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The as a - Stellar Characteristics Attendance Quiz

Are you here today? Here! (a) yes (b) no (c) see the sun in a different light! (d) a pun is the lowest form of humor, unless you thought of it yourself Exam Grades

• To help those of you who may have struggled on the first midterm, I am instituting the following exam grading policy: • The lower of your two midterms scores can be replaced by your final exam, if your final score is higher than either midterm • Thus, if you get a final exam score higher than either midterm, the exam portion of your grade (which is 60% of your total grade) will be 40% final exam, 20% higher midterm • If you get a final exam score lower than both midterms, your exam grade will be 20% final exam, 20% each of the two midterms • Thus, even if you bombed the first midterm, you can still do well in this class • This policy only applied to exams you take. If you skip the midterm, it will count as a zero, no matter what! • Remember, there is no curve in this class, so everyone wins with this policy! Today’s Topics

• Our Sun is a Star • What makes the Sun shine? • Historical views • (E = mc2) • Age of the Sun • Structure of the Sun • Stellar similarities and differences • Measuring Stellar Characteristics • Stellar • Stellar distances : the building blocks of the • Our Sun is one of billions of billions of stars in the Universe (400 billion in the alone) • The vast majority of the visible matter in the Universe is made of stars • Almost all the light from a is from the stars it contains • We will spend the next 2 weeks studying stars, starting with our Sun • How do they shine? • What gives them their colors? • What are they made of? • What are they like inside? • How are they born, how do they evolve, and how do they die? The Sun: some basic facts What are the known facts about the Sun that our models and theories have to explain? 5 1. The radius of the Sun is R¤ = 7 × 10 km (about 110 × RE) 30 2. The of the Sun is M¤ = 2 × 10 kg (about 300,000 × ME) 26 3. The luminosity of the Sun is L¤ = 4 × 10 W 4. The surface temperature of the Sun is T = 5800 K 5. The composition of the Sun is: 70% H, 28% He, 2% other - Demo

• To get some sense of scale we are going to do a Lecture Tutorial on the size of various objects and systems in the (Earth, Moon, Sun, Earth-Moon system, and Earth’s ) • To prepare for this, we are going to first do a demonstration using an Earth-Moon model Lecture Tutorial: Sun Size, pp. 113-115

• Work with one or more partners - not alone! • Get right to work - you have 10 minutes • Read the instructions and questions carefully. • Discuss the concepts and your answers with one another. Take to understand it now!!!! • Come to a consensus answer you all agree on. • Write clear explanations for your answers. • If you get stuck or are not sure of your answer, ask another group. • If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask me for help. Sun Size Quiz

If you determined that the diameter of a is 100 the diameter of the Sun, which is the most appropriate (closest) answer for the number of that could fit across this ? a) 100 b) 1,000 c) 10,000 d) 100,000 e) 1,000,000 What makes the Sun shine?

• What makes the Sun shine has been a mystery as old as • Ancient thinkers, drawing on their own experiences, suggested the Sun was a glowing ember of fire • However, once the process of chemical burning was understood, and people realized that the Sun was much further away than had been previously thought, it was shown that the Sun could only burn for a few thousand years this way • Also, a burning ember would cool over time, which was not seen What makes the Sun shine? • In the late 1800s, & Helmholtz suggested the idea that the Sun’s could come from a slow steady gravitational contraction • As the gas in the Sun became smaller, it loses gravitational potential energy, which can convert to • Calculations showed that this mechanism could keep the Sun shining for about 25,000,000 years, which sounds promising • However, around this time, geologists found evidence that the Earth was hundreds of million or even billions of years old (modern estimates are about 4.6 billion years) What makes the Sun shine?

