1. Chapter 22 Neutron Stars and Black Holes
Chapter 22 opener. This stunning image is actually a composite of three images taken by telescopes in orbit: optical light (in yellow) observed with Hubble, X-ray radiation (blue and green) with Chandra, and infrared radiation (red) with Spitzer. This object is known as Cassiopeia A, the remnant of a supernova whose radiation first reached Earth about 300 years ago. The small turquoise dot at the center may be a neutron star created in the blast, the sole survivor of the explosion. (NASA)

2. Units of Chapter 22 22.1 Neutron Stars 22.2 Pulsars
22.3 Neutron-Star Binaries
22.4 Gamma-Ray Bursts
22.5 Black Holes
22.6 Einstein’s Theories of Relativity
Special Relativity

3. Units of Chapter 22 (cont.)
22.7 Space Travel Near Black Holes
22.8 Observational Evidence for Black Holes
Tests of General Relativity
Gravity Waves: A New Window on the Universe

4. 22.1 Neutron Stars
After a Type I supernova, little or nothing remains of the original star.
After a Type II supernova, part of the core may survive. It is very dense—as dense as an atomic nucleus—and is called a neutron star.

5. Neutron stars, although they have 1–3 solar masses, are so dense that they are very small. This image shows a 1-solar-mass neutron star, about 10 km in diameter, compared to Manhattan:
Figure Neutron Star Neutron stars are not much larger than many of Earth’s major cities. In this fanciful comparison, a typical neutron star sits alongside Manhattan Island. (NASA)

6. Other important properties of neutron stars (beyond mass and size):
Rotation—as the parent star collapses, the neutron core spins very rapidly, conserving angular momentum. Typical periods are fractions of a second.
Magnetic field—again as a result of the collapse, the neutron star’s magnetic field becomes enormously strong.

7. 22.2 Pulsars
The first pulsar was discovered in It emitted extraordinarily regular pulses; nothing like it had ever been seen before.
After some initial confusion, it was realized that this was a neutron star, spinning very rapidly.
Figure Pulsar Radiation Pulsars emit periodic bursts of radiation. This recording shows the regular change in the intensity of the radio radiation emitted by the first such object discovered, known as CP Some of the object’s pulses are marked by arrows.

8. But why would a neutron star flash on and off?
This figure illustrates the lighthouse effect responsible:
Strong jets of matter are emitted at the magnetic poles. If the rotation axis is not the same as the magnetic axis, the two beams will sweep out circular paths. If the Earth lies in one of those paths, we will see the star pulse.
Figure Pulsar Model This diagram of the “lighthouse model” of neutron-star emission accounts for many of the observed properties of pulsars. Charged particles, accelerated by the magnetism of the neutron star, flow along the magnetic field lines, producing radiation that beams outward. At greater distances from the star, the field lines channel these particles into a high-speed outflow in the star’s equatorial plane, forming a pulsar wind. The beam sweeps across the sky as the neutron star rotates. If it happens to intersect Earth, we see a pulsar—much like a lighthouse beacon.

9. Pulsars radiate their energy away quite rapidly; the radiation weakens and stops in a few tens of millions of years, making the neutron star virtually undetectable.
Pulsars also will not be visible on Earth if their jets are not pointing our way.

10. There is a pulsar at the center of the Crab Nebula; the images show it in the “off” and “on” states. The disk and jets are also visible:
Figure Crab Pulsar In the core of the Crab Nebula (a), the Crab pulsar (c) blinks on and off about 30 times each second. In this pair of optical images, the pulsing can be clearly seen. In the right frame, the pulsar (arrow) is on; in the left frame, it is off. (b) This more recent Chandra X-ray image of the Crab, superimposed on a Hubble optical image, shows the central pulsar, as well as rings of hot X-ray-emitting gas in the equatorial plane, driven by the pulsar wind and moving rapidly outward. Also visible in the image is a jet of hot gas (not the beam of radiation from the pulsar) escaping perpendicular to the equatorial plane. (d) The light curve shows the main pulse and its precursor. (The latter is probably related to the beam directed away from Earth.) (ESO; NASA)

