Chapter 16--Properties of Stars

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multiple star systems containing three or more stars. Most are tiny, dim red stars such as Proxima Centauri—so dim that we cannot see them with the naked eye, despite the fact that they are relatively close. A few nearby stars, such as Sirius (2.6 parsecs), Vega (8 parsecs), Altair (5 parsecs), and Fomalhaut (7 parsecs), are white in color and bright in our sky, but most of the brightest stars in the sky lie farther away. Because so many nearby stars appear dim while many more distant stars appear bright, their luminosities must span a wide range. The Magnitude System Many amateur and professional astronomers describe stellar brightness using the ancient magnitude system devised by the Greek astronomer Hipparchus (c. 190–120 B.C.). The magnitude system originally classified stars according to how bright they look to our eyes—the only instruments available in ancient times. The brightest stars received the designation “first magnitude,” the next brightest “second magnitude,” and so on. The faintest visible stars were magnitude 6. We call these descriptions apparent magnitudes because they compare how bright different stars appear in the sky. Star charts (such as those in Appendix J) often use dots of different sizes to represent the apparent magnitudes of stars. In modern times, the magnitude system has been extended and more precisely defined (see Mathematical Insight 16.3). As a result, stars can have fractional apparent The modern magnitude system is defined so that each difference of 5 magnitudes corresponds to a factor of exactly 100 in brightness. For example, a magnitude 1 star is 100 times brighter than a magnitude 6 star, and a magnitude 3 star is 100 times brighter than a magnitude 8 star. Because 5 magnitudes corresponds to a factor of 100 in brightness, a single magnitude corresponds to a factor of (100) 1/5 2.512. The following formula summarizes the relationship between stars of different magnitudes: apparent brightness of Star 1 apparent brightness of Star 2 526 part V • Stellar Alchemy magnitudes, and a few bright stars have apparent magnitudes less than 1—which means brighter than magnitude 1. For example, the brightest star in the night sky, Sirius, has an apparent magnitude of 1.46. Appendix F gives the apparent magnitudes and solar luminosities for nearby stars and the brightest stars. The modern magnitude system also defines absolute magnitudes as a way of describing stellar luminosities. A star’s absolute magnitude is the apparent magnitude it would have if it were at a distance of 10 parsecs from Earth. For example, the Sun’s absolute magnitude is about 4.8, meaning that the Sun would have an apparent magnitude of 4.8 if it were 10 parsecs away from us—bright enough to be visible, but not conspicuous, on a dark night. Understanding the magnitude system is worthwhile because it is still commonly used. However, for the calculations in this book, it’s much easier to work with the luminosity–distance formula, so we will avoid using magnitude formulas in this book. astronomyplace.com The Hertzsprung–Russell Diagram Tutorial, Lessons 1–3 16.3 Stellar Surface Temperature The second basic property of stars (besides luminosity) needed for modern stellar classification is surface temperature. Measuring a star’s surface temperature is somewhat easier than measuring its luminosity because the measure- Mathematical Insight 16.3 The Modern Magnitude Scale (100 1/5 ) m 2 m 1 where m 1 and m 2 are the apparent magnitudes of Stars 1 and 2, respectively. If we replace the apparent magnitudes with absolute magnitudes (designated M instead of m), the same formula applies to stellar luminosities: luminosity of Star 1 luminosity of Star 2 (100 1/5 ) M 2 M 1 Example 1: On a clear night, stars dimmer than magnitude 5 are quite difficult to see. Today, sensitive instruments on large telescopes can detect objects as faint as magnitude 30. How much more sensitive are such telescopes than the human eye? Solution: We imagine that our eye sees “Star 1” with magnitude 5 and the telescope detects “Star 2” with magnitude 30. Then we compare: apparent brightness of Star 1 apparent brightness of Star 2 (100 1/5 ) 305 (100 1/5 ) 25 100 5 10 10 The magnitude 5 star is 10 10 ,or 10 billion, times brighter than the magnitude 30 star, so the telescope is 10 billion times more sensitive than the human eye. Example 2: The Sun has an absolute magnitude of about 4.8. Polaris, the North Star, has an absolute magnitude of 3.6. How much more luminous is Polaris than the Sun? Solution: We use Polaris as Star 1 and the Sun as Star 2: luminosity of Polaris luminosity of Sun (100 1/5 ) 4.8(3.6) (100 1/5 ) 8.4 100 1.7 2,500 Polaris is about 2,500 times more luminous than the Sun.
ment is not affected by the star’s distance. Instead, we determine surface temperature directly from the star’s color or spectrum. One note of caution: We can measure only a star’s surface temperature, not its interior temperature. (Interior temperatures are calculated with theoretical models [Section 15.3].) When astronomers speak of the “temperature” of a star, they usually mean the surface temperature unless they say otherwise. A star’s surface temperature determines the color of light it emits [Section 6.4].A red star is cooler than a yellow star, which in turn is cooler than a blue star. The naked eye can distinguish colors only for the brightest stars, but colors become more evident when we view stars through binoculars or a telescope (Figure 16.4). Astronomers can determine the “color” of a star more precisely by comparing its apparent brightness as viewed through two different filters [Section 7.3].For example, a cool star such as Betelgeuse, with a surface temperature of about 3,400 K, emits more red light than blue light and therefore looks much brighter when viewed through a red filter than when viewed through a blue filter. In contrast, a hotter star such as Sirius, with a surface temperature of about 9,400 K, emits more blue light than red light and looks brighter through a blue filter than through a red filter. Spectral Type Figure 16.4 This Hubble Space Telescope view through the heart of our Milky Way Galaxy reveals that stars emit light of many different colors. VIS The emission and absorption lines in a star’s spectrum provide an independent and more accurate way to measure its surface temperature. Stars displaying spectral lines of highly ionized elements must be fairly hot, while stars displaying spectral lines of molecules must be relatively cool [Section 6.4].Astronomers classify stars according to surface temperature by assigning a spectral type determined from the spectral lines present in a star’s spectrum. The hottest stars, with the bluest colors, are called spectral type O, followed in order of declining surface temperature by spectral types B, A, F, G, K, and M. The time-honored mnemonic for remembering this sequence, OBAFGKM, is “Oh Be A Fine Girl/Guy, Kiss Me!” Table 16.1 summarizes the characteristics of each spectral type. Each spectral type is subdivided into numbered subcategories (e.g., B0, B1,...,B9). The larger the number, the cooler the star. For example, the Sun is designated spectral type G2, which means it is slightly hotter than a G3 star but cooler than a G1 star. chapter 16 • Properties of Stars 527
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Chapter 16--Properties of Stars

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