Understanding Stellar Properties: Luminosity, Temperature, & Mass Measurements

1. Chapter 11Surveying the Stars

2. 11.1 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? And why do we care? Let’s say we want to find out how far away a star is… We can’t measure the distance directly And brightness is related to distance and luminosity But we can easily measure the brightness

4. Luminosity and distance are not so easy.

5. Luminosity and distance are not so easy. However…

6. if we can relatebrightness, luminosity, and distance…

7. we can calculate any of them if we know the other two.

8. This is very important and useful.

9. This is very important and useful. But first…

10. What is luminosity?

11. Luminosity: Amount of power a star radiates (joules/sec = watts)

12. Luminosity: Amount of power a star radiates (joules/sec = watts) Example: A100 W light bulb has a luminosity of 100 W

13. Luminosity: Amount of power a star radiates (joules/sec = watts) This is different from brightness:

14. Luminosity: Amount of power a star radiates (joules/sec = watts) This is different from brightness: Amount of starlight that reaches Earth (watts/square meter)

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

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

17. How are luminosity and brightness related?

18. How are luminosity and brightness related? • Luminosity passing through each sphere is the same

19. How are luminosity and brightness related? • Luminosity passing through each sphere is the same • But the area increases

20. How are luminosity and brightness related? • Luminosity passing through each sphere is the same • But the area increases • Area of sphere = 4πR2

21. How are luminosity and brightness related? • Luminosity passing through each sphere is the same • But the area increases • Area of sphere = 4πR2 • Divide luminosity by area to get apparent brightness.

22. The Inverse Square Law for Light The relationship between apparent brightness and luminosity depends on distance:

23. 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 as bright.

24. 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 as bright.

25. 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 as bright.

26. The relationship between apparent brightness and luminosity depends on distance: Measuring brightness is easy, so if we know how far away a star is, we can calculate its luminosity:

27. The relationship between apparent brightness and luminosity depends on distance: Measuring brightness is easy, so if we know how far away a star is, we can calculate its luminosity:

28. The relationship between apparent brightness and luminosity depends on distance: Measuring brightness is easy, so if we know how far away a star is, we can calculate its luminosity: Or if we know its luminosity, we can calculate its distance:

29. The relationship between apparent brightness and luminosity depends on distance: Measuring brightness is easy, so if we know how far away a star is, we can calculate its luminosity: Or if we know its luminosity, we can calculate its distance:

30. So how far away are these stars?

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

32. Apparent positions of the nearest stars shift by only about an arcsecond as Earth orbits the Sun, and the shift is smaller for more distant stars. Parallax of a Nearby Star

33. Apparent positions of the nearest stars shift by only about an arcsecond as Earth orbits the Sun, and the shift is smaller for more distant stars. • These very small angles explain why the Greeks were unable to detect parallax with their naked eyes. Parallax of a Nearby Star

34. Apparent positions of the nearest stars shift by only about an arcsecond as Earth orbits the Sun, and the shift is smaller for more distant stars. • These very small angles explain why the Greeks were unable to detect parallax with their naked eyes. • This inability helped delay the acceptance of the geocentric universe for more than 1500 years. Parallax of a Nearby Star

35. The parallax angle depends on distance. Parallax Angle as a Function of Distance

36. Parallax is measured by comparing snapshots taken at different times and measuring the angular size of the star’s shift in position. Measuring Parallax Angle

37. Parallax is measured by comparing snapshots taken at different times and measuring the angular size of the star’s shift in position. Measuring Parallax Angle

39. This is a right triangle

40. That means we can use trigonometry

42. For small angles: sinp ≈ p

43. So for small angles:

44. If you express p in arcseconds and d in parsecs…

45. Parallax and Distance

46. The apparent brightness of stars varies over a wide range

47. And there is also a wide range of luminosity

48. Range of luminosities Most luminous stars: 106LSun (LSun is luminosity of Sun)

49. Range of luminosities Most luminous stars: 106LSun Least luminous stars: 10−4LSun (LSun is luminosity of Sun)

50. Range of luminosities This is a wide range