Chapter 15--Our Sun - Geological Sciences

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p p Step 1 Step 2 Step 3 p n e gamma ray Key: e electron gamma ray e e positron p proton Total reaction p p n p p p p n p gamma ray n p p p p n n p n p p p e n p p e gamma ray gamma ray neutrino gamma ray p n n neutron Figure 15.7 Hydrogen fuses into helium in the Sun by way of the proton–proton chain. In step 1, two protons fuse to create a deuterium nucleus consisting of a proton and a neutron. In step 2, the deuterium nucleus and a proton fuse to form helium-3, a rare form of helium. In step 3, two helium-3 nuclei fuse to form helium-4, the common form of helium. overcome the electromagnetic repulsion between two positively charged nuclei [Section S4.2].In contrast to gravitational and electromagnetic forces, which drop off gradually as the distances between particles increase (by an inverse square law [Section 5.3]), the strong force is more like glue or Velcro: It overpowers the electromagnetic force over very small distances but is insignificant when the distances between particles exceed the typical sizes of atomic nuclei. The trick to nuclear fusion, therefore, is to push the positively charged nuclei close enough together for the strong force to outmuscle electromagnetic repulsion. The high pressures and temperatures in the solar core are just right for fusion of hydrogen nuclei into helium nuclei. The high temperature is important because the nuclei must collide at very high speeds if they are to come close enough together to fuse. (Quantum tunneling is also important to this process [Section S4.5].) The higher the temperature, the harder the collisions, making fusion reactions more likely at higher temperatures. The high pressure of the overlying layers is necessary because without it the hot plasma of the solar core would simply explode into space, shutting off the nuclear reactions. In the Sun, the pressure is high and steady, allowing some 600 million tons of hydrogen to fuse into helium every second. Hydrogen Fusion in the Sun: The Proton–Proton Chain Recall that hydrogen nuclei are nothing more than individual protons, while the most common form of helium consists of two protons and two neutrons. Thus, the overall hydrogen fusion reaction in the Sun is: p p 4 1 H p p p n n p 1 4 He energy However, collisions between two nuclei are far more common than three- or four-way collisions, so this overall reaction proceeds through steps that involve just two nuclei at a time. The sequence of steps that occurs in the Sun is called the proton–proton chain because it begins with collisions between individual protons (hydrogen nuclei). Figure 15.7 illustrates the steps in the proton–proton chain: Step 1. Two protons fuse to form a nucleus consisting of one proton and one neutron, which is the isotope of hydrogen known as deuterium. Note that this step converts a proton into a neutron, reducing the total nuclear charge from 2 for the two fusing protons to 1 for the resulting deuterium nucleus. The lost positive charge is carried off by a positron, the antimatter version of an electron with a positive rather than negative charge [Section S4.2].A neutrino—a subatomic particle with a very tiny mass—is also produced in this step.* The positron won’t last long, because it soon meets up with an ordinary electron, resulting *Producing a neutrino is necessary because of a law called conservation of lepton number: The number of leptons (e.g., electrons or neutrinos [Chapter S4]) must be the same before and after the reaction. The lepton number is zero before the reaction because there are no leptons. Among the reaction products, the positron (antielectron) has lepton number 1 because it is antimatter, and the neutrino has lepton number 1. Thus, the total lepton number remains zero. 502 part V • Stellar Alchemy
in the creation of two gamma-ray photons through matter– antimatter annihilation. Step 2. A fair number of deuterium nuclei are always present along with the protons and other nuclei in the solar core, since step 1 occurs so frequently in the Sun (about 10 38 times per second). Step 2 occurs when one of these deuterium nuclei collides and fuses with a proton. The result is a nucleus of helium-3, a rare form of helium with two protons and one neutron. This reaction also produces a gamma-ray photon. Step 3. The third and final step of the proton–proton chain requires the addition of another neutron to the helium-3, thereby making normal helium-4. This final step can proceed in several different ways, but the most common route involves a collision of two helium-3 nuclei. Each of these helium-3 nuclei resulted from a prior, separate occurrence of step 2 somewhere in the solar core. The final result is a normal helium-4 nucleus and two protons. Total reaction. Somewhere in the solar core, steps 1 and 2 must each occur twice to make step 3 possible. Six protons go into each complete cycle of the proton–proton chain, but two come back out. Thus, the overall proton–proton chain converts four protons (hydrogen nuclei) into a helium-4 nucleus, two positrons, two neutrinos, and two gamma rays. Each resulting helium-4 