* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 11: Stars, HR diagram.
International Ultraviolet Explorer wikipedia , lookup
Corona Borealis wikipedia , lookup
Auriga (constellation) wikipedia , lookup
Cassiopeia (constellation) wikipedia , lookup
Cygnus (constellation) wikipedia , lookup
Dyson sphere wikipedia , lookup
Observational astronomy wikipedia , lookup
H II region wikipedia , lookup
Perseus (constellation) wikipedia , lookup
Planetary habitability wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Malmquist bias wikipedia , lookup
Type II supernova wikipedia , lookup
Future of an expanding universe wikipedia , lookup
Cosmic distance ladder wikipedia , lookup
Stellar classification wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
Corvus (constellation) wikipedia , lookup
Stellar kinematics wikipedia , lookup
Standard solar model wikipedia , lookup
Hayashi track wikipedia , lookup
1 Announcements • TA feedback forms are online! find the link at the class website. Please take 5 minutes to tell your TAs your opinion. • Midterm scores will be posted at 3 pm There was an issue with the key, so I am checking all 175 scores by hand. We will curve the class AT THE END, including the scores for all the items that you get credit for: 20% Homework 10% Attendance to Discussion section 10% Attendance to lectures 30% Midterm 30% Final Exam (03/21/2013) For now you can see an ESTIMATE letter grade in case you need it. • Homework 5 is due this Thursday. 2 Chapter 15: Stars 3 Stars We can gather a lot of information about stars (mostly using what we already know from the 1st half of the class) 1. Distance? 2. Temperature? 3. Composition? 4. Mass? 5. Size? 4 1. Distance to stars • Summary: How to measure the distance to a star? • When the parallactic angle (P) is in arcseconds, the distance will be in parsecs 1 distance(parsec) = p(arcsec) 1parsec = 206264 × AU size distance 5 • Quizz #9 What is the distance to a star with a parallax of 0.5 arcsec? a) 1 parsec b) 2 parsec c) 0.5 parsec d) 5 parsec e) N.A. 1 distance = = 2parsec 0.5arcsec size distance 6 Stars We can gather a lot of information about stars (mostly using what we already know from the 1st half of the class) 1. Distance ✓ 1.1.Luminosity 2. Temperature? 3. Composition? 4. Mass? 5. Size? 7 1.1 Luminosity • We can measure the Flux (= energy/sec/meter2) by collecting it here on Earth. We also call it “apparent brightness”. • If we have both the flux and the distance... Luminosity = 4π(distance)2 × Flux we can get the luminosity of the star, which is an intrinsic property of it. Surface area of a sphere: 4π(radius)2 8 1.1 Luminosity • We can measure the Flux and Distance at any location, like, from Earth. • In the special case that the distance corresponds to the actual size of the star, then • “distance” becomes the radius of the star • Flux (or the apparent brightness) is related to the temperature by Flux = σT4 Luminosity = 4π(distance)2 × Flux Luminosity = 4π(radius)2 × σT4 9 1.1 Luminosity • Stars exhibit a range in luminosities • Most luminous stars: 106 LSun (that’s a million times the Sun!) • Least luminous stars: 10-4 LSun (or 1/10000 times the Sun) 10 Stars We can gather a lot of information about stars (mostly using what we already know from the 1st half of the class) 1. Distance ✓ 1.1.Luminosity✓ 2. Temperature? 3. Composition? 4. Mass? 5. Size? 11 2. Temperature • How can we measure the temperature of a star? • We can see the colors of stars (or at which wavelength do we see it emitting the most?) λpeak T = 2.9mmK • But just the color alone is not that much information... • What else can we do? 12 2. Temperature • How can we measure the temperature of a star? • We can see the colors of stars (or at which wavelength do we see it emitting the most?) λpeak T = 2.9mmK • But just the color alone is not that much information... • What else can we do? We can take a spectrum! • What do you think? A hotter star, would show more or less absorption lines than the sun? Think about what makes the lines. 