Chapter 15 Surveying the Stars PDF

Surveying the Stars Copyright © 2024 Pearson Education, Inc. All Rights Reserved 15.1 Properties of Stars Our goals for learning: – How do we measure stellar luminosities? – How do we measure stellar temperatures? – How do we measure stellar masses? C...

Surveying the Stars Copyright © 2024 Pearson Education, Inc. All Rights Reserved 15.1 Properties of Stars Our goals for learning: – How do we measure stellar luminosities? – How do we measure stellar temperatures? – How do we measure stellar masses? Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Do We Measure Stellar Luminosities? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Apparent Brightness The brightness of a star depends on both distance and luminosity. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Apparent Brightness Versus Luminosity (1 of 3) Luminosity: Amount of power a star radiates (energy per second = watts) Apparent brightness: Amount of starlight that reaches Earth (energy per second per square meter) Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 1 (1 of 2) Alpha Centauri and the Sun have about the same luminosity. Which one appears brighter? A. Alpha Centauri B. The Sun Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 1 (2 of 2) Alpha Centauri and the Sun have about the same luminosity. Which one appears brighter? A. Alpha Centauri Thecor ectan B. The Sun sweri s Copyright © 2024 Pearson Education, Inc. All Rights Reserved Apparent Brightness Versus Luminosity (2 of 3) The amount of luminosity passing through each sphere is the same. Area of sphere: 4  (radius )2 Divide luminosity by area to get brightness. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Apparent Brightness Versus Luminosity (3 of 3) The relationship between apparent brightness and luminosity depends on distance: Luminosity Apparent Brightness = 4  ( distance ) 2 We can determine a star's luminosity if we can measure its distance and apparent brightness: Luminosity = 4 ( distance )  (brightness ) 2 Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 2 (1 of 2) How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. It would be only 1/3 as bright. B. It would be only 1/6 as bright. C. It would be only 1/9 as bright. D. It would be three times brighter. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 2 (2 of 2) How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. It would be only 1/3 as bright. B. It would be only 1/6 as bright. Thecor ectan C. It would be only 1/ 9 as bright. sweri s D. It would be three times brighter. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Distance So how far away are these stars? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Parallax (1 of 2) Parallax is the apparent shift in position of a nearby object against a background of more distant objects. Apparent positions of nearest stars shift by about an arcsecond as Earth orbits the Sun. Parallax angle depends on distance. Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Parallax (2 of 2) Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Parallax (2 of 2) https://www.youtube.com/watch?v=iwlMmJs1f5o Copyright © 2024 Pearson Education, Inc. All Rights Reserved Parallax and Distance p = parallax angle 1 d ( in parsecs ) = p ( in arcseconds ) 1 d ( in light-years ) = 3.26  p ( in arcseconds ) Copyright © 2024 Pearson Education, Inc. All Rights Reserved Luminosity Range of Stars Most luminous stars: 106 LSun Least luminous stars: 10 −4 LSun ( LSun is luminosity of Sun) Copyright © 2024 Pearson Education, Inc. All Rights Reserved Handout Activity Let’s work on Activity Manual Pg. 17 - 18. Luminosity Brightness and the Inverse Square Law Copyright © 2024 Pearson Education, Inc. All Rights Reserved Clickers: Luminosity, Brightness and Inverse Square Law (5 questions) Scoring: 5 points for the correct answer 1 point for the wrong answer It’s worth guessing even if you have no idea Copyright © 2024 Pearson Education, Inc. All Rights Reserved How many square meters of the floor area are lit up by the lightbulb located 1 meter of the floor? (Q2) A–1 B-4 C – 2.28 D – 3.14 E – 12.56 Copyright © 2024 Pearson Education, Inc. All Rights Reserved If the lightbulb that is 1 meter away puts out 314 watts of light energy, how many watts per square meter of light energy does the floor receive from the lightbulb? (Q3) A – 100 B - 50 C – 25 D – 200 E – 12.5 Copyright © 2024 Pearson Education, Inc. All Rights Reserved How many square meters of the floor area are lit up by the lightbulb located 2 meters of the floor? (Q4) A–1 B-4 C – 2.28 D – 3.14 E – 12.56 Copyright © 2024 Pearson Education, Inc. All Rights Reserved If the lightbulb that is 2 meters away puts out 314 watts of light energy, how many watts per square meter of light energy does the floor receive from the lightbulb? (Q5) A – 100 B - 50 C – 25 D – 200 E – 12.5 Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which star is more luminous, the closer (star one) of the farther star (star three) ? (Q8a) A – Star one B – Star Three Copyright © 2024 Pearson Education, Inc. All Rights Reserved How much more luminous is Star Three (farther star) compared to Star One (closer star)? (Q8c) A–2 B-3 C–4 D–9 E – 12 Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Do We Measure Stellar Temperatures? