Chapter 16--Properties of Stars

More documents

Recommendations

Info

surface temperature to Betelgeuse, but far dimmer because of its much smaller size. White dwarfs are usually designated with the letters wd rather than with a Roman numeral. The Main Sequence The common trait of main-sequence stars is that, like our Sun, they are fusing hydrogen into helium in their cores. Because stars spend the majority of their lives fusing hydrogen, most stars fall somewhere along the main sequence of the H–R diagram. Why do main-sequence stars span such a wide range of luminosities and surface temperatures? By measuring the masses of stars in binary systems, astronomers have discovered that stellar masses decrease downward along the main sequence (Figure 16.11). At the upper end of the main sequence, the hot, luminous O stars can have masses as high as 100 times that of the Sun (100M Sun ). On the lower end, cool, dim M stars may have as little as 0.08 times the mass of the Sun (0.08M Sun ). Many more stars fall on the lower end of the main sequence than on the upper end, which tells us that low-mass stars are much more common than high-mass stars. The orderly arrangement of stellar masses along the main sequence tells us that mass is the most important attribute of a hydrogen-burning star. Luminosity depends directly on mass because the weight of a star’s outer layers determines the nuclear burning rate in its core. More weight means the star must sustain a higher nuclear burning rate in order to maintain gravitational equilibrium [Section 15.3]. Almost all stars are too distant for us to measure their radii directly. However, we can calculate a star’s radius from its luminosity with the aid of the thermal radiation laws. As given in Mathematical Insight 6.2, the amount of thermal radiation emitted by a star of surface temperature T is: emitted power per unit area sT 4 where the constant s 5.7 108 watt/(m2 Kelvin 4 ). The luminosity L of a star is its power per unit area multiplied by its total surface area. If the star has radius r, its surface area is given by the formula 4pr 2 .Thus: L 4pr 2 sT 4 With a bit of algebra, we can solve this formula for the star’s radius r: r L 4 4psT Example: Betelgeuse has a luminosity of 38,000LSun and a surface temperature of about 3,400 K. What is its radius? Solution: First, we must make our units consistent by converting the luminosity of Betelgeuse into watts. Remembering that LSun 3.8 1026 watts, we find: 534 part V • Stellar Alchemy Table 16.2 Stellar Luminosity Classes Class Description I Supergiants II Bright giants III Giants IV Subgiants V Main sequence The nuclear burning rate, and hence the luminosity, is very sensitive to mass. For example, a 10M Sun star on the main sequence is about 10,000 times more luminous than the Sun. The relationship between mass and surface temperature is a little subtler. In general, a very luminous star must either be very large or have a very high surface temperature, or some combination of both. Stars on the upper end of the main sequence are thousands of times more luminous than the Sun but only about 10 times larger than the Sun in radius. Thus, their surfaces must be significantly hotter than the Sun’s surface to account for their high luminosities. Main-sequence stars more massive than the Sun therefore have higher surface temperatures than the Sun, and those less massive than the Sun have lower surface temperatures. That is why the main sequence slices diagonally from the upper left to the lower right on the H–R diagram. Mathematical Insight 16.5 Calculating Stellar Radii LBet 38,000 LSun 38,000 3.8 1026 watts 1.4 1031 watts Now we can use the formula derived above to calculate the radius of Betelgeuse: r L 4psT 4 1.4 1031 watts 4p 5.7 108 watt m2 (3,400 K)4 3.8 1011 1.4 10 m 31 watts 9.6 107 watts m2 The radius of Betelgeuse is about 380 billion meters or, equivalently, 380 million kilometers. Note that this is more than twice the Earth–Sun distance of 150 million kilometers. K 4
Main-Sequence Lifetimes A star has a limited supply of core hydrogen and therefore can remain as a hydrogen-fusing main-sequence star for only a limited time—the star’s main-sequence lifetime (or hydrogen-burning lifetime). Because stars spend the vast majority of their lives fusing hydrogen into helium, we sometimes refer to the main-sequence lifetime as simply the “lifetime.” Like masses, stellar lifetimes vary in an orderly way as we move up the main sequence: Massive stars near the upper end of the main sequence have shorter lives than less massive stars near the lower end (see Figure 16.11). Why do more massive stars live shorter lives? A star’s lifetime depends on both its mass and its luminosity. Its mass determines how much hydrogen fuel the star initially contains in