1. Chapter 17

2. Chapter 17 The Stars
In 2013 the Hubble Space Telescope captured this spectacular image of the globular star cluster M15, a rich group of roughly 1 million stars spread across some 100 light-years of space. It lies 33,000 light-years away in the direction of the constellation Pegasus, and is estimated to be 12 billion years—more than twice the age of the Sun. Its central regions represent one of the densest stellar environments known in our Galaxy, with 100,000 stars packed into a volume a few light-years across–the distance from our Sun to its nearest neighbor in space. (ESA/NASA)

3. Units of Chapter 17 17.1 The Solar Neighborhood
17.2 Luminosity and Apparent Brightness
17.3 Stellar Temperatures
More Precisely 17-1 More on the Magnitude Scale
17.4 Stellar Sizes
More Precisely 17-2 Estimating Stellar Radii
17.5 The Hertzsprung–Russell Diagram

4. Units of Chapter 17 (cont.)
17.6 Extending the Cosmic Distance Scale
17.7 Stellar Masses
More Precisely 17-3 Measuring Stellar Masses in Binary Stars
17.8 Mass and Other Stellar Properties

5. 17.1 The Solar Neighborhood
Remember that stellar distances can be measured using parallax
Figure Stellar Parallax (a) For observations of stars made 6 months apart, the baseline is twice the Earth–Sun distance, or 2 AU. Compare with Figure 1.30, which shows the same geometry, but on a much smaller scale. (b) The parallactic shift (exaggerated here, and indicated by the white arrow) is usually measured photographically, as illustrated by the red star seen here. Images of the same region of the sky made at different times of the year determine a star’s apparent movement relative to background stars.

6. 17.1 The Solar Neighborhood
Nearest star to the Sun: Proxima Centauri, which is a member of the three-star system Alpha Centauri complex
Model of distances:
Sun is a marble, Earth is a grain of sand orbiting 1 m away
Nearest star is another marble 270 km away
Solar system extends about 50 m from Sun; rest of distance to nearest star is basically empty

7. 17.1 The Solar Neighborhood
The 30 closest stars to the Sun
Figure The Solar Neighborhood A plot of the 30 closest stars to the Sun, projected so as to reveal their three-dimensional relationships. All lie within 4 pc (about 13 light-years) of Earth. The circular gridlines represent distances from the Sun in the galactic plane; the vertical lines denote distances perpendicular to that plane.

8. 17.2 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.

9. 17.2 Luminosity and Apparent Brightness
Therefore, two stars that appear equally bright might be a closer, dimmer star and a farther, brighter one
Figure Luminosity Two stars A and B of different luminosities can appear equally bright to an observer on Earth if the brighter star B is more distant than the fainter star A.

10. 17.2 Luminosity and Apparent Brightness
Apparent luminosity is 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 magnitudes are dimmer.
Figure Apparent Magnitude This graph illustrates the apparent magnitudes of some astronomical objects and the limiting magnitudes (i.e., the faintest magnitudes attainable) of some telescopes used to observe them. (NASA; Photodisc/Getty Images; Irving Lindenblad/U.S. Naval Observatory; NASA; AURA)

11. 17.2 Luminosity and Apparent Brightness
If we know a star’s apparent magnitude and its distance from us, we can calculate its absolute luminosity.
Figure Inverse-Square Law As light moves away from a source such as a star, it steadily dilutes while spreading over progressively larger surface areas (depicted here as sections of spherical shells). Thus, the amount of radiation received by a detector (the source’s apparent brightness) varies inversely as the square of its distance from the source.

12. 17.3 Stellar Temperatures
The color of a star is indicative of its temperature. Red stars are relatively cool, whereas blue ones are hotter.
Figure Star Colors (a) The different colors of the stars composing the constellation Orion are easily distinguished in this photograph taken by a wide-field camera attached to a small telescope. The bright red star at the upper left is Betelgeuse (α); the bright blue-white star at the lower right is Rigel (β). (Compare with Figure 1.8.) The field of view of this photograph is wide, about 20° across. (b) An incredibly rich field of colorful stars, this time in the direction of the center of the Milky Way. Here, the field of view is just 2 arc minutes across—much smaller than in (a). (Pere Sanz/Alamy Stock Photo; J. Trauger/NASA/JPL)

13. 17.3 Stellar Temperatures Here are their spectra:
Figure Stellar Spectra Comparison of spectra observed for seven different stars having a range of surface temperatures. These are not actual spectra, which are messy and complex, but simplified artists’ renderings illustrating notable spectral features. The spectra of the hottest stars, at the top, show lines of helium and multiply ionized heavy elements. In the coolest stars, at the bottom, helium lines are absent, but lines of neutral atoms and molecules are plentiful. At intermediate temperatures, hydrogen lines are strongest.