11. The Crab pulsar also pulses in the gamma-ray spectrum:
Figure (a) The Crab and Geminga pulsars, which happen to lie fairly close (about 4.5 degrees) to one another in the sky. Unlike the Crab, Geminga is barely visible at optical wavelengths and undetectable in the radio region of the spectrum. (b) Sequence of Compton Gamma-Ray Observatory images showing Geminga’s 0.24-s pulse period. (The Crab’s 33-millesecond period is too rapid to be resolved by the detector.) (NASA)

12. 22.3 Neutron-Star Binaries
Bursts of X-rays have been observed near the center of our galaxy. A typical one appears below, as imaged in the X-ray spectrum:
Figure X-Ray Burster An X-ray burster produces a sudden, intense flash of X rays, followed by a period of relative inactivity lasting as long as several hours. Then another burst occurs. The bursts are thought to be caused by explosive nuclear burning on the surface of an accreting neutron star, similar to the explosions on a white dwarf that give rise to novae. (a) An optical photograph of the globular star cluster Terzan 2, showing a 2” dot at the center where the X-ray bursts originate. (b) X-ray images taken before and during the outburst. The most intense X-rays correspond to the position of the black dot shown in (a). (SAO)

13. These X-ray bursts are thought to originate on neutron stars that have binary partners.
The process is similar to a nova, but much more energy is emitted due to the extremely strong gravitational field of the neutron star.
Figure X-Ray Emission (a) Matter flows from a normal star toward a compact neutron-star companion and falls toward the surface in an accretion disk. As the gas spirals inward under the neutron star’s intense gravity, it heats up, becoming so hot that it emits X rays. In at least one instance—the peculiar object SS 433—some material may be ejected in the form of two high-speed jets of gas. (b) False-color radiographs of SS 433, made at monthly intervals (left to right), show the jets moving outward and the central source rotating under the gravitational influence of the companion star. (NRAO)

14. Most pulsars have periods between 0. 03 and 0
Most pulsars have periods between 0.03 and 0.3 seconds, but a new class of pulsar was discovered in the early 1980s: the millisecond pulsar.
Figure Millisecond Pulsar Gas from a companion star spirals down onto the surface of a neutron star. As the infalling matter strikes the star, it moves almost parallel to the surface, so it tends to make the star spin faster. Eventually, this process can result in a millisecond pulsar—a neutron star spinning at the incredible rate of hundreds of revolutions per second.

15. Millisecond pulsars are thought to be “spun-up” by matter falling in from a companion.
This globular cluster has been found to have 108 separate X-ray sources, about half of which are thought to be millisecond pulsars:
Figure Cluster X-Ray Binaries The dense core of the old globular cluster 47 Tucanae harbors more than 100 separate X-ray sources (shown in the Chandra image at the right). More than half of these are thought to be binary millisecond pulsars, still accreting small amounts of gas from their companions after an earlier period of mass transfer spun them up to millisecond speeds. (ESO; NASA)

16. In 1992, a pulsar was discovered whose period had unexpected, but very regular, variations.
These variations were thought to be consistent with a planet, which must have been picked up by the neutron star, not the progenitor star:
Figure Binary Exchange A neutron star can encounter a binary made up of two low-mass stars, ejecting one of them and taking its place. This mechanism provides a means of forming a binary system with a neutron-star component (which may later evolve into a millisecond pulsar) without having to explain how the binary survived the supernova explosion that formed the neutron star.

17. 22.4 Gamma-Ray Bursts
Gamma-ray bursts also occur, and were first spotted by satellites looking for violations of nuclear test-ban treaties. This map of where the bursts have been observed shows no “clumping” of bursts anywhere, particularly not within the Milky Way. Therefore, the bursts must originate from outside our Galaxy.
Figure Gamma-Ray Bursts (b) Positions on the sky of all the gamma-ray bursts detected by Compton Observatory during its nearly 9-year operating lifetime. The bursts appear to be distributed isotropically (uniformly) across the entire sky. The plane of the Milky Way Galaxy runs horizontally across the center of the map, which is also the direction to the center of our Galaxy. (NASA)

18. These are some sample luminosity curves for gamma-ray bursts:
Figure Gamma-Ray Bursts (a) Plots of intensity versus time (in seconds) for three gamma-ray bursts. Note the substantial differences between them. Some bursts are irregular and spiky, whereas others are much more smoothly varying. Whether this wide variation in the burst appearance means that more than one physical process is at work is presently unknown. (NASA)

