1. Chapter 10 Measuring the Stars

2. 10.1 The Solar Neighborhood
Parallax: look at apparent motion of object against distant background from two vantage points; knowing baseline allows calculation of distance

3. 10.1 The Solar Neighborhood
Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex

4. 10.1 The Solar Neighborhood
Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex
The “auditorium scale model”:

5. 10.1 The Solar Neighborhood
Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex
The “auditorium scale model”:
Sun is a BB, Earth is a biological cell orbiting 21.5 cm away

6. 10.1 The Solar Neighborhood
Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex
The “auditorium scale model”:
Sun is a BB, Earth is a biological cell orbiting 21.5 cm away
Nearest star (Proxima Centauri) is another BB 57 km away (in St Augustine)

7. 10.1 The Solar Neighborhood
Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex
The “auditorium scale model”:
Sun is a BB, Earth is a biological cell orbiting 21.5 cm away
Nearest star (Proxima Centauri) is another BB 57 km away (in St Augustine)
Solar system extends to near the top of the steps about 10 m from Sun; rest of distance to nearest star is basically empty

8. 10.1 The Solar Neighborhood
The 30 closest stars to the Sun:

9. End of 2 April 2007 Lecture

10. 10.1 The Solar Neighborhood
Barnard’s Star (top) has the largest proper motion of any star –

11. 10.1 The Solar Neighborhood
Barnard’s Star (top) has the largest proper motion of any star – proper motion is the actual shift of the star in the sky, after correcting for parallax.

12. 10.1 The Solar Neighborhood
Barnard’s Star (top) has the largest proper motion of any star – proper motion is the actual shift of the star in the sky, after correcting for parallax.
88 km/s

13. 10.1 The Solar Neighborhood
Barnard’s Star (top) has the largest proper motion of any star – proper motion is the actual shift of the star in the sky, after correcting for parallax.
The pictures in (a) were taken 22 years apart.

14. 10.1 The Solar Neighborhood
Barnard’s Star (top) has the largest proper motion of any star – proper motion is the actual shift of the star in the sky, after correcting for parallax.
The pictures in (a) were taken 22 years apart. (b) shows the actual motion of the Alpha Centauri complex.

15. 10.2 Luminosity and Apparent Brightness
Luminosity, or absolute brightness, is a measure of the total power radiated by a star.
Apparent brightness is how bright a star appears when viewed from Earth; it depends on the absolute brightness but also on the distance of the star:

16. 10.2 Luminosity and Apparent Brightness
This is an example of an inverse square law

17. 10.2 Luminosity and Apparent Brightness
As an exact equality instead of a proportionality:

18. 10.2 Luminosity and Apparent Brightness
So two stars that appear equally bright

19. 10.2 Luminosity and Apparent Brightness
So two stars that appear equally bright

20. 10.2 Luminosity and Apparent Brightness
So two stars that appear equally bright might be identical stars the same distance from us…

21. 10.2 Luminosity and Apparent Brightness
Or they might be a closer, dimmer star and a farther, brighter one:

22. 10.2 Luminosity and Apparent Brightness
Apparent brightness can also be measured using a magnitude scale, which is related to our perception.

23. 10.2 Luminosity and Apparent Brightness
Apparent brightness can also be measured using a magnitude scale, which is related to our perception.
It is a logarithmic scale; a change of 5 in magnitude corresponds to a change of a factor of 100 in apparent brightness.

24. 10.2 Luminosity and Apparent Brightness
Apparent brightness can also be measured using a magnitude scale, which is related to our perception.
It is a logarithmic scale; a change of 5 in magnitude corresponds to a change of a factor of 100 in apparent brightness.
It is also inverted – larger (more positive) magnitudes are dimmer.

25. 10.2 Luminosity and Apparent Brightness
The magnitudes listed here are apparent magnitudes

26. 10.2 Luminosity and Apparent Brightness
The magnitudes listed here are apparent magnitudes
Apparent magnitude is related to apparent brightness

27. 10.2 Luminosity and Apparent Brightness
The magnitudes listed here are apparent magnitudes
Apparent magnitude is related to apparent brightness
But luminosity is related to absolute magnitude

28. 10.2 Luminosity and Apparent Brightness
The magnitudes listed here are apparent magnitudes
Apparent magnitude is related to apparent brightness
But luminosity is related to absolute magnitude
Absolute magnitude = apparent magnitude at 10 parsecs

29. 10.2 Luminosity and Apparent Brightness
An equation relating apparent and absolute magnitudes to distance is

30. 10.2 Luminosity and Apparent Brightness
This is equivalent to the previous equation relating distance, apparent brightness, and luminosity

31. 10.2 Luminosity and Apparent Brightness
So there are two equations relating distance to apparent brightness and luminosity:

32. 10.3 Stellar Temperatures
The color of a star is indicative of its temperature. Red stars are relatively cool, while blue ones are hotter.