• The answer came when Einstein discovered his most famous equation, E = mc2, as part of his work on relativity • As shown at right, when 4 merge to form a 4He nucleus (also known as an alpha (α) ), mass is converted to energy • This process is known as nuclear fusion • As we will see, this mechanism is capable of allowing the Sun to shine at its current rate for 10 billion years Nuclear Fusion in the Sun’s core collide two at a time, so the reaction 4p → 4He + energy requires multiple steps 1. First two protons combine to form (2H), namely a and a ; since electric charge (and something called lepton number) must be conserved, a (e+) and a (ν) are emitted 2. Then each deuterium nucleus gets an additional proton to make 3He 3. Finally, two 3He nuclei fuse to form 4He plus two protons Nuclear Fusion • The positively charged protons in a nucleus repel each other, unless they are close enough (~10−15 m) for the strong to bind them together • Thus for nuclear fusion to occur, the protons must approach that close to each other • This requires very high speeds, implying very high temperatures • In fact, without a quantum effect known as tunneling no fusion would occur in the Sun at all • The temperature at the center of the Sun is about 15 million K, hot enough for protons to fuse together to make nuclei Nuclear Fusion The energy released can be calculated from E = mc2: −27 mp =1.673×10 kg

−27 4mp = 6.690 ×10 kg

−27 mHe = 6.643×10 kg Δm = 0.047 ×10−27 kg E = Δmc 2 = (0.047 ×10−27 kg)(3×108 m/s)2 = 4.23×10−12 J = 26.4 MeV • For comparison, the typical chemical reaction releases a few eV Nuclear Fusion • Thus the fraction of mass converted to energy is: Δm 0.047 ×10−27 kg = = 0.007 (0.7%) m 6.690 ×10−24 kg 1 kg H → 993 g He + 7 g converted to energy • 4.23 ×−12 J sounds small, but this reaction happens ~1038 times/second ⇒ 4 × 10((−12+38) J = 4 × 1026 J is released 26 each second or L¤= 4 × 10 W = 400,000,000,000,000,000,000,000,000 W • 600,000,000 tons of H is converted to 596,000,000 tons of He + energy each second! Age of the Sun

• To determine the approximate age of the Sun, we can divide the total mass of the Sun by the amount of converted to Helium each second 2 ×1030 kg t ≈ ≈ 3×1018 s ≈100 billion years ¤ 6 ×1011 kg/s • In fact, only about 10% of the Hydrogen in the Sun (in the core or center) will be converted to Helium, so the true lifetime of the Sun is 10 × shorter, or ~ 10 billion yrs

• Since tsolar sys ~ 4.6-5 billion years, the Sun is about halfway through its lifetime Stellar Interior Quiz II

The chemical composition of the Sun 3 billion years ago was different from what it is now in that it had a) more hydrogen b) more helium c) more d) molecular hydrogen e) It wasn’t different Structure of the Sun • For fusion to occur in the center of the Sun, the temperature must be about 15,000,000 K, whereas the surface is only 5800 K Q: Why is the center of the Sun so hot? A: Pressure! Q: Why is the pressure so high at the center of the Sun? A: ! • Consider the figure at right: • The person on the top has no to support • The person in the middle supports one other person • The person on the bottom has to support the two people above him Structure of the Sun • At every layer of the Sun, outward pressure must equal the pressure caused by the weight of the overlying material • Thus, the pressure in the interior must rise towards the center • At high pressures, the gas is pressed closer together (higher ) and becomes hotter (more frequent collisions lead to higher speeds ⇒ higher internal KE ⇒ higher temp) • How does energy escape? There are 2 mechanisms of energy transport 1. Random walk (radiative diffusion) 2. (like boiling) • It takes more than 100,000 years(!) for a released in the fusion reaction to make its way to the surface Stellar Interior Quiz III If fusion in the ceased today, worldwide panic would break out tomorrow as the Sun would begin to grow dimmer a) Yes, because the Earth would quickly freeze over b) Yes, because the Earth would no longer be bound to the solar system and would drift into c) Yes, because the Sun would collapse and the would soon follow d) No, it takes thousands of years for created in nuclear reactions at the solar core to reach the surface e) No, the Sun would continue to glow brightly for billions of years because of gravitational contraction The Solar Thermostat Stellar Interior Quiz IV

