Chapter 16--Properties of Stars

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orbit). In an eclipsing binary, we measure the time between eclipses. In a spectroscopic binary, we measure the time it takes the spectral lines to shift back and forth. Determining the average separation of the stars in a binary system is usually much more difficult. Except in rare cases in which we can measure the separation directly, we can calculate the separation only if we know the actual orbital speeds of the stars from their Doppler shifts. Unfortunately, a Doppler shift tells us only the portion of a star’s velocity that is directly toward us or away from us [Section 6.5].Because orbiting stars generally do not move directly along our line of sight, their actual velocities can be significantly greater than those we measure through the Doppler effect. The exceptions are eclipsing binary stars. Because these stars orbit in the plane of our line of sight, their Doppler shifts can tell us their true orbital velocities.* Eclipsing binaries are therefore particularly important to the study of stellar masses. As an added bonus, eclipsing binaries allow us to measure stellar radii directly. Because we know how fast the stars are moving across our line of sight as one eclipses the other, we can determine their radii by timing how long each eclipse lasts. Suppose two orbiting stars are moving in a plane perpendicular to our line of sight. Would the spectral features of these stars appear shifted in any way? Explain. astronomyplace.com The Hertzsprung–Russell Diagram Tutorial, Lessons 1–3 16.5 The Hertzsprung–Russell Diagram During the first decade of the twentieth century, a similar thought occurred independently to astronomers Ejnar Hertzsprung, working in Denmark, and Henry Norris Russell, working in the United States at Princeton University: Each decided to make a graph plotting stellar luminosities on one axis and spectral types on the other. Such graphs are now called Hertzsprung–Russell (H–R) diagrams.Soon after they began making their graphs, Hertzsprung and Russell uncovered some previously unsuspected patterns in the properties of stars. As we will see shortly, understanding these patterns and the H–R diagram is central to the study of stars. A Basic H–R Diagram THINK ABOUT IT Figure 16.10 displays an example of an H–R diagram. ● The horizontal axis represents stellar surface temperature, which, as we’ve discussed, corresponds to spectral type. Temperature increases from right to left because *In other binaries, we can calculate an actual orbital velocity from the velocity obtained by the Doppler effect if we also know the system’s orbital inclination. Astronomers have developed techniques for determining orbital inclination in a relatively small number of cases. 532 part V • Stellar Alchemy Hertzsprung and Russell based their diagrams on the spectral sequence OBAFGKM. ● The vertical axis represents stellar luminosity, in units of the Sun’s luminosity (LSun ). Stellar luminosities span a wide range, so we keep the graph compact by making each tick mark represent a luminosity 10 times larger than the prior tick mark. Each location on the diagram represents a unique combination of spectral type and luminosity. For example, the dot representing the Sun in Figure 16.10 corresponds to the Sun’s spectral type, G2, and its luminosity, 1LSun . Because luminosity increases upward on the diagram and surface temperature increases leftward, stars near the upper left are hot and luminous. Similarly, stars near the upper right are cool and luminous, stars near the lower right are cool and dim, and stars near the lower left are hot and dim. THINK ABOUT IT Explain how the colors of the stars in Figure 16.10 help indicate stellar surface temperature. Do these colors tell us anything about interior temperatures? Why or why not? The H–R diagram also provides direct information about stellar radii, because a star’s luminosity depends on both its surface temperature and its surface area or radius. Recall that surface temperature determines the amount of power emitted by the star per unit area: Higher temperature means greater power output per unit area [Section 6.4]. Thus, if two stars have the same surface temperature, one can be more luminous than the other only if it is larger in size. Stellar radii therefore must increase as we go from the high-temperature, low-luminosity corner on the lower left of the H–R diagram to the low-temperature, high-luminosity corner on the upper right. Patterns in the H–R Diagram Figure 16.10 also shows that stars do not fall randomly throughout the H–R diagram but instead fall into several distinct groups: ● Most stars fall somewhere along the main sequence, the prominent streak running from the upper left to the lower right on the H–R diagram. Our Sun is a mainsequence star. ● The stars along the top are called supergiants because they are very large in addition to being very bright. ● Just below the supergiants are the giants,which are somewhat smaller in radius and lower in luminosity (but still much larger and brighter than mainsequence stars of the same spectral type). ● The stars near the lower left are small in radius and appear white in color because of their high temperature. We call these stars white dwarfs.
When classifying a star, astronomers generally report both the star’s spectral type and a luminosity class that describes the region of the H–R diagram in which the star falls. Table 16.2 summarizes the luminosity classes: Luminosity class I represents supergiants, luminosity class III represents giants, luminosity class V represents main- luminosity (solar units) 10 6 10 5 10 4 10 3 10 2 10 1 0.1 10 2 10 3 10 4 10 5 60M Sun 10 Solar Radii Lifetime 10 7 yrs 1 Solar Radius 30M Sun 0.1 Solar Radius 10 2 Solar Radius 10 3 Solar Radius Sirius B increasing temperature 10 2 Solar Radii Centauri Spica 10MSun MAIN Lifetime 10 8 yrs Bellatrix 6MSun Achernar Lifetime 10 9 yrs Figure 16.10 An H–R diagram, one of astronomy’s most important tools, shows how the surface temperatures of stars (plotted along the horizontal axis) relate to their luminosities (plotted along the vertical axis). Several of the brightest stars in the sky are plotted here, along with a few of those closest to Earth. They are not drawn to scale—the diagonal lines, labeled in solar radii, indicate how large they are compared to the Sun. The lifetime and mass labels apply only to main-sequence stars (see Figure 16.11). (Star positions on this diagram are based on data from the Hipparcos satellite.) Rigel Sirius Deneb SEQUENCE sequence stars, and luminosity classes II and IV are intermediate to the others. For example, the complete spectral classification of our Sun is G2 V. The G2 spectral type means it is yellow in color, and the luminosity class V means it is a main-sequence star. Betelgeuse is M2 I, making it a red supergiant. Proxima Centauri is M5 V—similar in color and 3MSun Vega Procyon B 30,000 10,000 Sirius Altair Lifetime 10 10 yrs WHITE DWARFS 10 3 Solar Radii SUPERGIANTS Canopus Polaris Arcturus Procyon 1.5MSun GIANTS Pollux Aldebaran Lifetime 10 11 Sun Centauri A 1MSun Centauri B Ceti Eridani 61 Cygni A 61 Cygni B Lacaille 9352 0.3MSun Gliese 725 A Gliese 725 B yrs Barnard’s Star 0.1MSun Ross 128 Wolf 359 Proxima Centauri DX Cancri Betelgeuse Antares 6,000 3,000 surface temperature (Kelvin) decreasing temperature chapter 16 • Properties of Stars 533
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