1. Note that the following lectures include animations and PowerPoint effects such as fly ins and transitions that require you to be in PowerPoint's Slide Show mode (presentation mode).

2. Neutron Stars and Black Holes
Chapter 14
Neutron Stars and Black Holes

3. Guidepost
The preceding chapters have traced the story of stars from their birth as clouds of gas in the interstellar medium to their final collapse. This chapter finishes the story by discussing the kinds of objects that remain after a massive star dies.
How strange and wonderful that we humans can talk about places in the universe where gravity is so strong it bends space, slows time, and curves light back on itself! To carry on these discussions, astronomers have learned to use the language of relativity. Throughout this chapter, remember that our generalized discussions are made possible by astronomers studying general relativity in all its mathematical sophistication. That is, our understanding rests on a rich foundation of theory.
This chapter ends the story of individual stars. The next three chapters, however, extend that story to include the giant communities in which stars live— the galaxies.

4. Outline I. Neutron Stars A. Theoretical Prediction of Neutron Stars
B. The Discovery of Pulsars
C. A Model Pulsar
D. The Evolution of Pulsars
E. Binary Pulsars
F. The Fastest Pulsars
G. Pulsar Planets
II. Black Holes
A. Escape Velocity
B. Schwarzschild Black Holes
C. Black Holes Have No Hair
D. A Leap into a Black Hole
E. The Search for Black Holes

5. Outline (continued) III. Compact Objects with Disks and Jets
A. X-Ray Bursters
B. Accretion Disk Observations
C. Jets of Energy from Compact Objects
D. Gamma-Ray Bursts

6. The central core will collapse into a compact object of ~ a few Msun.
Neutron Stars
A supernova explosion of a M > 8 Msun star blows away its outer layers.
The central core will collapse into a compact object of ~ a few Msun.

7. Formation of Neutron Stars
Compact objects more massive than the Chandrasekhar Limit (1.4 Msun) collapse further.
 Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object:
p + e-  n + ne
 Neutron Star

8. Properties of Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density: r ~ 1014 g/cm3
 Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!

9. Discovery of Pulsars
Angular momentum conservation
=> Collapsing stellar core spins up to periods of ~ a few milliseconds.
Magnetic fields are amplified up to B ~ 109 – 1015 G.
(up to 1012 times the average magnetic field of the sun)
=> Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars

10. Pulsars / Neutron Stars
Neutron star surface has a temperature of ~ 1 million K.
Cas A in X-rays
Wien’s displacement law,
lmax = 3,000,000 nm / T[K]
gives a maximum wavelength of lmax = 3 nm, which corresponds to X-rays.

11. Pulsar Periods Over time, pulsars lose energy and angular momentum
=> Pulsar rotation is gradually slowing down.

12. Lighthouse Model of Pulsars
A Pulsar’s magnetic field has a dipole structure, just like Earth.
Radiation is emitted mostly along the magnetic poles.

13. Neutron Star
(SLIDESHOW MODE ONLY)

14. Images of Pulsars and Other Neutron Stars
The vela Pulsar moving through interstellar space
The Crab nebula and pulsar

15. The Crab Pulsar Remnant of a supernova observed in A.D. 1054
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054

16. The Crab Pulsar (2)
Visual image
X-ray image

17. Light Curves of the Crab Pulsar

18. Proper Motion of Neutron Stars
Some neutron stars are moving rapidly through interstellar space.
This might be a result of anisotropies during the supernova explosion forming the neutron star

19. Binary Pulsars
Some pulsars form binaries with other neutron stars (or black holes).
Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth...
…and shorten the pulsar period when it is approaching Earth.

20. Neutron Stars in Binary Systems: X-ray Binaries
Example: Her X-1
Star eclipses neutron star and accretion disk periodically
2 Msun (F-type) star
Neutron star
Orbital period = 1.7 days
Accretion disk material heats to several million K => X-ray emission

21. Pulsar Planets Some pulsars have planets orbiting around them.
Just like in binary pulsars, this can be discovered through variations of the pulsar period.
As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period.