33. 10.3 Stellar Temperatures
The radiation from stars is blackbody radiation; as the blackbody curve is not symmetric, observations at two wavelengths are enough to define the temperature:

34. 10.3 Stellar Temperatures
Stellar spectra are much more informative than the blackbody curves.
There are seven general categories of stellar spectra, corresponding to different temperatures.
From highest to lowest, those categories – called spectral classes or spectral types – are:
O B A F G K M

35. 10.3 Stellar Temperatures
The seven spectral types:

36. 10.3 Stellar Temperatures
The different spectral classes have distinctive absorption lines.

37. 10.4 Stellar Sizes
A few very large, very close stars can be imaged directly using speckle interferometry; this is Betelgeuse:

38. 10.4 Stellar Sizes
For the vast majority of stars that cannot be imaged directly, size must be calculated knowing the luminosity and temperature:
Giant stars have radii between 10 and 100 times the Sun’s.
Dwarf stars have radii equal to, or less than, the Sun’s.
Supergiant stars have radii more than 100 times the Sun’s.

39. 10.4 Stellar Sizes
Stellar radii vary widely:

40. 10.5 The Hertzsprung-Russell Diagram
The H-R diagram plots stellar luminosity against surface temperature.
This is an H-R diagram of a few prominent stars

41. 10.5 The Hertzsprung-Russell Diagram
The H-R diagram plots stellar luminosity against surface temperature.
This is an H-R diagram of a few prominent stars
There is not very much of a pattern

42. 10.5 The Hertzsprung-Russell Diagram
Once many stars are plotted on an H-R diagram, a pattern begins to form:

43. 10.5 The Hertzsprung-Russell Diagram
Once many stars are plotted on an H-R diagram, a pattern begins to form:
These are the 80 closest stars to us (within ~5 pc); note lines of constant radius.

44. 10.5 The Hertzsprung-Russell Diagram
Once many stars are plotted on an H-R diagram, a pattern begins to form:
These are the 80 closest stars to us (within ~5 pc); note lines of constant radius.
The darkened curve is called the Main Sequence, as this is where most stars are.

45. 10.5 The Hertzsprung-Russell Diagram
Once many stars are plotted on an H-R diagram, a pattern begins to form:
These are the 80 closest stars to us (within ~5 pc); note lines of constant radius.
The darkened curve is called the Main Sequence, as this is where most stars are.
Also indicated is the white dwarf region; these stars are hot but not very luminous, as they are quite small.

46. 10.5 The Hertzsprung-Russell Diagram
Once many stars are plotted on an H-R diagram, a pattern begins to form:
These are the 80 closest stars to us (within ~5 pc); note lines of constant radius.
The darkened curve is called the Main Sequence, as this is where most stars are.
Also indicated is the white dwarf region; these stars are hot but not very luminous, as they are quite small.
Note that most of the closest stars are not very luminous

47. 10.5 The Hertzsprung-Russell Diagram
An H-R diagram of the 100 brightest stars looks quite different:

48. 10.5 The Hertzsprung-Russell Diagram
An H-R diagram of the 100 brightest stars looks quite different:
These stars are all more luminous than the Sun. Two new categories appear here – the red giants and the blue giants.

49. 10.5 The Hertzsprung-Russell Diagram
An H-R diagram of the 100 brightest stars looks quite different:
These stars are all more luminous than the Sun. Two new categories appear here – the red giants and the blue giants.
Clearly, the brightest stars in the sky appear bright because of their enormous luminosities, not their proximity.

50. 10.5 The Hertzsprung-Russell Diagram
An H-R diagram of the 100 brightest stars looks quite different:
These stars are all more luminous than the Sun. Two new categories appear here – the red giants and the blue giants.
Clearly, the brightest stars in the sky appear bright because of their enormous luminosities, not their proximity.
Very few very luminous stars are nearby

51. End of 4 April 2007 Lecture

52. 10.5 The Hertzsprung-Russell Diagram
This is an H-R plot of about 20,000 stars. The main sequence is clear, as is the red giant region.
About 90% of stars lie on the main sequence; 9% are red giants and 1% are white dwarfs.