nucleus has a mass that is slightly less (by about 0.7%) than the combined mass of the four protons that created it. Overall, fusion in the Sun converts about 600 million tons of hydrogen into 596 million tons of helium every second. The “missing” 4 million tons of matter becomes energy in accord with Einstein’s formula E mc 2 .About 98% of the energy emerges as kinetic energy of the resulting helium nuclei and radiative energy of the gamma rays. As we will see, this energy slowly percolates to the solar surface, eventually emerging as the sunlight that bathes Earth. About 2% of the energy is carried off by the neutrinos. Neutrinos rarely interact with matter (because they respond only to the weak force [Section S4.2]), so most of the neutrinos created by the proton–proton chain pass straight from the solar core through the solar surface and out into space. The Solar Thermostat The rate of nuclear fusion in the solar core, which determines the energy output of the Sun, is very sensitive to temperature. A slight increase in temperature would mean a much higher fusion rate, and a slight decrease in temperature would mean a much lower fusion rate. If the Sun’s rate of fusion varied erratically, the effects on Earth might be devastating. Fortunately, the Sun’s central temperature is steady thanks to gravitational equilibrium—the balance between the pull of gravity and the push of internal pressure. Outside the solar core, the energy produced by fusion travels toward the Sun’s surface at a slow but steady rate. In this steady state, the amount of energy leaving the top of each gas layer within the Sun precisely balances the energy entering from the bottom (Figure 15.8). Suppose the core temperature of the Sun rose very slightly. The rate of nuclear fusion would soar, generating lots of extra energy. Because energy moves so slowly through the Sun, this extra energy would be bottled up in the core, causing an increase in the core pressure. The push of this pressure would temporarily exceed the pull of gravity, causing the core to expand and cool. With cooling, the fusion rate would drop back down. The expansion and cooling would continue until gravitational equilibrium was restored, at which point the fusion rate would return to its original value. An opposite process would restore the normal fusion rate if the core temperature dropped. A decrease in core temperature would lead to decreased nuclear burning, a drop in the central pressure, and contraction of the core. As the core shrank, its temperature would rise until the burning rate returned to normal. The response of the core pressure to changes in the nuclear fusion rate is essentially a thermostat that keeps the Sun’s central temperature steady. Any change in the core temperature is automatically corrected by the change in the fusion rate and the accompanying change in pressure. While the processes involved in gravitational equilibrium prevent erratic changes in the fusion rate, they also ensure that the fusion rate gradually rises over billions of years. Because each fusion reaction converts four hydrogen nuclei into one helium nucleus, the total number of independent particles in the solar core is gradually falling. This gradual reduction in the number of particles causes the solar core to shrink. The slow shrinking of the solar core means that it must generate energy more rapidly to counteract the stronger compression of gravity, so the solar core gradually gets hotter as it shrinks. Theoretical models indicate that the Sun’s core temperature should have increased enough to raise its fusion rate and the solar luminosity by about 30% since the Sun was born 4.6 billion years ago. How did the gradual increase in solar luminosity affect Earth? Geological evidence shows that Earth’s surface temperature has remained fairly steady since Earth finished forming more than 4 billion years ago, despite this 30% increase in the Sun’s energy output, because Earth has its own thermostat. This “Earth thermostat” is the carbon dioxide cycle. By maintaining a fairly steady level of atmospheric carbon dioxide, the carbon dioxide cycle regulates the greenhouse effect that maintains Earth’s surface temperature [Section 14.4]. “Observing” the Solar Interior We cannot see inside the Sun, so you may be wondering how we can know so much about what goes on underneath its surface. Astronomers can study the Sun’s interior in three different ways: through mathematical models of the chapter 15 • Our Star 503
Page 1 and 2: PART V STELLAR ALCHEMY
Page 3 and 4: I say Live, Live, because of the Su
Page 5 and 6: Table 15.1 Basic Properties of the
Page 7: COMMON MISCONCEPTIONS The Sun Is No
Page 11 and 12: Figure 15.9 Vibrations on the surfa
Page 13 and 14: Figure 15.11 This tank of dry-clean
Page 15 and 16: a This schematic diagram shows how
Page 17 and 18: weaker magnetic field stronger magn
Page 19 and 20: Figure 15.20 An X-ray image of the
Page 21 and 22: e quator N N N magnetic field line
Page 23 and 24: THE BIG PICTURE Putting Chapter 15
Page 25 and 26: Problems 9. Gravitational Contracti

Chapter 15--Our Sun - Geological Sciences

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