19. Distance measurements of some gamma bursts show them to be very far away—2 billion parsecs for the first one measured.
Occasionally the spectrum of a burst can be measured, allowing distance determination:
Figure Gamma-Ray Burst Counterparts Optical images of the gamma-ray burst GRB (the numbers simply mean December 14, 1997, the day the burst was recorded). Image (a), taken with the Keck telescope, shows the visible afterglow of the gamma-ray source (arrow) to be quite bright, comparable to two other prominent sources in the overlaid box. A spectrum of the afterglow showed it to be highly redshifted, placing it near the limits of the observable universe, almost 5 billion parsecs away. By the time the Hubble image (b) was taken (about two months after the Keck image and 4 months after the initial burst of gamma rays was detected by the Italian–Dutch Beppo-Sax satellite), the afterglow had faded, but a faint image of a host galaxy remains. The different colors result from the use of different filters to observe the light. (Keck; NASA)

20. Two models—merging neutron stars or a hypernova—have been proposed as the source of gamma-ray bursts:
Figure Gamma-Ray Burst Models Two models have been proposed to explain gamma-ray bursts. Part (a) depicts the merger of two neutron stars; part (b) shows the core collapse, implosion, and stalled supernova, or hypernova, of a single massive star. Both models predict a relativistic fireball, perhaps releasing energy in the form of jets, as shown.

21. 22.5 Black Holes
The mass of a neutron star cannot exceed about 3 solar masses. If a core remnant is more massive than that, nothing will stop its collapse, and it will become smaller and smaller and denser and denser.
Eventually, the gravitational force is so intense that even light cannot escape. The remnant has become a black hole.

22. The radius at which the escape speed from the black hole equals the speed of light is called the Schwarzschild radius.
The Earth’s Schwarzschild radius is about a centimeter; the Sun’s is about 3 km.
Once the black hole has collapsed, the Schwarzschild radius takes on another meaning—it is the event horizon. Nothing within the event horizon can escape the black hole.

23. 22.6 Einstein’s Theories of Relativity
Special relativity:
1. The speed of light is the maximum possible speed, and it is always measured to have the same value by all observers:
Figure Speed of Light (a) A bullet fired from a speeding car would be measured by an outside observer to have a speed equal to the sum of the speeds of the car and of the bullet. (b) A beam of light shining forward from a high-speed spacecraft would still be observed to have speed c, regardless of the speed of the spacecraft. The speed of light is thus independent of the speed of the source or of the observer.

24. Special relativity (cont.):
2. There is no absolute frame of reference, and no absolute state of rest.
3. Space and time are not independent but are unified as spacetime.

25. General relativity:
It is impossible to tell from within a closed system whether one is in a gravitational field or accelerating.
Figure Einstein’s Elevator A passenger in a closed elevator floating in space feels weight return—he feels a force exerted on his feet by the elevator floor. Einstein reasoned that no experiment conducted entirely within the elevator can tell the passenger whether the force is (a) due to the gravity of a nearby massive object or (b) caused by the acceleration of the elevator itself.

26. Matter tends to warp spacetime, and in doing so redefines straight lines (the path a light beam would take):
A black hole occurs when the “indentation” caused by the mass of the hole becomes infinitely deep.
Figure Curved Space (a) A pool table made of a thin rubber sheet sags when a weight is placed on it. Likewise, space is bent, or warped, in the vicinity of any massive object. (b) As the weight increases, so does the warping of space. A ball shown rolling across the table is deflected by the curvature of the surface, in much the same way as a planet’s curved orbit is determined by the curvature of spacetime produced by the Sun.

27. More Precisely 22-1: Special Relativity
In the late 19th century, Michelson and Morley did an experiment to measure the variation in the speed of light with respect to the direction of the Earth’s motion around the Sun.
They found no variation—light always traveled at the same speed. This later became the foundation of special relativity.
Taking the speed of light to be constant leads to some counterintuitive effects—length contraction, time dilation, the relativity of simultaneity, and the mass equivalent of energy.

28. 22.7 Space Travel Near Black Holes
The gravitational effects of a black hole are unnoticeable outside of a few Schwarzschild radii—black holes do not “suck in” material any more than an extended mass would.

