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Neil F. Comins • William J. Kaufmann III. Discovering the Universe Ninth Edition. CHAPTER 11 Characterizing Stars. Interstellar dust illuminated by a pulse of light emitted from the red giant star, V838 Monocerotis, in the center of the image. WHAT DO YOU THINK?.

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Neil F. Comins • William J. Kaufmann III

Discovering the Universe

Ninth Edition


Characterizing Stars


Interstellar dust illuminated by a pulse of light emitted from the red giant star, V838 Monocerotis, in the center of the image.

what do you think
  • How near to us is the closest star other than the Sun?
  • How luminous is the Sun compared with other stars?
  • What colors are stars, and why do they have these colors?
  • Are brighter stars hotter than dimmer stars?
  • Compared to the Sun, what sizes are other stars?
  • Are most stars isolated from other stars, as the Sun is?
in this chapter you will discover
In this chapter you will discover…
  • that the distances to many nearby stars can be measured directly, whereas 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

Using Parallax to Determine Distance

Our eyes change the angle between their line of sight 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 brain determine the distances to objects and is analogous to how astronomers determine the distance to objects in space.


Using Parallax to Determine Distance

As 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 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.


Apparent Magnitude Scale

(a) Several stars in and around the constellation Orion, labeled with their names and apparent magnitudes.

(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 and about m=+6.


The Inverse-Square Law

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 Inverse-Square Law

The car is seen at distances of 10 m, 20 m, and 30 m, showing the effect described in the previous image.


Temperature and Color

This beautiful Hubble Space Telescope image shows the variety of colors of stars.


Temperature and Color

These diagrams show the relationship between the color of a star and its surface temperature. The intensity of light emitted by three stars is plotted against wavelength. The range of visible wavelengths is indicated. The location of the peak of each star’s intensity curve, relative to the visible-light band, determines the apparent color of its visible light. The insets show stars of about these surface temperatures. Ultraviolet (uv) extends to 10 nm.


The Spectral Types

The corresponding spectral types are indicated on the right side of each spectrum. The hydrogen Balmer lines are strongest in stars with surface temperatures of about 10,000 K (called A-typestars). Cooler stars (G- and K-type stars) exhibit numerous atomic lines caused by various elements, indicating temperatures from 4000 to 6000 K. Several of 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 3700 K.


Classifying the Spectra of Stars

(a) Williamina Fleming (standing)

(b) Annie Jump Cannon

The modern classification scheme for stars, based on their spectra, was developed at the Harvard College Observatory in the late nineteenth century. Female astronomers, initially led by Edward C. Pickering and Williamina Fleming, and then by Annie Jump Cannon, analyzed hundreds of thousands of spectra. Social conventions of the time prevented most female astronomers from using research telescopes or receiving salaries comparable to those of men.


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. 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.


The Types of Stars and Their Sizes

On this H-R diagram, stellar luminosities are plotted 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 H­R 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.


Stellar Size and Spectra

These spectra are from two stars of the same spectral type (B8) and, hence, the same surface temperature (13,400 K) but different radii and luminosities: (a) the B8 supergiant Rigel (58,000 solar luminosities) in Orion, and (b) the B8 main-sequence star Algol (100 solar luminosities) in Perseus.


Luminosity Classes

Dividing the H-R diagram into regions, called luminosity classes,permits 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 indicates main-sequence stars. White dwarfs do not have their own luminosity class.


A Binary Star System

About one-third of the visible “stars” in our region of the Milky Way are actually double stars. Mizar in Ursa Major is a binary system with stars separated by only about 0.01 arcsec. The images and plots show the relative positions of the two stars over nearly half of their orbital period. The orbital motion of the two binary stars around each other is evident. Either star can be considered fixed in making such plots.


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 center of mass of the two children is at the fulcrum. When balanced, the heavier child is always closer to the fulcrum, just as the more massive star is closer to the center of mass of a binary star system.


Representative Light Curves of Eclipsing Binaries

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 right. During the 10.5-min eclipse, the dimmer but larger star in the binary system (an M6 V star) passed in front of the more luminous but smaller star (a white dwarf). The binary became so dim that it almost disappeared.


The Mass-Luminosity Relation

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 10 solar masses has roughly 3000 times the Sun’s luminosity ; one with 0.1 solar masses has a luminosity of only about 0.001 solar luminosities. To fit them on the page, the luminosities and masses are plotted using logarithmic scales.


The Mass-Luminosity Relation

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. As you move up the main sequence from the lower right to the upper left, the mass, luminosity, and surface temperature of main-sequence stars all increase.


Spectral Line Motion in Binary Star Systems

The diagramsindicate the positions and motions of the stars, labeled A and B, relative to Earth. Below each diagram is the spectrum we would observe for these two stars at each stage. The changes in colors (wavelengths) of the spectral lines are due to changes in the stars’ Doppler shifts, as seen from Earth.


Spectral Line Motion in Binary Star Systems

This graph displays the radial-velocity curves of the binary HD171978. (The HD means that this is a star from the Henry Draper Catalogue of stars.) The entire binary is moving away from us at 12km/s, which is why the pattern of radial velocity curves is displaced upward from the zero-velocity line.


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 around each other. (a)The stars are moving parallel to the line of sight, with one star approaching Earth, the other star receding, as in Stage 1 or 3 of Figure 11-15a. These motions produce two sets of shifted spectral lines. (b) Both stars are moving perpendicular to our line of sight, as in Stage 2 or 4 of Figure 11-15a. As a result, the spectral lines of the two stars have merged.

magnitude scales
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, which is the apparent shift of a star’s location against the background stars while 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.
magnitude scales1
Magnitude Scales
  • The luminosity of a star is the amount of energy emitted by it each second.
  • 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 from Earth.
the temperatures of stars
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
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 types and luminosity classes.
stellar masses
Stellar Masses
  • Binary stars are fairly 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.
stellar masses1
Stellar Masses
  • 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 Earth.
  • An eclipsing binary is a system whose orbits are viewed nearly edge on from Earth, so that one star periodically eclipses the other. Detailed information about the stars in an eclipsing binary can be obtained by studying the binary’s light curve.
key terms
Key Terms

spectral types

spectroscopic binary

spectroscopic parallax

stellar evolution

stellar parallax

stellar spectroscopy


visual binary

white dwarf

light curve


luminosity class

main sequence

main-sequence star

mass-luminosity relation

OBAFGKM sequence

optical double


radial-velocity curve

red giant

absolute magnitude

apparent magnitude

binary star

center of mass

close binary

eclipsing binary

giant star

Hertzsprung-Russell (H-R) diagram

initial mass function

inverse-square law

what did you think
  • How near to us is the closest star other than the Sun?
  • The closest star, Proxima Centauri, is about 40 trillion km (25 trillion mi) away. Light from there takes about 4 years to reach Earth.
what did you think1
  • 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 did you think2
  • What colors are stars, and why do they have these colors?
  • Stars are found in a wide range of colors, from red through violet as well as white. They have these colors because they have different surface temperatures.
what did you think3
  • 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 did you think4
  • Compared to the Sun, what sizes are other stars?
  • Stars range from more than 1000 times the Sun’s diameter to less than 1/100 the Sun’s diameter.
what did you think5
  • Are most stars isolated from other stars, as the Sun is?
  • No. In the vicinity of the Sun, one-third of the stars are found in pairs or larger groups.