its core. Its luminosity determines how rapidly the star uses up its fuel. Massive stars live shorter lives because, even though they start their lives with a larger supply of hydrogen, they consume their hydrogen at a prodigious rate. The main-sequence lifetime of our Sun is about 10 billion years [Section 15.1].A 30-solar-mass star has 30 times more hydrogen than the Sun but burns it with a luminosity some 300,000 times greater. Consequently, its lifetime is roughly 30/300,000 1/10,000 as long as the Sun’s—corresponding to a lifetime of only a few million years. Cosmically speaking, a few million years is a remarkably short time, which is one reason why massive stars are so rare: Most of the massive stars that have ever been born are long since dead. (A second reason is that lower-mass stars form in larger numbers than higher-mass stars [Section 17.2].) 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 30M Sun Lifetime 10 7 yrs Spica 10M Sun MAIN Lifetime 10 8 yrs 6M Sun Achernar SEQUENCE Sirius Lifetime 10 9 yrs 3M Sun Lifetime 10 10 yrs Sun 1.5M Sun 1M Sun Lifetime 10 Proxima Centauri 11 yrs 30,000 10,000 6,000 3,000 surface temperature (Kelvin) 0.3M Sun 0.1M Sun Figure 16.11 Along the main sequence, more massive stars are brighter and hotter but have shorter lifetimes. (Stellar masses are given in units of solar masses: 1M Sun 2 10 30 kg.) The fact that massive stars exist at all at the present time tells us that stars must form continuously in our galaxy. The massive, bright O stars in our galaxy today formed only recently and will die long before they have a chance to complete even one orbit around the center of the galaxy. THINK ABOUT IT Would you expect to find life on planets orbiting massive O stars? Why or why not? (Hint: Compare the lifetime of an O star to the amount of time that passed from the formation of our solar system to the origin of life on Earth.) On the other end of the scale, a 0.3-solar-mass star emits a luminosity just 0.01 times that of the Sun and consequently lives roughly 0.3/0.01 30 times longer than the Sun. In a universe that is now about 14 billion years old, even the most ancient of these small, dim M stars still survive and will continue to shine faintly for hundreds of billions of years to come. Giants, Supergiants, and White Dwarfs Giants and supergiants are stars nearing the ends of their lives because they have already exhausted their core hydrogen. Surprisingly, stars grow more luminous when they begin to run out of fuel. As we will discuss in the next chapter, a star generates energy furiously during the last stages of its life as it tries to stave off the inevitable crushing force of gravity. As ever-greater amounts of power well up from the core, the outer layers of the star expand, making it a giant or supergiant. The largest of these celestial behemoths have radii more than 1,000 times the radius of the Sun. If our Sun were this big, it would engulf the planets out to Jupiter. Because they are so bright, we can see giants and supergiants even if they are not especially close to us. Many of the brightest stars visible to the naked eye are giants or supergiants. They are often identifiable by their reddish color. Nevertheless, giants and supergiants are rarer than main-sequence stars. In our snapshot of the heavens, we catch most stars in the act of hydrogen burning and relatively few in a later stage of life. Giants and supergiants eventually run out of fuel entirely. A giant with a mass similar to that of our Sun ultimately ejects its outer layers, leaving behind a “dead” core in which all nuclear fusion has ceased. White dwarfs are these remaining embers of former giants. They are hot because they are essentially exposed stellar cores, but they are dim because they lack an energy source and radiate only their leftover heat into space. A typical white dwarf is no larger in size than Earth, although it may have a mass as great as that of our Sun. (Giants and supergiants with masses much larger than that of the Sun ultimately explode, leaving behind neutron stars or black holes as corpses [Section 17.4].) chapter 16 • Properties of Stars 535
Page 1 and 2: 16 Properties of Stars 16.1 Snapsho
Page 3 and 4: distance, it would appear dimmer by
Page 5 and 6: Every January, we see this: July d
Page 7 and 8: ment is not affected by the star’
Page 9 and 10: Brightest Key Absorption Wavelength
Page 11 and 12: ness of the system drops because so
Page 13: When classifying a star, astronomer
Page 17 and 18: ter can contain more than a million
Page 19 and 20: luminosity (solar units) 10 6 10 5
Page 21 and 22: True Statements? Decide whether eac
Page 23: astronomyplace.com Astronomy Place

Chapter 16--Properties of Stars

Create successful ePaper yourself

Delete template?

Save as template?