22. Neutron stars can not exist with masses > 3 Msun
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars:
Neutron stars can not exist with masses > 3 Msun
We know of no mechanism to halt the collapse of a compact object with > 3 Msun.
It will collapse into a single point – a singularity:
=> A Black Hole!

23. Escape Velocity vesc vesc vesc
Velocity needed to escape Earth’s gravity from the surface: vesc ≈ 11.6 km/s.
vesc
Now, gravitational force decreases with distance (~ 1/d2) => Starting out high above the surface => lower escape velocity.
vesc
vesc
If you could compress Earth to a smaller radius => higher escape velocity from the surface.

24. The Schwarzschild Radius
=> There is a limiting radius where the escape velocity reaches the speed of light, c:
____
2GM
Rs =
Vesc = c c2
G = Universal const. of gravity
M = Mass
Rs is called the Schwarzschild Radius.

25. Schwarzschild Radius and Event Horizon
No object can travel faster than the speed of light
=> nothing (not even light) can escape from inside the Schwarzschild radius
We have no way of finding out what’s happening inside the Schwarzschild radius.
“Event horizon”

26. Schwarzschild Radius of Black Hole
(SLIDESHOW MODE ONLY)

27. Black Holes in Supernova Remnants
Some supernova remnants with no pulsar / neutron star in the center may contain black holes.

28. Schwarzschild Radii

29. “Black Holes Have No Hair”
Matter forming a black hole is losing almost all of its properties.
Black Holes are completely determined by 3 quantities:
Mass
Angular Momentum
(Electric Charge)

30. General Relativity Effects Near Black Holes
An astronaut descending down towards the event horizon of the BH will be stretched vertically (tidal effects) and squeezed laterally.

31. General Relativity Effects Near Black Holes (2)
Time dilation
Clocks starting at 12:00 at each point.
After 3 hours (for an observer far away from the BH):
Clocks closer to the BH run more slowly.
Time dilation becomes infinite at the event horizon.
Event Horizon

32. General Relativity Effects Near Black Holes (3)
Gravitational Red Shift
All wavelengths of emissions from near the event horizon are stretched (red shifted).
 Frequencies are lowered.
Event Horizon

33. Observing Black Holes Mass > 3 Msun => Black hole!
No light can escape a black hole
=> Black holes can not be observed directly.
If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and radial velocity.
Mass > 3 Msun
=> Black hole!

34. End States of Stars
(SLIDESHOW MODE ONLY)

35. Candidates for Black Hole
Compact object with > 3 Msun must be a black hole!

36. Compact Objects with Disks and Jets
Black holes and neutron stars can be part of a binary system.
Matter gets pulled off from the companion star, forming an accretion disk.
=> Strong X-ray source!
Heats up to a few million K.

37. X-Ray Bursters Several bursting X-ray sources have been observed:
Rapid outburst followed by gradual decay
Repeated outbursts: The longer the interval, the stronger the burst

38. The X-Ray Burster 4U 1820-30 In the cluster NGC 6624 Optical
Ultraviolet

39. Black-Hole vs. Neutron-Star Binaries
Black Holes: Accreted matter disappears beyond the event horizon without a trace.
Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the neutron star surface.

40. Black Hole X-Ray Binaries
Accretion disks around black holes
Strong X-ray sources
Rapidly, erratically variable (with flickering on time scales of less than a second)
Sometimes: Quasi-periodic oscillations (QPOs)
Sometimes: Radio-emitting jets

41. Radio Jet Signatures
The radio jets of the Galactic black-hole candidate GRS

42. Model of the X-Ray Binary SS 433
Optical spectrum shows spectral lines from material in the jet.
Two sets of lines: one blue-shifted, one red-shifted
Line systems shift back and forth across each other due to jet precession

43. Gamma-Ray Bursts (GRBs)
Short (~ a few s), bright bursts of gamma-rays
GRB of May 10, 1999: 1 day after the GRB
2 days after the GRB
Later discovered with X-ray and optical afterglows lasting several hours – a few days
Many have now been associated with host galaxies at large (cosmological) distances.
Probably related to the deaths of very massive (> 25 Msun) stars.