If the center of the Sun could be heated slightly, the nuclear reactions would occur faster and hence release more heat, so the Sun’s core would a) collapse b) expand and hence heat up even more c) expand and hence cool back to its previous temperature d) explode Today’s Topics II

• Stellar similarities and differences • Measuring Stellar Characteristics • Stellar luminosity • Stellar distances People: commonalities and differences • People have much in common • Same basic structure (2 arms, 2 legs, 2 eyes, 1 nose, etc.) • Made up of same stuff (bone, tissue, blood, etc.) • Get energy the same way (eating food) • People also differ in detail • Short, tall, fat, thin • Eye, hair, skin color • Some live a long time, some don’t • Different lifestyles Stars: commonalities and differences • Stars are like people in this way • Stars have much in common • Balls of hot gas • Made of 70% H, 28% He, 2% everything else • Get energy from nuclear fusion • Stars also differ • Luminosity • Mass • Temperature (color) • Size (radius) • Lifetime • End their differently Stellar Luminosity • Apparent brightness is a measure of how bright a star appears on Earth • Luminosity is a measure of how much energy per second (W) a star emits • The apparent brightness of an object declines with distance (inverse square) Luminosity Apparent brightness = 4π × (distance)2 • If we measure apparent brightness (energy/sec/m2) and we know distance, we can get the luminosity of the star • For Sun, apparent brightness = 1400 W/m2 and d = 150 million km = 1.5 × 1011 m L = 4π(1400 W/m2)(1.5 ×1011 m)2 = 4 ×1026 W

Brightness Quiz

Two identical stars, one 5 light years from Earth, and a second 50 light years from Earth are discovered. How much fainter does the farther star appear to be? a) square root of 10 b) 10 c) 100 d) 1,000 e) the farther star does not appear fainter, since it is identical Distance and

• It is relatively easy to measure apparent brightness of a star • Distance is much harder to measure • For nearby stars (d ≤ 3000 ly) we can use the technique of parallax • You can quickly understand parallax by putting your finger in front of your face, then alternate closing your two eyes - note how your finger appears to move relative to the more distant objects in the room (Image at right) Ch. 15 - Introduction to Parallax Distance and Parallax

• As the Earth the Sun, relatively nearby stars appear to move relative to more distant stars • Because even the nearest stars are so distant, there is a simple relationship between distance and apparent a star moves 1 d (in ) = p (in arcseconds)

• 1 ≈ 3.26 light years

Parallax Quiz I

You observe two stars over the course of a year (or more) and find that both stars have measurable parallax . Star X has a parallax angle of 1 arcsecond. Star Y has a parallax angle of 1/2 an arcsecond. Which star is closer? a) Star X is closer b) Star Y is closer c) They are the same distance d) There is not enough information to tell Lecture Tutorial: The Parsec, pp. 37-39

• Work with one or more partners - not alone! • Get right to work - you have 15 minutes • Read the instructions and questions carefully. • Discuss the concepts and your answers with one another. Take time to understand it now!!!! • Come to a consensus answer you all agree on. • Write clear explanations for your answers. • If you get stuck or are not sure of your answer, ask another group. • If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask me for help. Parallax Quiz II

Which of the following stars is closest to us? a) (parallax angle = 0.29") b) Ross 780 (parallax angle = 0.21") c) (parallax angle = 0.04") d) (parallax angle = 0.38") Parallax Quiz III

On Earth, the parallax angle for the star Procyon is 0.29 arcseconds. If you were to measure Procyon’s parallax angle from , what would the parallax angle be? (Note: Earth’s orbital radius is larger than Venus’s orbital radius a) more than 0.29 arcseconds b) 0.29 arcseconds c) less than 0.29 arcseconds d) zero arcseconds (no parallax) Stellar

• Stellar luminosities vary from 0.0001 L¤–1,000,000 L¤, ten orders of • Note that most of the stars in this image are at the same distance, so their relative apparent brightness is the same as their relative luminosities

• Note that there are many more faint stars than bright stars, suggesting that less luminous stars are far more common