planets? Why or why not? (Hint)

PROBLEMS

1. The angular momentum of a solid body (see much more Precisely 15-1) is proportional to its angular velocity times the square that its radius. Making use of the law of preservation of angular momentum, estimate how quick a collapsed stellar core would spin if its early stage spin price was 1 change per day and its radius decreased from 10,000 kilometres to 10 km. (Hint)

2. What would certainly your mass be if you to be composed completely of neutron-star material, of thickness 3

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1017 kg/m3? (Assume that your average density is 1000 kg/m3.) to compare this v the mass of (a) the Moon. (b) a usual 1-km asteroid. (Hint)

3. calculation the surface gravity and also escape speed of 1.4—solar fixed neutron star through a radius of 10 km. (Hint)

4. use the radius—luminosity—temperature relationship to calculation the luminosity of a 10-km-radius ghost star for temperatures the 105 K, 107 K, and 109 K. What carry out you conclude about the visibility of spirit stars? might the brightest that them it is in plotted on our H—R diagram? (Hint)

5. A gamma-ray detector of area 0.5 m2 observing a gamma-ray burst documents photons having total energy 10-8 joules. If the burst arisen 1000 Mpc away, calculation the total amount of energy it released (assuming that the energy was emitted isotropically). Just how would this figure adjust if the burst occurred 10,000 pc away instead, in the gloriole of ours Galaxy? What if it occurred within the Oort cloud the our own solar system, at a street of 50,000 A.U.? (Hint)

6. A 10-km-radius neutron star is spinning 1000 times per second. Calculate the rate of a point on that is equator, and compare it v the rate of light. (Consider the equator together the one of a circle, and also recall that circumference = 2

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r.) additionally calculate the orbital speed of a fragment in a circular orbit just above the neutron star"s surface. (Hint)

7. Supermassive black holes are thought to exist in the centers of some galaxies. What would certainly be the Schwarzschild radii of black holes of 1 million and also 1 exchange rate solar masses, respectively? just how does the first black hole to compare in dimension with the Sun? exactly how does the 2nd compare in dimension with the solar system? (Hint)

8. calculation the tidal pressure on a 2-m-tall human being falling feet first into a 1—solar mass black color hole—that is, compute the difference in the forces acting on his head and also his feet just prior to his feet cross the occasion horizon. Repeat the calculation for a 1—million solar mass black hole and also for a 1 billion—solar mass black color hole. Compare these pressures with the person"s weight on planet of 600 N. (See an ext Precisely 2-2.) (Hint)

9. What room the mass and also Schwarzschild radius of a black hole having a blackbody temperature equal to the of the Sun—6000 K? (See much more Precisely 22-3.) What is the black color hole"s luminosity? (Hint)

10. using the data provided in the message (assume the top limit top top the stated selection for the black-hole mass), calculation the orbital separation of Cyg X-1. If the companion star"s radius is 20 million km, verify (approximately) the the black hole"s tidal field is adequate to attract matter from the companion"s surface. (Hint)

PROJECTS

1.

See more: Take Me To The River Chicken Fighting, Take Me To The River

countless amateur astronomers enjoy transforming their telescopes on the ninth-magnitude companion to Cygnus X-1, the sky"s most famous black-hole candidate. Because none of us can see in X-rays, no sign of noþeles unusual have the right to be seen. Still, it"s fun to gaze toward this an ar of the heavens and also contemplate Cygnus X-1"s powerful energy emission and strange properties. Even without a telescope, that is simple to find the region of the heavens wherein Cygnus X-1 resides. The constellation Cygnus consists of a recognizable star pattern, or asterism, in the shape of a large cross. This asterism is referred to as the northern Cross. The star in the center of the crossbar is called Sadr. The star in ~ the bottom the the overcome is called Albireo. Around midway along an imaginary line between Sadr and Albireo lies the star Eta Cygni. Cygnus X-1 is situated slightly much less than 0.5° native this star. Through or without a telescope, sketch what you see.

2. collection up a show of the densities of various huge objects—an interstellar cloud, a star, a terrestrial planet, a white dwarf, and also a spirit star. Pick a common object the is easily held in her hand, miscellaneous that would be familiar to anyone—an apple, because that example. Because that the lowest densities, calculate how big a volume would contain the object"s tantamount mass. For high densities, calculation how many of the objects would need to be fit right into a typical volume, such as 1 cm3. This volume is far better for this task than 1 m3 due to the fact that most people do no appreciate how huge a volume 1 m3 is. Existing your demonstration to your class or to part other group of students. Call them about each huge object and also how it come by that is density.