44. New Terms neutron star pulsar lighthouse model pulsar wind glitch
magnetar
gravitational radiation
millisecond pulsar
singularity
black hole
event horizon
Schwarzschild radius (RS)
Kerr black hole
ergosphere
time dilation
gravitational red shift
X-ray burster
quasi-periodic oscillations (QPOs)
gamma-ray burster
soft gamma-ray repeater (SGR)
hypernova
collapsar

45. Discussion Questions
1. Has the existence of neutron stars been sufficiently tested to be called a theory, or should it be called a hypothesis? What about the existence of black holes?
2. Why would you expect an accretion disk around a star the size of the sun to be cooler than an accretion disk around a compact object?
3. In this chapter, we imagined what would happen if we jumped into a Schwarzschild black hole. From what you have read, what do you think would happen to you if you jumped into a Kerr black hole?

46. Quiz Questions
1. What is the lower limit for the mass of neutron stars?
a. About 0.08 solar masses.
b. About 0.4 solar masses
c. Exactly 1 solar mass.
d. About 1.4 solar masses.
e. Between 2 and 3 solar masses.

47. Quiz Questions
2. White dwarfs and neutron stars are both end products of stellar evolution. White dwarfs are composed of mostly carbon, oxygen, and electrons, whereas neutron stars are composed of mostly neutrons. What happens to the protons in the atomic nuclei and the degenerate electrons that were inside the star that creates a neutron star?
a. The protons and electrons, being charged particles, are all ejected during the supernova event by the strong magnetic field.
b. The electrons and protons combine to form neutrons and neutrinos.
c. Protons decay into neutrons and positrons and neutrinos. The positrons combine with the electrons and form pairs of gamma rays.
d. The protons remain in the neutron star and the electrons are ejected by the magnetic field.
e. Our understanding of atomic nuclei is not yet good enough to determine what happens to them.

48. Quiz Questions
3. Why don't we use visible-wavelength telescopes to locate neutron stars?
a. Neutron stars have wavelengths of maximum intensity in the X-ray band of the electromagnetic spectrum.
b. Neutron stars are too cold to emit visible light.
c. Neutron stars have strong magnetic fields.
d. Neutron stars pulse too rapidly.
e. Neutron stars are very small.

49. Quiz Questions
4. What prevents neutron stars from contracting to a smaller size?
a. Gas pressure fueled by hydrogen fusion.
b. Gas pressure fueled by helium fusion.
c. Gas pressure fueled by carbon fusion.
d. Degenerate neutrons.
e. Degenerate electrons.

50. Quiz Questions 5. Why do we expect that neutron stars spin rapidly?
a. The law of conservation of energy.
b. The law of conservation of angular momentum.
c. Equatorial jets spin them up.
d. Both a and b above.
e. All of the above.

51. Quiz Questions 6. Why are pulsars so hot? a. Helium flash.
b. The CNO cycle proceeds rapidly.
c. Active fusion of elements heavier than carbon.
d. Gravitational energy was converted into thermal energy during formation.
e. Active fusion of elements heavier than iron produces vast amounts of energy.

52. Quiz Questions
7. Why does the short length of pulsar pulses eliminate normal stars as possible pulsars?
a. Normal stars are unchanging and eternal.
b. Normal stars are too cool to emit radio pulses.
c. Normal stars do not have strong enough magnetic fields.
d. The small size of normal stars prohibits the emission of pulses this short.
e. An object cannot emit pulses that are shorter than the time it takes light to cross its diameter.

53. Quiz Questions 8. How can a neutron star not be a pulsar?
a. Its magnetic field may be too weak to generate beams of radiation.
b. A pulsar may be too old and rotate too slowly to pulse.
c. A pulsar's magnetic field may not sweep past Earth.
d. Both a and b above.
e. All of the above.

54. Quiz Questions
9. What type of pulsars have been observed to emit visible pulses?
a. Young pulsars.
b. Slow pulsars.
c. Old pulsars.
d. Nearby pulsars.
e. Both b and c above.