53. 10.6 Extending the Cosmic Distance Scale
The H-R diagram can be used to measure distances to stars

54. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax: has nothing to do with parallax, but does use spectroscopy in finding the distance to a star.

55. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax: has nothing to do with parallax, but does use spectroscopy in finding the distance to a star.
Measure the star’s apparent magnitude and spectral class

57. The seven spectral types:

58. 10.3 Stellar Temperatures
The different spectral classes have distinctive absorption lines.

59. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax: has nothing to do with parallax, but does use spectroscopy in finding the distance to a star.
Measure the star’s apparent magnitude and spectral class
Use spectral class to estimate luminosity

61. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax: has nothing to do with parallax, but does use spectroscopy in finding the distance to a star.
Measure the star’s apparent magnitude and spectral class
Use spectral class to estimate luminosity
Apply inverse-square law to find distance.

62. 10.6 Extending the Cosmic Distance Scale

63. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs:

64. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
But there is a problem…

65. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
But there is a problem…
Look at the steps again:

66. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
But there is a problem…
Look at the steps again:
Measure the star’s apparent magnitude and spectral class

67. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
But there is a problem…
Look at the steps again:
Measure the star’s apparent magnitude and spectral class
Use spectral class to estimate luminosity

68. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
But there is a problem…
Look at the steps again:
Measure the star’s apparent magnitude and spectral class
Use spectral class to estimate luminosity
Apply inverse-square law to find distance.

69. 10.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
But there is a problem…
Look at the steps again:
Measure the star’s apparent magnitude and spectral class
Use spectral class to estimate luminosity
Apply inverse-square law to find distance.

71. 10.6 Extending the Cosmic Distance Scale
The spectroscopic parallax calculation can be misleading if the star is not on the main sequence.

72. 10.6 Extending the Cosmic Distance Scale
The spectroscopic parallax calculation can be misleading if the star is not on the main sequence. The width of spectral lines can be used to define luminosity classes:

74. 10.6 Extending the Cosmic Distance Scale
The spectroscopic parallax calculation can be misleading if the star is not on the main sequence. The width of spectral lines can be used to define luminosity classes:

75. 10.6 Extending the Cosmic Distance Scale
In this way, giants and supergiants can be distinguished from main sequence stars.

76. 10.6 Extending the Cosmic Distance Scale
In this way, giants and supergiants can be distinguished from main sequence stars.
And that makes a difference:

77. Stellar
mass

78. One of the most important things about a star
Stellar
mass
One of the most important things about a star

79. Stellar
mass
How do we
find
it?

80. 10.7 Stellar Masses
Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.

81. 10.7 Stellar Masses
Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.

82. 10.7 Stellar Masses
Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.
Orbits of visual binaries can be observed directly.

83. 10.7 Stellar Masses
Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.
Orbits of visual binaries can be observed directly.
Doppler shifts in spectroscopic binaries allow measurement of motion.

84. 10.7 Stellar Masses
Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.
Orbits of visual binaries can be observed directly.
Doppler shifts in spectroscopic binaries allow measurement of motion.
The period of eclipsing binaries can be measured using intensity variations.

85. 10.7 Stellar Masses

86. 10.7 Stellar Masses

87. 10.7 Stellar Masses
Mass is the main determinant of where a star will be on the Main Sequence:

89. 10.7 Stellar Masses
Stellar mass distributions – there are many more small stars than large ones!

91. The central temperature goes up only slightly with mass

92. The central temperature goes up only slightly with mass
But the luminosity goes up much faster

93. The central temperature goes up only slightly with mass
But the luminosity goes up much faster
This is because the rate of fusion increases nearly as the fourth power of temperature

94. The central temperature goes up only slightly with mass
But the luminosity goes up much faster
This is because the rate of fusion increases nearly as the fourth power of temperature
So it increases much faster than the mass does

95. The central temperature goes up only slightly with mass
But the luminosity goes up much faster
This is because the rate of fusion increases nearly as the fourth power of temperature
So it increases much faster than the mass does
This allows us to estimate the lifetime of a star

98. Summary of Chapter 10
Distance to nearest stars can be measured by parallax
Apparent brightness is as observed from Earth; depends on distance and absolute luminosity
Spectral classes correspond to different surface temperatures
Stellar size is related to luminosity and temperature

99. Summary of Chapter 10
H-R diagram is plot of luminosity vs. temperature; most stars lie on main sequence
Distance ladder can be extended using spectroscopic parallax
Masses of stars in binary systems can be measured
Mass determines where star lies on main sequence