13 • 2. Temperature: Stellar classification A hotter star, would show more or less absorption lines than the sun? Less! Because the electrons would stop ‘belonging’ to a particular atom, so no absorption lines (from going to higher energy levels). Sun 14 2. Temperature: Stellar classification • A hotter star, would show more or less absorption lines than the sun? Less! Because the electrons would stop ‘belonging’ to a particular atom (ionized atoms), so no absorption lines (from going to higher energy levels). • It wasn’t until 1925 that Cecilia Payne related the temperature of stars to the spectral classes. • Sun 15 2. Temperature: Stellar classification • A hotter star, would show more or less absorption lines than the sun? Less! Because the electrons would stop ‘belonging’ to a particular atom, so no absorption lines (from going to higher energy levels). • When ordered from hottest to coolest, the order reads OBAFGKM (Why? because first they were ordered by the strength of the hydrogen lines and they went ABCD...) Sun 16 2. Temperature: Stellar classification • A hotter star, would show more or less absorption lines than the sun? Less! Because the electrons would stop ‘belonging’ to a particular atom (ionized atoms), so no absorption lines (from going to higher energy levels). • When ordered from hottest to coolest, the order reads OBAFGKM Valentine’s Day mnemonic: Oh Be A Fine Girl/Guy Kiss Me Sun 17 Stars We can gather a lot of information about stars (mostly using what we already know from the 1st half of the class) 1. Distance✓ 1.1.Luminosity✓ 2. Temperature✓ 3. Composition? 4. Mass? 5. Size? 18 3. Composition • We already took a spectrum, and got the temperature of our star. But a spectrum has a lot more information than that. • We can measure individual lines (and quantum mechanics) to obtain the relative amounts of different elements. Sun 19 Stars We can gather a lot of information about stars (mostly using what we already know from the 1st half of the class) 1. Distance✓ 1.1.Luminosity✓ 2. Temperature✓ 3. Composition✓ 4. Mass? 5. Size? 21 4. Mass • How can we measure the mass of a star? • We can use Newton’s version of Kepler’s third law! When we used it for a planet orbiting a star, we neglected the mass of the planet. 3 a G(M + m) = 2 P 4π 2 • 0 a3 GM = 2 P 4π 2 But if now we would like to measure the mass of a star instead... it is hard to directly see planets outside our solar system Binary stars! Albireo 22 • 4. Mass If the system now has two stars, we cannot neglect either of the masses because they are comparable a3 G(M1 + M2 ) = 2 P 4π 2 • a: semi-major axis P: period G: gravitational constant M1: mass of star 1 M2: mass of star 2 Albireo 23 • 4. Mass Binary systems: • Visual binaries: In this case we can directly measure the orbital motions of the stars Sirius A and B separation: 7.6 arcsec Caveat: inclination angle. 24 • 4. Mass Binary systems: • Visual binaries: In this case we can directly measure the orbital motions of the stars • Eclipsing binaries: if the system is close to edge on, the stars will block each other’s light from us 25 • 4. Mass Binary systems: • Visual binaries: In this case we can directly measure the orbital motions of the stars • Eclipsing binaries: if the system is close to edge on, the stars will block each other’s light from us • Spectroscopy binaries: use the doppler shifts in the spectral lines of both objects. 26 Stars We can gather a lot of information about stars (mostly using what we already know from the 1st half of the class) 1. Distance✓ 1.1.Luminosity✓ 2. Temperature✓ 3. Composition✓ 4. Mass✓ 5. Size? 27 • 5. Size Stefan-Boltzmann law: • If we know the flux and distance, then we can get the luminosity Luminosity = Flux × 4π(dist)2 • • We can use the temperature (from the spectra) and the luminosity to get the radius of the star Luminosity = σT4 × 4π(radius)2 Luminosity (radius) = σT4 × 4π 2 28 Stars: summary of properties Luminosity (from apparent brightness (flux) and distance) 10−4 L⊙ − 106 L⊙ Temperature (from color and spectral lines) 3,000 K - 50,000 K Mass (from binary systems) 0.08M⊙ − 100M⊙ Size (from S-B law, measured distance and temperature) 0.001R ⊙ −1000R⊙ ?? ⊙ :values for the Sun 35 The Herzsprung-Russel Diagram We are able to determine the characteristics of stars: temperature, mass, size, distance, etc. But we would like to gain insight to how they work and evolve. Let’s begin with something more familiar: Humans. Description? Height, weight, hair color/length, eye color, age, address, etc. Are these characteristics related? Not related, just a scatter plot Hair color Height 37 The Herzsprung-Russel Diagram We are able to determine the characteristics of stars: temperature, mass, size, distance, etc. But we would like to gain insight to how they work and evolve. Let’s begin with something more familiar: Humans. Description? Height, weight, hair color/length, eye color, age, address, etc. Are these characteristics related? Not related, just a scatter plot Address Height 38 The Herzsprung-Russel Diagram We are able to determine the characteristics of stars: temperature, mass, size, distance, etc. But we would like to gain insight to how they work and evolve. Let’s begin with something more familiar: Humans. Description? Height, weight, hair color/length, eye color, age, address, etc. Are these characteristics related? Related! not SIMPLE, but we can learn something from this Age Height 40 The Herzsprung-Russel Diagram Stars now.... Description? temperature, luminosity, size, mass, radius, etc. Are these characteristics related? This is what the Herzsprung-Russel (or HR from now on) is all about. Luminosity Notice that the temperature axis is flipped! Temperature 41 The Herzsprung-Russel Diagram Stars now.... Description? temperature, luminosity, size, mass, radius, etc. Are these characteristics related? This is what the Herzsprung-Russel (or HR from now on) is all about. Example: HR diagrams for two clusters M67 (young) and M4 (old) What can we learn from this? 46 HR Diagram Relations between luminosity, mass, size and temperature of stars. Which star is hottest? Star A : Wien’s law C Which star is most luminous? Star C B Which star is the biggest? Star C D A E 48 HR Diagram Relations between luminosity, mass, size and temperature of stars. Where are most of the stars? In the “Main sequence” 50 The Main Sequence There is a very tight relationship between luminosity and temperature We see that the Sun is in this sequence... Then there is something in common between the Sun and the rest of the stars in the main sequence.... They are all burning H into He in their cores More luminous = hotter = more massive! Less luminous = cooler = less massive! 51 The Main Sequence If we have a higher mass star, how can we keep it from collapsing under its own weight? The pressure needs to balance the gravitational force. Higher mass = higher core pressure and higher core temperature fusion rate increases until it supports the star’s mass Lower mass = lower core pressure and lower core temperature fusion rate matches the weight of the outer layers 52 The Main Sequence If we have a higher mass star, how can we keep it from collapsing under its own weight? The pressure needs to balance the gravitational force. L∝M 4 Luminosity is proportional to the mass to the fourth power. M as ss eq u en c e 53 The Main Sequence: summary The main sequence is where the stars that are burning H into He are (most of them). More luminous stars are hotter. More luminous stars are more massive. Also, more luminous stars are bigger. M as ss eq u en c e 54 The Main Sequence If we have a higher mass star, how can we keep it from collapsing under its own weight? The pressure needs to balance the gravitational force. L∝M 4 Luminosity is proportional to the mass to the fourth power. More massive stars give out more energy (more mass)... They will run out of fuel sooner! M as ss eq u en c e 55 Stellar evolution How is the lifespan of a star related to its mass? Lifespan is just how long will the hydrogen supply last. Lifetime = energy supply / rate of energy consumption Lifetime = energy supply / (energy/sec) Since E=mc2 Lifetime = constant * Mass/ luminosity Lifetime ∝ Mass/ Luminosity But L is proportional to M4 Lifetime ∝ Mass/ Mass4 Lifetime∝1/M3 M as ss eq u en ce 56 Stellar evolution How is the lifespan of a star related to its mass? Lifetime ∝ M−3 The Sun will last about 10 billion years How about a star with M = 10 Msun? Lifetime10M⊙ ∝ (10M⊙ )−3 Lifetime10M⊙ (10M⊙ )−3 = Lifetime⊙ M−3 ⊙ Lifetime10M⊙ 10−3 M−3 ⊙ = Lifetime⊙ M−3 ⊙ Lifetime10M⊙ Lifetime⊙ = 103 M as ss eq u en ce 57 Stellar evolution How is the lifespan of a star related to its mass? Lifetime ∝ M−3 The Sun will last about 10 billion years How about a star with M = 10 Msun? Lifetime10M⊙ Lifetime⊙ = 103 It would last only 1/1000 times the lifespan of the Sun! M as ss eq u en ce 58 Stellar evolution High mass stars: Are more luminous Have large radius Are bluer (hotter) Live shorter lives Low mass stars: Are dimmer Are smaller Are redder (cooler) Live longer lives