14. 17.3 Stellar Temperatures
Characteristics of the spectral classifications

15. 17.4 Stellar Sizes
A few very large, very close stars can be imaged directly using the Hubble Space Telescope. This is Betelgeuse.
Figure Betelgeuse (a) The supergiant star Betelgeuse is large enough and close enough for astronomers to resolve its size directly. At its largest, the variable star Betelgeuse is roughly 600 times the size of the Sun, making its photosphere comparable to Jupiter’s orbit. This false color ultraviolet view was taken by the Hubble Space Telescope. Hints of surface features, thought to be storms similar to (but much larger than) those found on the Sun, can be seen. (b) These infrared views of Betelgeuse from the Very Large Telescope in Chile show the swollen star puffing out huge plumes of gas into its surroundings. (NASA/ESA/ESO)

16. 17.4 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

17. 17.4 Stellar Sizes Stellar radii vary widely
Figure Stellar Sizes Illustrated here are the different sizes of several well-known stars. Only part of the red-giant star Antares can be shown on this scale, and the supergiant Betelgeuse would fill the entire page.

18. 17.5 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.
Figure H–R Diagram of Well-Known Stars A plot of luminosity against surface temperature (or spectral class) is a useful way to compare stars. Plotted here are the data for some stars mentioned earlier in the text. The Sun, which has a luminosity of 1 solar unit and a temperature of 5800 K, is a G-type star. The B-type star Rigel, at top left, has a temperature of about 11,000 K and a luminosity more than 10,000 times that of the Sun. The M-type star Proxima Centauri, at bottom right, has a temperature of about 3000 K and a luminosity less than 1/10,000 that of the Sun. (See also Overlay 1 of the acetate insert.)

19. 17.5 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; note the dashed 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.
Figure H–R Diagram of Nearby Stars Most stars have properties within the long, thin, shaded region of the H–R diagram known as the main sequence. The points plotted here are for stars lying within about 5 pc of the Sun. Each dashed diagonal line corresponds to a constant stellar radius.

20. 17.5 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.
Figure H–R Diagram of Brightest Stars An H–R diagram for the 100 brightest stars in the sky is biased in favor of the most luminous stars—which appear toward the upper left—because we can see them more easily than we can the faintest stars. (Compare with Figure 17.14, which shows only the closest stars.)

21. 17.5 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.
Figure Hipparcos H–R Diagram This simplified version of one of the most complete H–R diagrams ever compiled represents more than 20,000 data points, as measured by the European Hipparcos spacecraft for stars within a few hundred parsecs of the Sun.

22. 17.6 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

23. 17.6 Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
Figure Stellar Distances Knowledge of a star’s luminosity and apparent brightness can yield an estimate of its distance. Astronomers use this third rung on the distance ladder, called spectroscopic parallax, to measure distances as far out as individual stars can be clearly discerned—several thousand parsecs.

24. 17.7 Stellar Masses
Spectroscopic binaries can be measured using their Doppler shifts—analogous to extrasolar planets measured using star wobble
Figure Spectroscopic Binary Properties of binary stars can be determined by measuring the periodic Doppler shift of one star relative to the other while moving in their orbits. This is a single-line system, in which only one spectrum (from the brighter component) is visible.

25. 17.7 Stellar Masses
Finally, eclipsing binaries can be measured using the changes in luminosity—analogous to measuring transiting exoplanets
Figure Eclipsing Binary If the two stars in a binary-star system eclipse one another, additional information on their radii and masses can be obtained by observing the periodic decrease in starlight as one star passes in front of the other.

26. 17.7 Stellar Masses
Mass is the main determinant of where a star will be on the main sequence
Figure Stellar Masses More than any other stellar property, mass determines a star’s position on the main sequence. Low-mass stars are cool and faint; they lie at the bottom of the main sequence. Very massive stars are hot and bright; they lie at the top of the main sequence.

27. 17.8 Mass and Other Stellar Properties
This pie chart shows the distribution of stellar masses. The more massive stars are much rarer than the least massive.
Figure Stellar Mass Distribution The range of masses of main-sequence stars, as determined from careful measurement of stars in the solar neighborhood.

28. 17.8 Mass and Other Stellar Properties
Mass is correlated with radius and is very strongly correlated with luminosity
Figure Stellar Radii and Luminosities (a) Dependence of stellar radius on mass for main-sequence stars. Actual measurements show that the radius increases nearly in proportion to the mass over much of the range (as indicated by the straight line drawn through the data points). (b) Dependence of main-sequence luminosity on mass. The luminosity increases roughly as the fourth power of the mass. (indicated again by the straight line)

29. 17.8 Mass and Other Stellar Properties
Mass is also related to stellar lifetime
Using the mass–luminosity relationship

30. 17.8 Mass and Other Stellar Properties
So the most massive stars have the shortest lifetimes—they have a lot of fuel but burn it at a very rapid pace.
On the other hand, small red dwarfs burn their fuel extremely slowly and can have lifetimes of a trillion years or more.