1. Chapter 15 Surveying the Stars

2. 15.1 Properties of Stars Our goals for learning
How do we measure stellar luminosities?
How do we measure stellar temperatures?
How do we measure stellar masses?

3. How do we measure stellar luminosities?

4. The apparent brightness (flux) of a star depends
on both distance and luminosity

5. Power output at source (energy per second = Watts)
Luminosity: O
Power output at source (energy per second = Watts)
Flux (apparent brightnesss):
Amount of starlight that reaches Earth =
(watts per square meter)

6. Luminosity (power) passing through each sphere is the same
R = radius of sphere
Surface area of sphere A = 4πR2
Divide luminosity by area to get apparent brightness
Called ‘flux’.
f = L/4πR2

7. We can determine a star’s luminosity if we can measure its distance and flux:
L = 4π R2 f
Luminosity Distance Relation

8. Thought Question
How would the apparent brightness of Alpha Centauri change if it were three times farther away?
A. It would be only 1/3 as bright
B. It would be only 1/6 as bright
C. It would be only 1/9 as bright
D. It would be three times brighter

9. Thought Question
How would the apparent brightness of Alpha Centauri change if it were three times farther away?
A. It would be only 1/3 as bright
B. It would be only 1/6 as bright
C. It would be only 1/9 as bright
D. It would be three times brighter

10. So how far are these stars, if we would like their Luminosity?

11. Parallax: For stars closer than about 1000 Lyrs, we use
the apparent shift in position of a nearby object against a background of more distant objects
Intro_to_parllax.swf

12. Apparent positions of nearest stars shift by a little less than an arc-second as Earth orbits Sun

13. Parallax angle depends on distance
Parallax_angle_vs_distance.swf

14. Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star

16. Parallax and Distance

17. Most luminous stars:
106 LSun
Least luminous stars:
10-4 LSun
(LSun is luminosity of Sun)

18. The Magnitude Scale (traditional apparent brightness—flux has easier math) Hipparchus rated visible stars from m = A 1 is 2.52 times brighter than a 2, for example.

19. How do we measure stellar temperatures?

20. Every object emits thermal radiation with a spectrum that depends on its temperature

21. An object of fixed size grows more luminous as its temperature rises
L = σT^4
Surface must be at constant temperature.
Temp_and_luminosity.swf

22. Properties of Thermal Radiation
Hotter objects emit more light per unit area at all frequencies.
Hotter objects emit photons with peak with shorter wavelength.
Remind students that the intensity is per area; larger objects can emit more total light even if they are cooler.

23. Hottest stars:
50,000 K
Coolest stars:
3,000 K
(Sun’s surface is 5,800 K)

24. Level of ionization also reveals a star’s temperature
106 K
Level of ionization also reveals a star’s temperature
105 K
Ionized
Gas
(Plasma)
104 K
103 K
Neutral Gas
Molecules
102 K
10 K
Solid

25. The relative darkness of particular Absorption lines in star’s
spectrum tell us its ionization level.

26. Darkness of lines in a star’s spectrum correspond to a spectral type that reveals its temperature (Annie Jump Cannon 1912)
(Hottest) O B A F G K M (Coolest)

27. (Hottest) O B A F G K M (Coolest)
Remembering Spectral Types
(Hottest) O B A F G K M (Coolest)
Oh, Be A Fine Girl (Guy), Kiss Me
Only Boys Accepting Feminism Get Kissed Meaningfully

28. Which kind of star is hottest?
Thought Question
Which kind of star is hottest?
A. M star
B. F star
C. A star
D. K star

29. Which kind of star is hottest?
Thought Question
Which kind of star is hottest?
A. M star
B. F star
C. A star
D. K star

30. Pioneers of Stellar Classification
Annie Jump Cannon and the “calculators” at Harvard laid the foundation of modern stellar classification AJ

31. How do we measure stellar masses?

32. The orbit of a binary star system depends on strength of gravity
I’m not sure where this came from, if it’s not on the CD, let me know.
The orbit of a binary star system depends on strength of gravity

33. Types of Binary Star Systems
Visual Binary
Eclipsing Binary
Spectroscopic Binary
About half of all stars are in multiple systems
(mostly binaries).

34. Visual Binary
We can directly observe the orbital motions of these stars

35. Eclipsing Binary We can measure periodic eclipses
Download an eclipsing binary animation from:
We can measure periodic eclipses

36. Spectroscopic Binary
Download a spectroscopic binary animation from:
R. Pogge, Ohio State University
We determine the orbit by measuring Doppler shifts

37. We can measure mass using gravity (later we learn other ways)
We can measure mass using gravity (later we learn other ways). For binary star systems, know one mass and get the other from orbital period and average separation.
p = period
a = average separation
4π2
G (M1 + M2)
p2 = a3
Isaac Newton

38. Most massive stars:
130 MSun
Least massive stars:
0.08 MSun
(MSun is the mass of the Sun)

39. What have we learned? How do we measure stellar luminosities?
If we measure a star’s apparent brightness and distance, we can compute its luminosity with the inverse square law for light
Parallax tells us distances to the nearest stars
How do we measure stellar temperatures?
A star’s color and spectral type both reflect its temperature

40. 15.2 Patterns among Stars Our goals for learning
What is a Hertzsprung-Russell diagram?
What is the significance of the main sequence?
What are giants, supergiants, and white dwarfs?
Why do the properties of some stars vary?

41. What is a Hertzsprung-Russell diagram?

42. An H-R diagram plots the luminosity versus temperature of stars (going up to the left).

43. Generate_hr_diagr.swf

44. Most stars fall somewhere on the main sequence of the H-R diagram

45. Large radius --this corner giants and supergiants
Stars with lower T and higher L than main-sequence stars must have larger radii:
giants and supergiants

46. Small radius-- this corner. white dwarfs
Stars with higher T and lower L than main-sequence stars must have smaller radii:
white dwarfs
Small radius--
this corner.