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Spectral Type and Temperature (2 of 3) Cecilia Payne-Gaposchkin showed in her PhD dissertation published in 1925 that the level of ionization also reveals a star's temperature. This tied spectral types to stellar temperatures. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Spectral Type and Temperature (3 of 3) Table 15.1 The Spectral Sequence Absorption lines in star's spectrum thus tell us its ionization level and temperature. Astronomers have sometimes extended the classification to types L, T, and Y. These objects are cooler than M type and emit in the infrared. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Temperatures (1 of 2) Every object emits thermal radiation with a spectrum that depends on its temperature. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Properties of Thermal Radiation 1. Hotter objects emit more light per unit area at all frequencies. 2. Hotter objects emit photons with a higher average energy. Therefore, an object of fixed size grows more luminous as its temperature rises. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Temperatures (Wien’s displacement law) (2 of 2) Hottest stars: 50,000 K Coolest stars: 3000 K (Sun's surface is 5800 K.) 𝑏 𝜆𝑝𝑒𝑎𝑘 = 𝑇 Where b is a constant with value b = 2.898 x 10-3 m K (meters x Kelvin) Copyright © 2024 Pearson Education, Inc. All Rights Reserved Temperature Range of stars – Orion Betelgeuse ~3800 K Mintaka ~31,800 K Rigel ~12,100 K Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Does Color Correspond to the Surface Temperature of a Star? (1 of 2) a. The hottest stars are “red hot.” b. The hottest stars are “bluish white.” c. The coldest stars are yellow. d. Temperature does not relate to a star’s color. Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Does Color Correspond to the Surface Temperature of a Star? (2 of 2) a. The hottest stars are “red hot.” b. The hottest stars are “bluish white.” c. The coldest stars are yellow. d. Temperature does not relate to a star’s color. Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Do We Measure Stellar Masses? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Measuring Stellar Masses and Radii (1 of 2) The orbit of a binary star system depends on strength of gravity. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Types of Binary Star Systems Visual binary Spectroscopic binary Eclipsing binary About half of all stars are in binary systems. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Visual Binary We can directly observe the orbital motions of these stars. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Spectroscopic Binary We determine the orbit by measuring Doppler shifts. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Eclipsing Binary We can measure periodic eclipses. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Measuring Stellar Masses and Radii (2 of 2) We measure mass using gravity. Direct mass measurements are possible only for stars in binary star systems. 4 2 p2 = a3 G ( M1 + M2 ) p = period a = average separation Copyright © 2024 Pearson Education, Inc. All Rights Reserved Need Two Out of Three Observables to Measure Mass: 1. Orbital period (p) 2. Orbital separation (a or r = radius) 3. Orbital velocity (v) For circular orbits, v = 2 r  p. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Mass Most massive stars: 100MSun Least massive stars: 0.08 MSun ( MSun is the mass of the Sun.) Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Have We Learned? (1 of 5) How do we measure stellar luminosities? – If we measure a star's apparent brightness and distance, we can compute its luminosity with the inverse square law for light. – Parallax tells us distances to the nearest stars. How do we measure stellar temperatures? – A star's color and spectral type both reflect its temperature. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Have We Learned? (2 of 5) How do we measure stellar masses? – Newton's version of Kepler's third law tells us the total mass of a binary system, if we can measure the orbital period (p) and average orbital separation of the system (a). Copyright © 2024 Pearson Education, Inc. All Rights Reserved Handout Activity Let’s work on Activity Manual Pg. 25 - 26. Electromagnetic radiation and Thermal Spectra Copyright © 2024 Pearson Education, Inc. All Rights Reserved Clickers: Luminosity, Brightness and Inverse Square Law (5 questions) Scoring: 5 points for the correct answer 1 point for the wrong answer It’s worth guessing even if you have no idea Copyright © 2024 Pearson Education, Inc. All Rights Reserved If photon A has half the energy of photon B, then photon A will have ________ the frequency of photon B and ________ the wavelength of photon B A – half, half B – half, double C – double, half D – double, double Copyright © 2024 Pearson Education, Inc. All Rights Reserved According to Figure 1, at what luminosity does the Sun emit the highest luminosity per unit area and unit wavelength? A – 200 THz B – 400 THz C – 600 THz D – 800 THz Copyright © 2024 Pearson Education, Inc. All Rights Reserved At what frequency will the star with T=3900 K emit the highest luminosity per unit area and unit wavelength? A – 200 THz B – 400 THz C – 600 THz D – 800 THz Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which region has the reddest light? R1 R2 R3 A – R1 B – R2 C – R3 Copyright © 2024 Pearson Education, Inc. All Rights Reserved 15.2 Patterns Among Stars Our goals for learning: – What is a Hertzsprung-Russell diagram? – What is the significance of the main sequence? – What are giants, supergiants, and white dwarfs? – Why do the properties of some stars vary? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Hertzsprung-Russell Diagram (1 of 4) An H-R diagram plots the luminosity and temperature of stars. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Hertzsprung-Russell Diagram (2 of 4) Most stars fall somewhere on the main sequence of the H-R diagram. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Hertzsprung-Russell Diagram (3 of 4) Stars with lower T and higher L than main-sequence stars must have larger radii. These stars are called giants and supergiants. L = σAT4 Copyright © 2024 Pearson Education, Inc. All Rights Reserved Hertzsprung-Russell Diagram (1 of 4) An H-R diagram plots the luminosity and temperature of stars. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Hertzsprung-Russell Diagram (4 of 4) Stars with higher T and lower L than main-sequence stars must have smaller radii. These stars are called white dwarfs. P = σAT4 Copyright © 2024 Pearson Education, Inc. All Rights Reserved Hertzsprung-Russell Diagram (1 of 4) An H-R diagram plots the luminosity and temperature of stars. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Luminosity Classes A star's full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star): I supergiant II bright giant III giant IV subgiant V main sequence Examples: Sun G2 V Sirius A1 V Proxima Centauri M5.5 V Betelgeuse M2 I Copyright © 2024 Pearson Education, Inc. All Rights Reserved Hertzsprung-Russell Diagram H-R diagram depicts: temperature, color, spectral type, luminosity, radius Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 5 (1 of 2) Which star is the hottest? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 5 (2 of 2) Which star is the hottest? A Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 6 (1 of 2) Which star is the most luminous? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 6 (2 of 2) Which star is the most luminous? B Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 7 (1 of 2) Which star is a main-sequence star? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 7 (2 of 2) Which star is a main-sequence star? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 8 (1 of 2) Which star has the largest radius? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question 8 (2 of 2) Which star has the largest radius? Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is the Significance of the Main Sequence? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Lifetimes Along the Main Sequence (1 of 3) Main-sequence stars are fusing hydrogen into helium in their cores like the Sun. Luminous main- sequence stars are hot (blue). Less luminous ones are cooler (yellow or red). Copyright © 2024 Pearson Education, Inc. All Rights Reserved Lifetimes Along the Main Sequence (2 of 3) Mass measurements of main-sequence stars show that the hot, blue stars are much more massive than the cool, red ones. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Lifetimes Along the Main Sequence (3 of 3) The mass of a normal, hydrogen-fusing star determines its luminosity and spectral type. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Mass Is the Most Fundamental Property Core pressure and temperature of a higher-mass star need to be larger in order to balance gravity. Higher core temperature boosts fusion rate, leading to larger luminosity. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Properties Review (1 of 2) Luminosity: from brightness and distance 10 −4 Lsun − 106 Lsun Temperature: from color and spectral type 3000 K − 50,000 K Mass: from period (p) and average separation (a) of binary star orbit 0.08 MSun − 100MSun Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Properties Review (2 of 2) Luminosity: from brightness and distance ( 0.08Msun ) 10−4 Lsun − 106 Lsun (100Msun ) Temperature: from color and spectral type ( 0.08Msun ) 3000 K − 50,000 K (100M sun ) Mass: from period (p) and average separation (a) of binary star orbit 0.08MSun − 100MSun Copyright © 2024 Pearson Education, Inc. All Rights Reserved Mass and Lifetime (1 of 3) Sun’s life expectancy: 10 billion years Until core hydrogen (10% of total) is used up Copyright © 2024 Pearson Education, Inc. All Rights Reserved Mass and Lifetime (2 of 3) Sun’s life expectancy: 10 billion years Until core hydrogen (10% of total) is used up Life expectancy of 10MSun star: 10 times as much fuel, uses it 104 times as fast 10 million years ~ 10 billion years  10 / 10 4 Copyright © 2024 Pearson Education, Inc. All Rights Reserved Mass and Lifetime (3 of 3) Sun’s life expectancy: 10 billion years Until core hydrogen (10% of total) is used up Life expectancy of 10 MSun star: 10 times as much fuel, uses it 104 times as fast 10 million years  10 billion years  10 / 10 4 Life expectancy of 0.1MSun star: 0.1 times as much fuel, uses it 0.01 times as fast 10 million years  10 billion years  0.1/ 0.01 Copyright © 2024 Pearson Education, Inc. All Rights Reserved Main-Sequence Star Summary High-Mass Star: High luminosity Short-lived Larger radius Blue Low-Mass Star: Low luminosity Long-lived Small radius Red Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Are Giants, Supergiants, and White Dwarfs? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Sizes of Giants and Supergiants Copyright © 2024 Pearson Education, Inc. All Rights Reserved Off the Main Sequence Stellar properties depend on both mass and age: Those that have finished fusing H to He in their cores are no longer on the main sequence. All stars become larger and redder after exhausting their core hydrogen: giants and supergiants. Most stars end up small and white after fusion has ceased: white dwarfs. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question Which star is most like our A Sun? D B C Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question Which star is most like our A Sun? D B B C Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question Which of these stars will have A changed the least 10 billion years D from now? B C Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question Which of these stars will have A changed the least 10 billion years D from now? B C C Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question Which of these stars can be no A more than 10 million years old? D B C Copyright © 2024 Pearson Education, Inc. All Rights Reserved Thought Question Which of these stars can be no A more than 10 million years old? D A B C Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Have We Learned? (3 of 5) What is a Hertzsprung-Russell diagram? – An H-R diagram plots stellar luminosity of stars versus surface temperature (or color or spectral type). What is the significance of the main sequence? – Normal stars that fuse H to He in their cores fall on the main sequence of an H-R diagram. – A star’s mass determines its position along the main sequence (high-mass: luminous and blue; low-mass: faint and red). Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Have We Learned? (4 of 5) What are giants, supergiants, and white dwarfs? – All stars become larger and redder after core hydrogen burning is exhausted: giants and supergiants. – Most stars end up as tiny white dwarfs after fusion has ceased. Why do the properties of some stars vary? – Some stars fail to achieve balance between power generated in the core and power radiated from the surface. Copyright © 2024 Pearson Education, Inc. All Rights Reserved 15.3 Star Clusters Our goals for learning: – What are the two types of star clusters? – How do we measure the age of a star cluster? Copyright © 2024 Pearson Education, Inc. All Rights Reserved What are the Two Types of Star Clusters? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Clusters (1 of 5) Open cluster: A few thousand loosely packed stars Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Clusters (2 of 5) Globular cluster: Up to a million or more stars in a dense ball bound together by gravity Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Do We Measure the Age of a Star Cluster? Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Clusters (3 of 5) Massive blue stars die first, followed by white, yellow, orange, and red stars. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Star Cluster Age (1 of 2) The Pleiades cluster now has no stars with life expectancy less than around 100 million years. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Star Cluster Age (2 of 2) The main-sequence turnoff point of a cluster tells us its age. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Clusters (4 of 5) To determine accurate ages, we compare models of stellar evolution to the cluster data. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Stellar Clusters (5 of 5) Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Have We learned? (5 of 5) What are the two types of star clusters? – Open clusters are loosely packed and contain up to a few thousand stars. – Globular clusters are densely packed and contain hundreds of thousands of stars. How do we measure the age of a star cluster? – A star cluster's age roughly equals the life expectancy of its most massive stars still on the main sequence. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Handout Activity Let’s work on Activity Manual Pg. 49 - 50. H-R Diagram Copyright © 2024 Pearson Education, Inc. All Rights Reserved Clickers: Luminosity, Brightness and Inverse Square Law (5 questions) Scoring: 5 points for the correct answer 1 point for the wrong answer It’s worth guessing even if you have no idea Copyright © 2024 Pearson Education, Inc. All Rights Reserved Are the stars you studies in the Star Cluster Yamato main-sequence stars? (Q5) A – Yes B – No Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which of the following ages is the best match to the age of the Star Cluster Yamato? (Q6) A – 50 million years B – 3 billion years C – 20 billion years Copyright © 2024 Pearson Education, Inc. All Rights Reserved