1. Chapter 11: Characterizing Stars

2. The Inverse-Square Law
FIGURE 11-3 The Inverse-Square Law (a) This drawing
shows how the same amount of radiation from a light source
must illuminate an ever-increasing area as the distance from the
light source increases. The decrease in brightness follows the
inverse-square law, which means, for example, that tripling the
distance decreases the brightness by a factor of 9.
The same amount of radiation from a light source must illuminate an ever-increasing area as the distance from the light source increases. The decrease in brightness follows the inverse-square law. This means, for example, that tripling the distance decreases the brightness by a factor of 9.

3. Temperature and Color
FIGURE 11-4 Temperature and Color (a) This beautiful Hubble Space Telescope image shows the variety of
colors of stars. (b) This diagram shows the relationship between the color of a star and its surface
temperature. The intensity of light emitted by three hypothetical stars is plotted against wavelength (compare
with Figure 4-2). The range of visible wavelengths is indicated. Where the peak of a star’s intensity curve lies
relative to the visible light band determines the apparent color of its visible light. The insets show stars of about
these surface temperatures. UV stands for ultraviolet, which extends to 10 nm. See Figure 3-4 for more on
wavelengths of the spectrum. (a: Hubble Heritage Team/AURA/STScI/NASA; left inset: Andrea Dupree/Harvard-
Smithsonian CFA, Ronald Gilliland/STScI, NASA and ESA; center inset: NSO/AURA/NSF; right inset: Till Credner, Allthesky.com)
The intensity of light emitted by three hypothetical stars is plotted against wavelength. The range of visible wavelengths is indicated. Where the peak of a star’s intensity curve lies relative to the visible light band determines the apparent color of its visible light. The insets show stars of about these surface temperatures.

4. Hertzsprung-Russell Diagram
Luminosities of stars are plotted against their spectral types.
Luminosity and spectral type are correlated.
Main-sequence stars fall along the red curve.
Giants are to the right and supergiants are on the top.
White dwarfs are below the main sequence.
FIGURE 11-7 A Hertzsprung-Russell Diagram On an H-R
diagram, the luminosities of stars are plotted against their
spectral types. Each dot on this graph represents a star whose
luminosity and spectral type have been determined. Some well known
stars are identified. The data points are grouped in just a
few regions of the diagram, revealing that luminosity and
spectral type are correlated: Main-sequence stars fall along the
red curve, giants are to the right, supergiants are on the top,
and white dwarfs are below the main sequence. The absolute
magnitudes and surface temperatures are listed at the right and
top of the graph, respectively. These are sometimes used on H-R
diagrams instead of luminosities and spectral types. (

5. “Oh, Be A Fine Guy/Girl, Kiss Me!”
Spectral Classes
“Oh, Be A Fine Guy/Girl, Kiss Me!”

6. Types of Stars and Their Sizes
Stellar luminosities are graphed against the surface temperatures.
Dashed diagonal lines indicate stellar radii.
For stars of the same radius, hotter stars are more luminous than cooler stars.
FIGURE 11-8 The Types of Stars and Their Sizes On this
H-R diagram stellar luminosities are graphed against the surface
temperatures of stars. The dashed diagonal lines indicate stellar
radii. For stars of the same radius, hotter stars (corresponding to
moving from right to left on the H-R diagram), glow more
intensely and are more luminous (corresponding to moving
upward on the diagram) than cooler stars. While individual stars
are not plotted, we show the regions of the diagram in which
main-sequence, giant, supergiant, and white dwarf stars are found.
Note that the Sun is intermediate in luminosity, surface
temperature, and radius; it is very much a middle-of-the-road star.

7. The Mass-Luminosity Relation
Luminosities and masses are plotted using logarithmic scales.
The more massive a star, the more luminous the star.
FIGURE The Mass-Luminosity Relation (a) For main sequence
stars, mass and luminosity are directly correlated—the
more massive a star, the more luminous it is. A main-sequence
star of mass 10 M has roughly 3000 times the Sun’s luminosity
(3000 L); one with 0.1 M has a luminosity of only about
0.001 L. To fit them on the page, the luminosities and masses
are plotted using logarithmic scales.