29. Matter encountering a black hole will experience enormous tidal forces that will both heat it enough to radiate, and tear it apart:
Figure Black-Hole Heating Any matter falling into the clutches of a black hole will become severely distorted and heated. This sketch shows an imaginary planet being pulled apart by a black hole’s gravitational tides.

30. A probe nearing the event horizon of a black hole will be seen by observers as experiencing a dramatic redshift as it gets closer, so that time appears to be going more and more slowly as it approaches the event horizon.
This is called a gravitational redshift—it is not due to motion, but to the large gravitational fields present.
The probe, however, does not experience any such shifts; time would appear normal to anyone inside.

31. Similarly, a photon escaping from the vicinity of a black hole will use up a lot of energy doing so; it cannot slow down, but its wavelength gets longer and longer
Figure Gravitational Redshift As a photon escapes from the strong gravitational field close to a black hole, it must expend energy to overcome the hole’s gravity. This energy does not come from a change in the speed at which the photon travels. (That speed is always 300,000 km/s, even under these extreme conditions.) Rather, the photon “gives up” energy by increasing its wavelength. Thus, the photon’s frequency changes, and the photon is (red)shifted into a less energetic region of the spectrum. This figure shows the effect on two beams of radiation, one of visible light and one of X rays, emitted from a space probe as it nears the event horizon of a 1-solar-mass black hole. (Note that the light is not coming from within the black hole itself.) The beams are shifted to longer and longer wavelengths as they move farther from the event horizon.

32. What’s inside a black hole?
No one knows, of course; present theory predicts that the mass collapses until its radius is zero and its density is infinite, but it is unlikely that this actually happens.
Until we learn more about what happens in such extreme conditions, the interiors of black holes will remain a mystery.

33. 22.8 Observational Evidence for Black Holes
Black holes cannot be observed directly, as their gravitational fields will cause light to bend around them.
Figure Gravitational Light Deflection The gravitational bending of light around the edges of a small, massive black hole makes it impossible to observe the hole as a black dot superimposed against the bright background of its stellar companion.

34. This bright star has an unseen companion that is a strong X-ray emitter called Cygnus X-1, which is thought to be a black hole:
Figure Cygnus X-1 (a) The brightest star in this photograph is a member of a binary system whose unseen companion, called Cygnus X-1, is a leading black hole candidate. (b) An X-ray image of field of view outlined by the rectangle in part (a). Of course, X rays cannot be seen directly; X rays emitted by the Cygnus X-1 source were captured in space by an X-ray detector aboard a satellite, changed into radio signals for transmission to the ground, and changed again into electronic signals that were then viewed on a video screen, from which this picture was taken. (Harvard-Smithsonian Center for Astrophysics)

35. The existence of black-hole binary partners for ordinary stars can be inferred by the effect the holes have on the star’s orbit, or by radiation from infalling matter.
Figure Black-Hole Binary Artist’s conception of a binary system containing a large, bright, visible star and an invisible, X-ray-emitting black hole. This painting is based on data obtained from detailed observations of Cygnus X-1. (L. Chaisson)

36. 22.8 Observational Evidence for Black Holes
Cygnus X-1 is a very strong black-hole candidate:
Its visible partner is about 25 solar masses.
The system’s total mass is about 35 solar masses, so the X-ray source must be about 10 solar masses.
Hot gas appears to be flowing from the visible star to an unseen companion.
Short time-scale variations indicate that the source must be very small.

37. There are several other black-hole candidates as well, with characteristics similar to those of Cygnus X-1.
The centers of many galaxies contain supermassive black holes—about 1 million solar masses.
Figure Active Galaxy Many galaxies are thought to harbor massive black holes at their centers. Shown here in false color is the galaxy 3C296. Blue color shows the distribution of stars in the central elliptical galaxy; red shows huge jets of radio emission extending 500,000 light-years across. (See also the opening image of Chapter 24.) (NRAO)

38. Recently, evidence for intermediate-mass black holes has been found; these are about 100 to 1000 solar masses. Their origin is not well understood.
Figure Intermediate-Mass Black Holes? X-ray observations (inset below) of the interior of the starburst galaxy M82 (at top, about 100,000 light-years across and 12 million light-years away) reveal a collection of bright sources thought to be the result of matter accreting onto intermediate-mass black holes. The black holes are probably young, have masses between 100 and 1000 times the mass of the Sun, and lie relatively far (about 600 light-years) from the center of M82. The brightest (and possibly most massive) intermediate-mass black hole candidate is marked by an arrow. (Subaru; NASA)

39. More Precisely 22-1: Tests of General Relativity
Deflection of starlight by the sun’s gravity was measured during the solar eclipse of 1919; the results agreed with the predictions of general relativity.

