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Measuring the Stars: Parallax, Magnitudes, and Colors

This chapter explores the different methods used to measure the stars, including parallax, magnitudes, and colors. Discover how astronomers calculate distances and determine the brightness and size of stars.

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Measuring the Stars: Parallax, Magnitudes, and Colors

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  1. 1

  2. Chapter 10 Measuring the Stars 2

  3. Outline • Parallax • Magnitudes • Colors • Sizes • H-R diagrams 3

  4. Chapter 10 Parallax 4

  5. Figure P.12Parallax Geometry 5

  6. Figure P.11Parallax Recall information from Chapter 0 6

  7. Figure 10.1Stellar Parallax 7

  8. Distance Analogy • If the Sun is a marble… • The Earth is a grain of sand 1 m away. • The solar system is ~100 m in diameter 8

  9. Distance Analogy • If the Sun is a marble… • The Earth is a grain of sand 1 m away. • The solar system is ~100 m in diameter • The next star is in Albuquerque! 9

  10. Figure 10.2Sun’s Neighborhood 10

  11. Parallax Measurements • Earth-based measurements can typically be made to 0.03”, or to a distance of ~30 parsecs (pc) • Distances to several thousand stars are known this way. • The Hipparcos satellite extends the distance to ~200 pc, so distances to nearly one million stars can be measured with parallax. 11

  12. Figure 10.3Real Space Motion - Barnard’s Star 22 years apart • Nearby stars also show proper motion, or transverse velocities. • Only a few hundred show more than 1”/yr 12

  13. If a star has a parallax of 0.04”, then its distance must be A) 4 light years. B) 25 parsecs C) 25 light years. D) 40 parsecs. E) .04 parsecs 13

  14. If a star has a parallax of 0.04”, then its distance must be A) 4 light years. B) 25 parsecs C) 25 light years. D) 40 parsecs. E) .04 parsecs 14

  15. Chapter 10 Magnitudes 15

  16. If Venus is magnitude -4.4, and Sirius is magnitude -1.4, then A) Sirius is ~15.8x brighter than Venus B) Sirius is ~3x brighter than Venus C) Venus is ~15.8x brighter than Sirius D) Venus is ~3x brighter than Sirius 16

  17. If Venus is magnitude -4.4, and Sirius is magnitude -1.4, then A) Sirius is ~15.8x brighter than Venus B) Sirius is ~3x brighter than Venus C) Venus is ~15.8x brighter than Sirius D) Venus is ~3x brighter than Sirius 17

  18. More Precisely 10-1More on the Magnitude Scale • Absolute magnitude is how bright a star would appear at 10pc. (a very arbitrary distance) • The Sun’s absolute magnitude is +4.8 18

  19. Magnitudes • Apparent Magnitude • how bright it looks • depends on distance • brightness depends on distance2 • Absolute Magnitude • Only depends on Luminosity (how much energy is being produced) • Does not change with distance • At 10pc, Apparent magnitude= Absolute magnitude 19

  20. Magnitudes and Distance • Example: • 2 flashlights have the same luminosity • flashlight A = apparent “brightness” 4.0 units • flashlight B = apparent “brightness” 2.0 units • Which is closer and by how much? 20

  21. Magnitudes and Distance • Example: • 2 flashlights have the same luminosity • flashlight A = apparent “brightness” 4.0 units • flashlight B = apparent “brightness” 2.0 units • Which is closer and by how much? • Calculate brightness ratio • Star A is 2.0x brighter 21

  22. Magnitudes and Distance • Example: • 2 flashlights have the same luminosity • flashlight A = apparent “brightness” 4.0 units • flashlight B = apparent “brightness” 2.0 units • Which is closer and by how much? • Calculate brightness ratio • Star A is 2.0x brighter • Calculate distance ratio • Star B = sqrt(2.0) = 1.41 times farther away 22

  23. Magnitudes and Distance • Example: • 2 stars, both have Absolute magnitude = 3.0 • Star A = apparent magnitude 4.0 • Star B = apparent magnitude 7.5 • Calculate magnitude difference • Difference of 3.5 magnitudes 23

  24. Magnitudes and Distance • Example: • 2 stars, both have Absolute magnitude = 3.0 • Star A = apparent magnitude 4.0 • Star B = apparent magnitude 7.5 • Calculate magnitude difference • Difference of 3.5 magnitudes • Calculate brightness difference • Brightness difference of 2.512(3.5) = 25.1x 24