8. The Mass-Luminosity Relation
Each dot represents a main-sequence star.
The number next to each dot is the mass of that star in solar masses.
Mass, luminosity, and surface temperature of main-sequence stars increase from lower right to upper left
(b) On this H-R diagram, each dot represents a main-sequence star. The number next to
each dot is the mass of that star in solar masses (M). As you
move up the main sequence from the lower right to the upper
left, the mass, luminosity, and surface temperature of mainsequence
stars all increase.

9. WHAT DO YOU THINK? How near is the closest star other than the Sun?
Is the Sun brighter than other stars, or just closer?
What colors are stars?
Are brighter stars hotter?
What sizes are stars?
Are most stars isolated from other stars, as the Sun is?

10. You will discover… • that the distances to many nearby stars can be
measured directly, while the distances to farther ones are determined indirectly
• the observed properties of stars on which
astronomers base their models of stellar evolution
• how astronomers analyze starlight to determine a
star’s temperature and chemical composition
• how the total energy emitted by stars and their
surface temperatures are related
• the different classes of stars
• the variety and importance of binary star systems
• how astronomers calculate stellar masses

11. FIGURE 11-1 Using Parallax to Determine Distance (a, b) Our eyes change angle as we
look at things that are different distances away. Our eyes are adjusting for the parallax of the
things we see. This change helps our brains determine the distances to objects and is
analogous to how astronomers determine the distance to objects in space. (c) As the Earth orbits the
Sun, a nearby star appears to shift its position against the background of distant stars. The star’s
parallax angle (p) is equal to the angle between the Sun and Earth as seen from the star. The stars on
the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale,
the closest star, other than the Sun, would be about 5 km (3.2 mi) away. (d) The closer the star is to us,
the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of
the parallax angle p (in arcseconds), d = 1/p. (a and b: Richard Megna/Fundamental Photographs, NYC)
Our eyes change angle as we look at things that are different distances away.
As the Earth orbits the
Sun, a nearby star appears to shift its position against the background of distant stars.

12. Our eyes are adjusting for the parallax of the things we see.
FIGURE 11-1 Using Parallax to Determine Distance (a, b) Our eyes change angle as we
look at things that are different distances away. Our eyes are adjusting for the parallax of the
things we see. This change helps our brains determine the distances to objects and is
analogous to how astronomers determine the distance to objects in space. (c) As the Earth orbits the
Sun, a nearby star appears to shift its position against the background of distant stars. The star’s
parallax angle (p) is equal to the angle between the Sun and Earth as seen from the star. The stars on
the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale,
the closest star, other than the Sun, would be about 5 km (3.2 mi) away. (d) The closer the star is to us,
the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of
the parallax angle p (in arcseconds), d = 1/p. (a and b: Richard Megna/Fundamental Photographs, NYC)
Our eyes are adjusting for the parallax of the
things we see.
The closer the star is to us,
the greater the parallax angle p.

13. Apparent Magnitude Scale
FIGURE 11-2 Apparent Magnitude Scale (a) Several stars in
and around the constellation Orion are labeled with their names
and apparent magnitudes. For a discussion of star names, see
Guided Discovery: Star Names. (b) Astronomers denote the
brightnesses of objects in the sky by their apparent magnitudes.
Stars visible to the naked eye have magnitudes between
m = –1.44 (Sirius) and about m = +6. CCD (charge-coupled
device) photography through the Hubble Space Telescope or a
large Earth-based telescope can reveal stars and other objects
nearly as faint as magnitude m = +30. (a: Okiro Fujii, L’Astronomie)
Astronomers denote the
brightness of objects in the sky by apparent magnitudes. Stars visible to the naked eye have magnitudes between m = –1.44 and about
m = +6.
Several stars in and around the constellation Orion labeled with their names and apparent magnitudes

14. Principal Types of Stellar Spectra
FIGURE 11-5 Principal Types of Stellar Spectra
This figure shows the spectra for stars with different surface temperatures. The corresponding spectral types are indicated on the right side of each spectrum. (Note
that stars of each spectral type have a range of temperature.) The hydrogen Balmer lines are strongest in stars with surface temperatures of about 10,000 K (called A-type stars). Cooler stars (G- and K-type stars) exhibit numerous atomic lines caused by various elements, indicating temperatures from 4000 to 6000 K. The broad, dark bands in the spectrum of the coolest stars (M-type stars) are caused by titanium oxide (TiO) molecules, which can exist only if the temperature is below about 3500 K. Recall from Section 4–5 that the roman numeral I after a chemical symbol means that the absorption line is caused by a neutral atom; a numeral II means that the absorption is caused by atoms that have each lost one electron. (R. Bell, University of Maryland, and M. Briley, University of Wisconsin at Oshkosh)

