1. Charles Hakes Fort Lewis College1

2. Charles Hakes Fort Lewis College2 Chapter 10 Measuring the Stars

3. Charles Hakes Fort Lewis College3 Outline Parallax Magnitudes Colors Sizes H-R diagrams

4. Charles Hakes Fort Lewis College4 Chapter 10 Parallax

5. Charles Hakes Fort Lewis College5 Figure P.12 Parallax Geometry

6. Charles Hakes Fort Lewis College6 Figure P.11 Parallax Recall information from Chapter 0

7. Charles Hakes Fort Lewis College7 Figure 10.1 Stellar Parallax

8. Charles Hakes Fort Lewis College8 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

9. Charles Hakes Fort Lewis College9 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!

10. Charles Hakes Fort Lewis College10 Figure 10.2 Sun ’ s Neighborhood

11. Charles Hakes Fort Lewis College11 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.

12. Charles Hakes Fort Lewis College12 Figure 10.3 Real 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

13. Charles Hakes Fort Lewis College13 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. Charles Hakes Fort Lewis College14 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

15. Charles Hakes Fort Lewis College15 Chapter 10 Magnitudes

16. Charles Hakes Fort Lewis College16 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. Charles Hakes Fort Lewis College17 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

18. Charles Hakes Fort Lewis College18 More Precisely 10-1 More 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

19. Charles Hakes Fort Lewis College19 Magnitudes Apparent Magnitude how bright it looks depends on distance brightness depends on distance 2 Absolute Magnitude Only depends on Luminosity (how much energy is being produced) Does not change with distance At 10pc, Apparent magnitude= Absolute magnitude

20. Charles Hakes Fort Lewis College20 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?

21. Charles Hakes Fort Lewis College21 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

22. Charles Hakes Fort Lewis College22 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

23. Charles Hakes Fort Lewis College23 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

24. Charles Hakes Fort Lewis College24 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

25. Charles Hakes Fort Lewis College25 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

26. Charles Hakes Fort Lewis College26 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. Charles Hakes Fort Lewis College27 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.

28. Charles Hakes Fort Lewis College28 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 log 10 (r/10pc) r = 10pc x 10 (m-M)/5

29. Charles Hakes Fort Lewis College29 Chapter 10 Star Temperatures (Colors)

30. Charles Hakes Fort Lewis College30 Figure 10.7 Star Colors – Orion (20°) and the Milky Way Center (2 ’ )

31. Charles Hakes Fort Lewis College31 Which star would be the hottest? A) Blue B) White C) Yellow D) Orange E) Red

32. Charles Hakes Fort Lewis College32 Which star would be the hottest? A) Blue B) White C) Yellow D) Orange E) Red

33. Charles Hakes Fort Lewis College33 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.

34. Charles Hakes Fort Lewis College34 Figure 10.8 Blackbody Curves

35. Charles Hakes Fort Lewis College35 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,...

36. Charles Hakes Fort Lewis College36 Figure 10.9 Stellar 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

37. Charles Hakes Fort Lewis College37 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

38. Charles Hakes Fort Lewis College38 Star Spectral Classification New order is: O, B, A, F, G, K,M. Remember the order... Oh, Be A Fine Girl/(Guy) Kiss Me

39. Charles Hakes Fort Lewis College39 Chapter 10 Star Sizes

40. Charles Hakes Fort Lewis College40 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  radius 2 x T 4 (  means proportional to)

41. Charles Hakes Fort Lewis College41 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  r 2  T 4 (= means equal)

42. Charles Hakes Fort Lewis College42 Star Sizes Can directly measure the radius on very few stars. (~dozen)

43. Charles Hakes Fort Lewis College43 Figure 10.10 Betelgeuse

44. Charles Hakes Fort Lewis College44 Star Sizes Can directly measure the radius on very few stars. (~dozen) Can calculate the radius if you know the luminosity and the temperature.

45. Charles Hakes Fort Lewis College45 Figure 10.11 Stellar Sizes Giants - radius between 10x and 100x solar Supergiants - larger (up to 1000x) Dwarf - radius comparable to or smaller than the sun.

46. Charles Hakes Fort Lewis College46 Chapter 10 HR Diagrams

47. Charles Hakes Fort Lewis College47 Figure 10.12 H–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!

48. Charles Hakes Fort Lewis College48 Figure 10.15 Hipparcos H–R Diagram Plot many stars and notice that 90% fall on the “main sequence”. Add radius lines, and now have luminosity temperature radius

49. Charles Hakes Fort Lewis College49 Figure 10.14 H–R Diagram of 100 Brightest Stars Most very bright stars are also distant

50. Charles Hakes Fort Lewis College50 Figure 10.13 H–R Diagram of Nearby Stars Most close stars are very dim Best estimate now is that 80% of stars are red dwarfs

51. Charles Hakes Fort Lewis College51 Three Minute Paper Write 1-3 sentences. What was the most important thing you learned today? What questions do you still have about today’s topics?

52. Charles Hakes Fort Lewis College52 Review What was the most important thing you learned? Absolute magnitude is how bright a star would appear at 10 parsecs A difference of 5 magnitudes corresponds to exactly a factor of 100 in brightness …take the difference in magnitudes and use it in an exponential equation: brightness = (100.2 ) mag

53. Charles Hakes Fort Lewis College53 Group Exercise Given that: one magnitude is a factor of 100 0.2 = 2.511886 Venus magnitude is -4.6 Faintest stars visible in Durango ~+6.5 (Approximately) How Much brighter is Venus than the dimmest star visible in Durango?

54. Charles Hakes Fort Lewis College54 Group Exercise Given that: one magnitude is a factor of 100 0.2 = 2.511886 Venus magnitude is -4.6 Faintest stars visible in Durango ~+6.5 (Approximately) How Much brighter is Venus than the dimmest star visible in Durango? What is the magnitude difference? How does this difference relate to brightness?

55. Charles Hakes Fort Lewis College55 Compared to the 5800K photosphere, sunspots at 4500K emit what percent energy? A) 26% B) 36% C) 46% D) 56% E) 66%

56. Charles Hakes Fort Lewis College56 Compared to the 5800K photosphere, sunspots at 4500K emit what percent energy? A) 26% B) 36% C) 46% D) 56% E) 66%

57. Charles Hakes Fort Lewis College57 What peak wavelength is emitted in the core of the Sun (T=10 7 K)? A).29 cm B).29 mm C).29 nm D).29  m E).29 km

58. Charles Hakes Fort Lewis College58 What peak wavelength is emitted in the core of the Sun (T=10 7 K)? A).29 cm B).29 mm C).29 nm D).29  m E).29 km

59. Charles Hakes Fort Lewis College59 Three Minute Paper Write 1-3 sentences. What was the most important thing you learned today? What questions do you still have about today’s topics?