  25. Magnitudes and Distance • Example: • 2 stars, both have Absolute magnitude = 3.0 • Star A = apparent magnitude 4.0 • Star B = apparent magnitude 7.5 • Calculate magnitude difference • Difference of 3.5 magnitudes • Calculate brightness difference • Brightness difference of 2.512(3.5) = 25.1x • Calculate distance difference • Star B = sqrt(25.1) = 5 times farther away 25

  26. Two stars both have parallaxes of 0.023”. Star A is magnitude +2.3 and star B is magnitude +7.3 A) star A must be 10x closer. B) star B must be 10x more luminous. C) star A is both 100x brighter and more luminous. D) star A is both 100x brighter and larger. E) we can conclude nothing. 26

  27. Two stars both have parallaxes of 0.023”. Star A is magnitude +2.3 and star B is magnitude +7.3 A) star A must be 10x closer. B) star B must be 10x more luminous. C) star A is both 100x brighter and more luminous. D) star A is both 100x brighter and larger. E) we can conclude nothing. 27

  28. Distance calculations • Absolute magnitude is the apparent magnitude if the object is 10 parsecs away. • Absolute magnitude and luminosity refer to the same thing. • Sun absolute magnitude is 4.8 • Sun luminosity is 1 solar luminosity. • If you know the luminosity, how exactly do you find the distance? m - M = 5 log10 (r/10pc) r = 10pc x 10(m-M)/5 28

  29. Chapter 10 Star Temperatures (Colors) 29

  30. Figure 10.7Star Colors – Orion (20°) and the Milky Way Center (2’) 30

  31. Which star would be the hottest? A) Blue B) White C) Yellow D) Orange E) Red 31

  32. Which star would be the hottest? A) Blue B) White C) Yellow D) Orange E) Red 32

  33. Star Temperatures • Recall Wien’s Law – (peak frequency  Temperature) • You do not need to measure the intensity at many wavelengths to find the peak. • Because you know the shape of the curve (~Blackbody) you only need two points. 33

  34. Figure 10.8Blackbody Curves 34

  35. Element Spectra • Note - The spectrum of an element can “change” as the temperature changes. • Line locations do NOT change • The intensity of different lines can change. • Historical Classification of star types • According to the intensity of the H lines • Labeled A,B,C,D,... 35

  36. Figure 10.9Stellar Spectra • Very hot stars • Most H ionized (weak spectrum) • He spectrum stronger • Medium T stars • stronger H lines • Cooler stars • Lines from heavier elements • Some molecular lines 36

  37. Star Spectral Classification • Modern Classification of star types • According to star temperature • Historical labels kept (A,B,C,D,...), but order changed • New order, from hottest to coldest is: O, B, A, F, G, K ,M. • Other letters removed from classification 37

  38. Star Spectral Classification • New order is: O, B, A, F, G, K ,M. • Remember the order... • Oh, Be AFine Girl/(Guy) Kiss Me 38

  39. Chapter 10 Star Sizes 39

  40. Star Sizes • The luminosity of a star depends on the stars diameter as well as its temperature. • When radius is combined with Stefan’s Law: luminosity  radius2 x T4 ( means proportional to) 40

  41. Star Sizes • The luminosity of a star depends on the stars diameter as well as its temperature. • When surface area is combined with Stefan’s Law: luminosity = 4r2T4 (= means equal) 41

  42. Star Sizes • Can directly measure the radius on very few stars. (~dozen) 42

  43. Figure 10.10Betelgeuse 43

  44. Star Sizes • Can directly measure the radius on very few stars. (~dozen) • Can calculate the radius if you know the luminosity and the temperature. 44

  45. Figure 10.11Stellar Sizes • Giants - radius between 10x and 100x solar • Supergiants - larger (up to 1000x) • Dwarf - radius comparable to or smaller than the sun. 45

  46. Chapter 10 HR Diagrams 46

  47. Figure 10.12H–R Diagram of Well-Known Stars • Plot the luminosity vs. temperature. • This is called a Hertzsprung-Russell (H-R) diagram • Need to plot more stars! 47

  48. Figure 10.15Hipparcos H–R Diagram • Plot many stars and notice that 90% fall on the “main sequence”. • Add radius lines, and now have • luminosity • temperature • radius 48

  49. Figure 10.14H–R Diagram of 100 Brightest Stars • Most very bright stars are also distant 49

  50. Figure 10.13H–R Diagram of Nearby Stars • Most close stars are very dim • Best estimate now is that 80% of stars are red dwarfs 50

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