15. Classifying the Spectra of Stars
FIGURE 11-6 Classifying the Spectra of Stars The modern
classification scheme for stars based on their spectra was
developed at the Harvard College Observatory in the late
nineteenth century. Women astronomers, initially led by Edward
C. Pickering (not shown) and Williamina Fleming, standing in (a),
and then by Annie Jump Cannon (b), analyzed hundreds of
thousands of spectra. Social conventions of the time prevented
most women astronomers from using research telescopes or
receiving salaries comparable to those of men. (a: Harvard College
Observatory; b: © Bettmann/CORBIS)
Annie Jump Cannon
Williamina Fleming (standing)

16. Luminosity Classes
Luminosity classes permit finer distinctions between giants and supergiants.
Ia and Ib encompass the supergiants.
II, III, and IV indicate giants of different brightness.
V is the main-sequence stars.
White dwarfs do not have a luminosity class.
FIGURE 11-9 Luminosity Classes It is convenient to divide
the H-R diagram into regions called luminosity classes. These
subdivisions permit finer distinctions between giants and
supergiants. Luminosity classes Ia and Ib encompass the
supergiants. Luminosity classes II, III, and IV indicate giants of
different brightness. Luminosity class V is the main-sequence
stars. White dwarfs do not have their own luminosity class.

17. Binary Star System
FIGURE A Binary Star System About one-half of the
visible “stars” are actually double stars. (zeta) Ursae Majoris in
Ursa Major is a binary system with stars separated by only
about 0.01 arcseconds. The images surrounding this diagram
show the relative positions of the two stars over half of their
orbital period. The orbital motion of the two binary stars about
each other is evident. Either star can be considered fixed in
making such plots. (Navy Prototype Optical Interferometer, Flagstaff,
Arizona. Courtesy of Dr. Christian A. Hummel)
ζ Ursae Majoris is a binary system with stars separated by only about 0.01 arcseconds.

18. Center of Mass of a Binary Star System
FIGURE Center of Mass of a Binary Star System
(a) Two stars move in elliptical orbits around a common center
of mass. Although the orbits cross each other, the two stars are
always on opposite sides of the center of mass and thus never
collide. (b) A seesaw balances if the fulcrum is at the center of
mass of the two children. When balanced, the heavier child is
always closer to the fulcrum.

19. Spectral Line Motion in Binary Star Systems
FIGURE Spectral Line Motion in
Binary Star Systems (a) The drawings at
the top indicate the positions and motions
of the stars, labeled A and B relative to the Earth (below the
diagram), and their spectra at four selected moments (Stages 1,
2, 3, and 4) during an orbital period. (b) This graph displays the
radial-velocity curves of the binary HD (The HD means
that this is a star from the Henry Draper Catalogue of stars.)
The entire binary is moving away from us at 12 km/s, which is
why the pattern of radial velocity curves is displaced upward
from the zero-velocity line.
The radial-velocity curves of the binary HD

20. Double-Line Spectroscopic Binary
FIGURE A Double-Line Spectroscopic Binary The
spectrum of the double-line spectroscopic binary (kappa)
Arietis has spectral lines that shift back and forth as the two
stars revolve about each other. (a) The stars are moving parallel
to the line of sight with one star approaching Earth, the other
star receding as in Stages 1 or 3 of Figure 11-13a. These motions
produce two sets of shifted spectral lines. (b) Both stars are
moving perpendicular to our line of sight as in Stages 2 or 4 of
Figure 11-13a. As a result, the spectral lines of the two stars have
merged. (Lick Observatory)
Kappa Arietis has spectral lines that shift back and forth as the two stars revolve about each other.

