Exploring Stars: Luminosities, Temperatures & Masses

1. Chapter 15Surveying the Stars Insert TCP 5e Chapter 15 Opener

2. 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?

3. How do we measure stellar luminosities?

4. The brightness of a star depends on both distance and luminosity

5. 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) Insert TCP 5e Figure 15.1

6. Thought Question These two stars have about the same luminosity -- which one appears brighter? A. Alpha Centauri B. The Sun

7. Luminosity (energy) passing through each sphere is the same. Area of sphere = 4πr2 (radius)2 Divide luminosity by area to get brightness. Luminosity 4π (radius)2 Since the area of sphere increases with increasing distance from star, brightness decreases. If we know a star’s distance and apparent brightness, we can determine its luminosity. Luminosity = 4π(distance)2 x (apparent brightness) Brightness =

8. Thought Question 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

9. So how far are these stars and how would you measure their distances?

10. Parallax is the apparent shift in position of a nearby object against a background of more distant objects

11. Apparent positions of nearest stars shift by about an arcsecond of parallax as Earth orbits Sun

12. Parallax angle depends on distance

13. p 1 AU - This is a right triangle. - Use a little trigonometry. sin p = 1 AU/d d = 1 AU/sin p

14. Parallax and Distance Note: 1 parsec = 3.26 light years

15. Most luminous stars: 106 LSun That’s 1 million x! Least luminous stars: 10-4 LSun (LSun is luminosity of Sun)

16. The Magnitude Scales • Apparent Magnitude Scale: • Developed by Hiparchus (190 – 120 B.C.) • Classifies stars on how bright they look to human eyes. • Scale runs backwards • 1 = brightest • 6 = faintest • Absolute Magnitude Scale: • It is the apparent magnitude a star would have if it were located 10 parsecs (32.6 light-years) from Earth. • Earth would only have an absolute magnitude of 4.8 if moved 10 parsecs away; rather faint compared to other stars.

17. The Magnitude Scale Note: A difference in magnitude of 5 is equivalent to a difference in luminosity or brightness of 100.

18. How do we measure stellar temperatures?

19. Every object emits thermal radiation with a spectrum that depends on its temperature

20. An object of fixed size grows more luminous as its temperature rises The temperature increases as more energy is released.

21. Properties of Thermal Radiation Hotter objects emit more light per unit area at all frequencies. Hotter objects emit photons with a higher average energy.

22. Hottest stars: 50,000 K Coolest stars: 3,000 K The Sun Surface T = 5,800 K

23. 106 K Ionized Gas (Plasma) 105 K 104 K 103 K Neutral Gas Liquid 102 K Solid 10 K As temperature increases, the phases of matter transition from solid to liquid to gas and finally to a plasma of ionized gas where the atoms are stripped of their electrons.

24. Absorption lines in star’s spectrum tell us ionization level

25. Lines in a star’s spectrum correspond to a spectral type that reveals its temperature (Hottest) O B A F G K M (Coolest)

26. Remembering Spectral Types (Hottest) O B A F G K M (Coolest) • Oh, Be A Fine Girl/Guy, Kiss Me • Only Boys Accepting Feminism Get Kissed Meaningfully

27. Thought Question Which kind of star is hottest? A. M star B. F star C. A star D. K star

28. How do we measure stellar masses?

29. Binary Star Systems What is a binary star system? • A binary star system occurs when two stars orbit each other. • The orbit of a binary star system depends on strength of gravity

30. Types of Binary Star Systems • Visual Binary • Eclipsing Binary • Spectroscopic Binary Think About This! About half of all stars are in binary systems.

31. Visual Binary We can directly observe the orbital motions of these stars

32. Eclipsing Binary Periodic eclipses cause fluctuations in apparent brightness. This is the same method being used by Kepler and other telescopes to find extrasolar planets.

33. Spectroscopic Binary Blue Shift – When moving towards us. Red Shift – When moving away from us. We determine the orbital period by measuring Doppler shifts

34. 4π2 G (M1 + M2) p2 = a3 To measure the mass of a binary system, we can use Newton’s version of Kepler’s third law of motion (p2 = a3). Direct mass measurements of each of the stars is possible only for stars in binary star systems. Must know any two of: p = period a = average separation v = relative orbital velocity (star 1 vs. star 2)

35. Most massive stars: 100 MSun Least massive stars: 0.08 MSun (MJupiter = 0.001MSun) (MSun is the mass of the Sun)

36. What have we learned? • 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

37. What have we learned? • 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)

38. 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?

39. What is a Hertzsprung-Russell diagram?

40. Luminosity Temperature An H-R diagram plots the luminosity and temperature of stars

42. Most stars fall somewhere on the main sequence of the H-R diagram Our Sun is part of the main sequence Main Sequence

43. Large radius Stars with lower T and higher L than main-sequence stars must have larger radii: giants and supergiants Main Sequence

44. Small radius Stars with higher T and lower L than main-sequence stars must have smaller radii: white dwarfs Our Sun will become a white dwarf when it dies Main Sequence

45. 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

46. Luminosity Temperature H-R diagram depicts: • Temperature • Color • Spectral Type • Luminosity • Radius

47. Which star is the hottest? Luminosity A Temperature

48. Which star is the most luminous? C Luminosity Temperature

49. Which star is a main-sequence star? Luminosity D Temperature

50. Which star has the largest radius? C Luminosity Temperature