55. Quiz Questions
10. Why are all pulsars not located in supernova remnants?
a. Pulsars persist longer than supernova remnants.
b. Some pulsars given high velocities upon formation can flee the scene of destruction.
c. Some pulsars are the result of mergers rather than supernova events.
d. Both a and b above.
e. All of the above.

56. Quiz Questions 11. Why do the millisecond pulsars spin so fast?
a. They have all been formed recently.
b. The impact of a large planet has spun them up.
c. Accretion of matter from a nearby binary companion spins them up.
d. Their strong magnetic field couples with the interstellar magnetic field.
e. They really spin at half their pulse rate, as both magnetic poles sweep past Earth.

57. Quiz Questions
12. Which of the following is an accurate description of the Schwarzschild radius?
a. It is the radius of a black hole singularity.
b. It is the radius to which an object must shrink to become a black hole.
c. It is the radius of the event horizon surrounding a black hole singularity.
d. Both a and b above.
e. Both b and c above.

58. Quiz Questions
13. What is the difference between a Schwarzschild black hole and a Kerr black hole?
a. Mass.
b. Electric charge.
c. Angular momentum.
d. Both b and c above.
e. All of the above.

59. Quiz Questions
14. What changes would occur if the Sun were replaced with a one-solar-mass black hole?
a. Earth's orbit would not change.
b. Earth would be sucked into the Sun.
c. The planets would disappear from view.
d. Extreme tidal forces would severely fracture Earth's lithosphere.
e. Both a and c above.

60. Quiz Questions
15. What property does matter inside the event horizon of a black hole retain?
a. Mass.
b. Mass and angular momentum.
c. Mass, angular momentum, and electric charge.
d. Mass, angular momentum, electric charge, and temperature.
e. Mass, angular momentum, electric charge, temperature, and luminosity.

61. Quiz Questions
16. Which of the following describes the gravitational red shift?
a. The reddening of starlight by interstellar dust grains.
b. A reduction in the energy of photons as they move away from objects.
c. The angular change in a star's position when observed during a solar eclipse.
d. The alternating Doppler effect due to two bodies whose orbital plane contains our line of sight.
e. We are unable to tell whether an object is moving away from us or we are moving away from the object.

62. Quiz Questions
17. What observational evidence do we have that stellar death black holes really exist?
a. Hollowed-out green spheres are sucking up matter in star forming regions and emitting gamma rays.
b. Some X-ray binaries have an unseen object with masses greater than 3 solar masses.
c. Some X-ray binaries emit pulses of radiation at radio wavelengths.
d. We see areas that block the light from more distant objects.
e. The observed glitches in the periods of pulsars.

63. Quiz Questions
18. What is the source of the continuous X-rays emitted by a close binary system that contains a compact object?
a. The system’s magnetic field accelerates ionized matter, emitting synchrotron radiation.
b. An accretion disk around the compact object is heated by friction.
c. Matter impacting the surface of the compact object.
d. The companion star is superheated by tidal forces.
e. The hot surface of the compact object.

64. Quiz Questions
19. Some X-ray novae emit bursts of energy and others do not. In addition, those with energy bursts are about 100 times as luminous as those without bursts. What type of compact objects are responsible for these two types of X-ray novae?
a. Those with bursts contain black holes and those without bursts contain neutron stars.
b. Those with bursts contain neutron stars and those without bursts contain black holes.
c. Those with bursts contain white dwarfs and those without bursts contain neutron stars.
d. Those with bursts contain neutron stars and those without bursts contain white dwarfs.
e. Those with bursts contain black holes and those without bursts contain white dwarfs.

65. Quiz Questions
20. What may be responsible for the observed gamma ray bursters?
a. Neutron star merger.
b. Hypernovae.
c. Magnetars.
d. Both a and b above.
e. All of the above.

66. Answers
1. d
2. b
3. e
4. d
5. b
6. d
7. e
8. e
9. a
10. d
11. c
12. e
13. c
14. e
15. c
16. b
17. b
18. b
19. b
20. d