21. Light Curves of Eclipsing Binaries
FIGURE Representative Light Curves of
Eclipsing Binaries The shape of the light curve (in
blue) reveals details about the two stars that make up
an eclipsing binary. Illustrated here are (a) a partial eclipse and
(b) a total eclipse. (c) The binary star NN Serpens, indicated by
the arrow, undergoes a total eclipse. The telescope was moved
during the exposure so that the sky drifted slowly from left to
(a) a partial eclipse (b) a total eclipse (c) The binary star NN Serpens

22. WHAT DID YOU THINK? How near is the closest star other than the Sun?
Proxima Centauri is about 40 trillion kilometers (25 trillion miles) away. It takes light about 4 years to reach the Earth from there.
How luminous is the Sun compared with other stars?
The most luminous stars are about a million times brighter and the least luminous stars are about a hundred thousand times dimmer than the Sun.
What colors are stars?
Stars are found in a wide range of colors, from red through violet, as well as white.

23. WHAT DID YOU THINK? Are brighter stars hotter than dimmer stars?
Not necessarily. Many brighter stars, such as red giants, are cooler but larger than hotter, dimmer stars, such as white dwarfs.
What sizes are stars?
Stars range from more than 1000 times the Sun’s diameter to less than 1/100 the Sun’s diameter.
Are most stars isolated from other stars, as the Sun is?
No. In the vicinity of the Sun, two-thirds of the stars are found in pairs or larger groups.

24. Key Terms absolute magnitude apparent magnitude binary star
center of mass
close binary
dwarf star
eclipsing binary
giant star
Hertzsprung-Russell (H-R)
diagram
initial mass function
inverse-square law
light curve
luminosity
luminosity class
main sequence
mass-luminosity relation
OBAFGKM sequence
optical double
photometry
radial-velocity curve
red giant
spectral types
spectroscopic binary
spectroscopic parallax
stellar evolution
stellar parallax
stellar spectroscopy
supergiant
visual binary
white dwarf
Summary of Key Ideas
• Stars differ in size, luminosity, temperature, color, mass, and
chemical composition—facts that help astronomers understand
stellar structure and evolution.
Magnitude Scales
• Determining stellar distances from Earth is the first step
to understanding the nature of the stars. Distances to the
nearer stars can be determined by stellar parallax, the
apparent shift of a star’s location against the background
stars while the Earth moves along its orbit around the Sun.
The distances to more remote stars are determined using
spectroscopic parallax.
• The apparent magnitude of a star, denoted m, is a measure
of how bright the star appears to Earth-based observers. The
absolute magnitude of a star, denoted M, is a measure of the
star’s true brightness and is directly related to the star’s energy
output, or luminosity.
• The absolute magnitude of a star is the apparent magnitude
it would have if viewed from a distance of 10 pc. Absolute
magnitudes can be calculated from the star’s apparent magnitude
and distance.
• The luminosity of a star is the amount of energy emitted by
it each second.
The Temperatures of Stars
• Stellar temperatures can be determined from stars’ colors or
stellar spectra.
• Stars are classified into spectral types (O, B, A, F, G, K, and
M) based on their spectra or, equivalently, their surface
temperatures.
Types of Stars
• The Hertzsprung-Russell (H-R) diagram is a graph on
which luminosities of stars are plotted against their spectral
types (or, equivalently, their absolute magnitudes are plotted
against surface temperatures). The H-R diagram reveals the
existence of four major groupings of stars: main-sequence
stars, giants, supergiants, and white dwarfs.
• The mass-luminosity relation expresses a direct correlation
between a main-sequence star’s mass and the total energy it emits.
• Distances to stars can be determined using their spectral
type and luminosity class.
Stellar Masses
• Binary stars are surprisingly common. Those that can be
resolved into two distinct star images (even if it takes a telescope
to do this) are called visual binaries.
• The masses of the two stars in a binary system can be computed
from measurements of the orbital period and orbital
dimensions of the system.
• Some binaries can be detected and analyzed, even though the
system may be so distant (or the two stars so close together)
that the two star images cannot be resolved with a telescope.
• A spectroscopic binary is a system detected from the periodic
shift of its spectral lines. This shift is caused by the
Doppler effect as the orbits of the stars carry them alternately
toward and away from the Earth.
• An eclipsing binary is a system whose orbits are viewed
nearly edge-on from the Earth, so that one star periodically
eclipses the other. Detailed information about the stars in an
eclipsing binary can be obtained by studying its light curve.
• Mass transfer occurs between binary stars that are close
together.