40. Another prediction—the orbit of Mercury should precess due to general relativistic effects near the Sun; again, the measurement agreed with the prediction.

41. Discovery 22-1: Gravity Waves: A New Window on the Universe
General relativity predicts that orbiting objects should lose energy by emitting gravitational radiation. The amount of energy is tiny, and these waves have not yet been observed directly.
However, a neutron-star binary system has been observed (two neutron stars); the orbits of the stars are slowing at just the rate predicted if gravity waves are carrying off the lost energy.

42. This figure shows LIGO, the Laser Interferometric Gravity-wave Observatory, designed to detect gravitational waves. It has been operating since 2003, but no waves have been detected yet.

43. A pulsar is a pulsating star.
a star which emits extremely regular pulses of radio waves.
a black hole capturing stars.
a star whose light output is controlled by intelligent life.

44. The crab nebula is
a supernova remnant.
a newly forming star.
an h-2 region.
a black hole.

45. We observe ordinary pulsars in what region of the spectrum?
x-ray
radio
optical
infrared

46. What phenomenon provides observational evidence for the existence of neutron stars?
Cepheids
Quasars
planetary nebula
pulsars

47. The mass of a neutron star
equals the mass of the original star from which it formed.
must be greater than 3 solar masses.
must be greater than 1 solar masses.
must be less than 3 solar masses.

48. We believe that pulsars slow down because
they are converting energy of rotation into radiation.
they are dragging companion stars around.
of friction with the interstellar medium.
of the conservation of angular momentum.

49. We expect neutron stars to spin rapidly because
they conserved angular momentum.
they have high orbital velocities.
they have high densities.
they have high temperatures.

50. To about what size would the Earth have to be compressed to become a black hole?
about a centimeter.
about 10 kilometers.
about 100 kilometers.
the Earth could not become a black hole under any circumstances.

51. Place the objects below in increasing order of density.
black hole, neutron star, white dwarf.
neutron star, black hole, white dwarf.
white dwarf, neutron star, black hole.
neutron star, white dwarf, black hole.

52. The event horizon
is believed to be a singularity.
is a crystalline layer.
has a radius equal to the Schwarzschild radius.
marks the inner boundary of a planetary nebula.

53. According to Einstein's general theory of relativity, what will happen to an object thrown into a black hole after it crosses the Schwarzschild radius?
it is crushed into a singularity.
it is thrown back at the speed of light.
it is trapped forever.
(a) and (b)
(a) and (c)

54. If the sun could magically and suddenly become a black hole (of the same mass) the Earth would
continue in its same orbit.
be pulled closer, but not necessarily into the black hole.
be pulled into the black hole.
fly off into space.

55. The concept that you cannot distinguish between effects due to gravitation and effects due to the acceleration from other forces is known as:
the General Theory of Relativity.
the Special Theory of Relativity.
the Principle of Equivalence.
Newton's First Law of Motion.

56. Summary of Chapter 22 Supernova may leave behind a neutron star.
Neutron stars are very dense, spin rapidly, and have intense magnetic fields.
Neutron stars may appear as pulsars due to the lighthouse effect.
A neutron star in a close binary may become an X-ray burster or a millisecond pulsar.
Gamma-ray bursts are probably due to two neutron stars colliding or hypernova.

57. Summary of Chapter 22 (cont.)
If core remnant is more than about 3 solar masses, it collapses into black hole.
We need general relativity to describe black holes; it describes gravity as the warping of spacetime.
Anything entering within the event horizon of a black hole cannot escape.
The distance from the event horizon to the singularity is called the Schwarzschild radius.

58. Summary of Chapter 22 (cont.)
A distant observer would see an object entering black hole subject to extreme gravitational redshift and time dilation.
Material approaching a black hole will emit strong X-rays.
A few such X-ray sources have been found and are black-hole candidates.