47. A star’s full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star):
I - supergiant
II - bright giant
III - giant
IV - subgiant
V - main sequence
Examples: Sun - G2 V
Sirius - A1 V
Proxima Centauri - M5.5 V
Betelgeuse - M2 I

48. H-R diagram depicts: Temperature Color Spectral Type Luminosity Radius
Mass, if on
Main Sequence
Luminosity
Temperature

49. Which star is the hottest?B
Which star is the hottest? D
Luminosity A
Temperature

50. Which star is the hottest?B
Which star is the hottest? D
Luminosity A A
Temperature

51. Which star is the most luminous?B
Which star is the most luminous? D
Luminosity A
Temperature

52. C B
Which star is the most luminous? C D
Luminosity A
Temperature

53. C B
Which star is a main-sequence star? D
Luminosity A
Temperature

54. Which star is a main-sequence star?B
Which star is a main-sequence star? D D
Luminosity A
Temperature

55. C B
Which star has the largest radius? D
Luminosity A
Temperature

56. C B
Which star has the largest radius? C D
Luminosity A
Temperature

57. What is the significance of the main sequence?

58. Main-sequence stars are fusing hydrogen into helium in their cores like the Sun
Luminous main-sequence stars are hot (blue)
Less luminous ones are cooler (yellow or red)

59. Mass measurements of main-sequence stars show that the hot, blue stars are much more massive than the cool, red ones—Mass can thus be
Plotted going down as you go down the main sequence. MASS—
LUMINOSITY Relation.
High-mass stars
Low-mass stars

60. High-mass stars
The mass of a normal, hydrogen-burning star determines its luminosity and spectral type!
Low-mass stars

61. Core pressure and temperature of a higher-mass star need to be larger in order to balance gravity.
Higher core temperature boosts fusion rate, leading to larger luminosity.

62. Stellar Properties Luminosity: from brightness and distance
10-4 LSun LSun
Temperature: from color and spectral type
3,000 K ,000 K
Mass: from period (p) and average separation (a) of binary-star orbit (or mass-luminosity relation for main sequence stars).
0.08 MSun MSun

63. Stellar Properties Review
Luminosity: from brightness and distance
10-4 LSun LSun
Temperature: from color and spectral type
3,000 K ,000 K
Mass: from period (p) and average separation (a)
of binary-star orbit
0.08 MSun MSun
(0.08 MSun)
(100 MSun)
(0.08 MSun)
(100 MSun)

64. Mass & Lifetime
Sun’s life expectancy: 10 billion years

65. Mass & Lifetime Sun’s life expectancy: 9 billion years
Until core hydrogen
(10% of total) is
used up
Sun’s life expectancy: 9 billion years

66. Mass & Lifetime Sun’s life expectancy: 10 billion years
Until core hydrogen
(10% of total) is
used up
Sun’s life expectancy: 10 billion years
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 million years ~ 10 billion years x 10 / 104

67. Mass & Lifetime Sun’s life expectancy: 9 billion years
Until core hydrogen
(10% of total) is
used up
Sun’s life expectancy: 9 billion years
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 million years ~ 10 billion years x 10 / 104
Life expectancy of 0.1 MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
100 billion years ~ 10 billion years x 0.1 / 0.01

68. Main-Sequence Star Summary
High Mass:
High Luminosity
Short-Lived
Large Radius
Blue
Low Mass:
Low Luminosity
Long-Lived
Small Radius
Red

69. What are giants, supergiants, and white dwarfs?

70. Off the Main Sequence
Stellar properties depend on both mass and age: those that have finished fusing H to He in their cores are no longer on the main sequence
All stars become larger and redder after exhausting their core hydrogen: giants and supergiants
Small stars end up small and white after fusion has ceased: white dwarfs

71. Which star is most like our Sun?D
Luminosity B C
Temperature

72. A
Which star is most like our Sun? D B
Luminosity B C
Temperature

73. A
Which of these stars will have changed the least 10 billion years from now? D
Luminosity B C
Temperature

74. A
Which of these stars will have changed the least 10 billion years from now? D
Luminosity B C C
Temperature

75. A
Which of these stars can be no more than 10 million years old? D
Luminosity B C
Temperature

76. A
Which of these stars can be no more than 10 million years old? D
Luminosity A B C
Temperature

77. Why do the properties of some stars vary?

78. Variable Stars
Any star that varies significantly in brightness with time is called a variable star
Some stars vary in brightness because they cannot achieve proper balance between power welling up from the core and power radiated from the surface
Such a star alternately expands and contracts, varying in brightness as it tries to find a balance

79. Pulsating Variable Stars
The light curve of this pulsating variable star shows that its brightness alternately rises and falls over a 50-day period

80. Cepheid Variable Stars
Most pulsating variable stars inhabit an instability strip on the H-R diagram
The most luminous ones are known as Cepheid variables

81. 15.3 Star Clusters Our goals for learning
What are the two types of star clusters?
How do we measure the age of a star cluster?

82. What are the two types of star clusters?

83. Open cluster: A few thousand young (Pop I) stars: not bound.

84. Useful movies to download:
Globular cluster visualization
Stellar collision simulation:
Globular cluster: Up to a million or more stars bound together by gravity—these are generally very old (Population II).

85. How do we measure the age of a star cluster?

86. Pleiades now has no stars with life expectancy less than around 100 million years
Main-sequence
turnoff

87. Main-sequence turnoff point of a cluster tells us its age

88. To determine accurate ages, we compare models of stellar evolution to the cluster data
Hr_diagr_and_age_of_cluster.swf

89. Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old