Neil F. Comins • William J. Kaufmann III Discovering the Universe Ninth Edition CHAPTER 11 Characterizing Stars Stars Come in Many Colors (Hubble Heritage Team/ AURA/STScI/NASA)

Interstellar dust illuminated by a pulse of light emitted from the red giant star, V838 Monocerotis, in the center of the image. [NASA, ESA, and H. H. Bond ([STScI]) Interstellar dust illuminated by a pulse of light emitted from the red giant star, V838 Monocerotis, in the center of the image.

An Astronomer’s Almanac

The Stars

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… 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 FIGURE 11-1 Using Parallax to Determine Distance (a, b) 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. (Mark Andersen/JupiterImages) 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. FIGURE 11-1 Using Parallax to Determine Distance (c) 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 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.

Apparent Magnitude Scale FIGURE 11-2 Apparent Magnitude Scale Several stars in and around the constellation Orion, 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 = +6.0. However, 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) (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 FIGURE 11-3 The Inverse-Square Law (a) 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, which means, for example, that tripling the distance decreases the brightness by a factor of 9.

The Inverse-Square Law FIGURE 11-3 The Inverse-Square Law (b) The car is seen at distances of 10 m, 20 m, and 30 m, showing the effect described in part (a). (Royalty Free/CORBIS) 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 FIGURE 11-4 Temperature and Color (a) This beautiful Hubble Space Telescope image shows the variety of colors of stars. (Hubble Heritage Team/AURA/STScI/NASA) 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. FIGURE 11-4 Temperature and Color (b) 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 (compare with Figure 4-2). 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. See Figure 3-6 for more on wavelengths of the spectrum. (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 Spectral Types FIGURE 11-5 The Spectra of 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. 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. 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) 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-type stars). 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.

(a) Williamina Fleming (standing) Classifying the Spectra of Stars (a) Williamina Fleming (standing) (b) Annie Jump Cannon 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. Female astronomers, initially led by Edward C. Pickering (not shown) and (a) Williamina Fleming, standing, and then by (b) 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: Harvard College Observatory; b: © Bettmann/CORBIS) 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. 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.

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. FIGURE 11-8 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 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.

Stellar Size and Spectra FIGURE 11-9 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. (From W. W. Morgan, P. C. Keenan, and E. Kellman, An Atlas of Stellar 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. FIGURE 11-10 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 FIGURE 11-11 A Binary Star System About one-third of the objects we see as “stars” in our region of the Milky Way Galaxy 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. (Technically, this pair of stars is Mizar A and its dimmer companion. These two are bound to another binary pair, Mizar B and its dimmer companion.) (Navy Prototype Optical Interferometer, Flagstaff, AZ. Courtesy of Dr. Christian A. Hummel) 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 FIGURE 11-12 Center of Mass of a Binary Star System 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. (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. FIGURE 11-13 Representative Light Curves of Eclipsing Binaries The shape of the light curve (blue) reveals that the pairs of stars have orbits in planes nearly perpendicular to our line of sight. They also provide 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 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. (European Southern Observatory)

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. FIGURE 11-14 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. FIGURE 11-14 The Mass-Luminosity Relation (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. 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 diagrams indicate 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. FIGURE 11-15 Spectral Line Motion in Binary Star Systems The diagrams at the top indicate 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 HD 171978. (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. FIGURE 11-15 Spectral Line Motion in Binary Star Systems The graph displays the radial-velocity curves of the binary HD 171978. (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.

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. FIGURE 11-16 A Double-Line Spectroscopic Binary The spectrum of the double-line spectroscopic binary κ (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 11-15. 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 11-15. As a result, the spectral lines of the two stars have merged. (Lick Observatory)

Summary of Key Ideas

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 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 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 types and luminosity classes.

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 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 absolute magnitude light curve spectral types apparent magnitude binary star center of mass close binary eclipsing binary giant star Hertzsprung-Russell (H-R) diagram initial mass function inverse-square law light curve luminosity luminosity class main sequence main-sequence star 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

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 THINK? 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 THINK? 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 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 DID YOU THINK? 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 THINK? 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.