Prepared by Lisa M. Will, San Diego City College

1. Lecture Slides CHAPTER 10: Measuring the Stars Understanding Our Universe SECOND EDITION Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal Prepared by Lisa M. Will, San Diego City College

2. Measuring the Stars • Understand the properties of light and atoms. • Determine stellar properties – brightness, mass, temperature, size, composition. • Organize stars on the HR diagram.

3. Distance

4. Distance (Cont.) • Our brains compare views of our left and right eyes to get nearby distances. • Depth perception comes from stereoscopic vision.

5. Distance: Parallax • Parallax: change in position caused by a change in the position of the observer. • The only direct way to measure the distance to a star is from the parallax.

6. Distance: Nearby Stars • As Earth orbits the Sun, nearby stars change their positions against the background stars. • Comparing the position six months apart yields the distance.

7. Distance: Parallax Vs. Distance • The greater the parallax, the smaller the distance. • The parallaxes of real stars are tiny and are typically measured in small fractions of a degree known as arcseconds.

8. Distance: Definitions and Conversion Factors Some useful definitions and conversion factors: • 1 arcminute = 1/60 of a degree. • 1 arcsecond = 1/60 of an arcminute = 1/3600 of a degree. • Parsec: distance at which the parallax is equal to one arcsecond. • 1 parsec = 3.26 light-years.

9. Calculating distance from parallax • If Distance d in parsecs and parallax p is in arcseconds, • Then d(pc) = 1/p(arcsec) • Remember, 1parsec (parallax-second) = 3.26 light years. • Example: the parallax of a star is measured to be 0.75 arcsec. What is the star’s distance from earth? • Answer: d = 1/(.75) = 1.33 parsecs • Answer in light years = 1.33*3.26 = 4.34 light years • (this is about the distance to the nearest star)

10. Brightness Luminosity: the amount of light emitted by an object. => Luminosity is a star’s intrinsic brightness.

11. Brightness: Luminosity and Distance • Observed brightness depends on both the luminosity and the distance. => A dim star could have a low luminosity or be far away; A bright star could be close or have a high luminosity.

12. Brightness: Magnitude Some useful definitions: • Brightness of a star is measured by logarithmic magnitude. => Brighter objects have a smaller magnitude. • Apparent magnitude: how bright the star appears to us in the sky. This generally a number between 0 (very bright) and 6 (faintest human eye can see in a dark sky). A difference in magnitude of 1 is a factor in brightness of 2.5. Venus can have a negative apparent magnitude!

13. Absolute magnitude: how bright the star would be at a fixed distance of 10 parsecs from us. This is useful because it allows us to quickly compare the true luminosity of each object if we imagine that every object is at the same distance from us! M = m – 5log(d) +5 or m-M = 5log(d) -5 M = absolute magnitude M = apparent (observed) magnitude. You will not have to calculate logarithms on the the exam, but you need to understand magnitudes.

14. Class Question Which of the following apparent magnitudes is the brightest? 2 1 0 -3

15. Which star is the brightest? Which is the faintest? Star m (apparent magnitude) Rigel 0.12 Sirius -1.46 Betelgeuse 0.42 Regulus 1.35 Deneb 1.25

16. Star A has m = 2.3. Star B has m = 5.3 • Which is brighter, and by how much? Answer: Star A is brighter by exactly 3 magnitudes. 2 magnitudes is 2.5*2.5*2.5= 15.6 times brighter! • Note that 5 magnitudes difference is a factor of 100 in brightness!

17. Brightness: Luminosity Luminosity is usually expressed in terms of the solar luminosity: 1 L The most luminous stars are 106L. The least luminous are 10-4L. Low-luminosity stars are more common than high luminosity stars.

18. Composition Atoms consist of protons, neutrons, and electrons. Protons and neutrons are found in the nucleus. Electrons surround the nucleus in a “cloud.”

19. Composition: Energies Electrons can only have certain energies; other energies are not allowed. Each type of atom has a unique set of energies, typically illustrated with an energy level diagram.

20. Composition: Energies (Cont.)

21. Composition: Energies (Cont.)

22. Composition: Energy State The lowest energy state is called the groundstate. Energy levels above the ground state are called excited states. The atom can go from one energy state to another, but never have an energy in between.

23. Composition: Visual Analogy

24. Composition: Emission Emission: an electron emits a photon and drops to a lower energy state, losing energy. The photon’s energy is equal to the energy difference between the two levels.

25. Composition: Absorption Absorption: an electron absorbs the energy of a photon to jump to a higher energy level. The photon’s energy must be equal to the energy difference between the two levels.

26. Composition: Spectral Fingerprints of Atoms The wavelengths at which atoms emit and absorb radiation form unique spectral fingerprints for each atom.

27. Composition: Spectral Fingerprints of Atoms (Cont.)

28. Composition: Spectral Fingerprints of Atoms (Cont.)

29. Composition: Spectral Fingerprints of Atoms (Cont.)

30. Composition: Absorption Lines For stars, astronomers look at the dark absorption lines in stars’ spectra. These absorption lines help determine a star’s temperature, composition, density, pressure, and more.

31. Composition: Absorption and Emission Lines

32. Composition: Classification of Stars The spectra of stars were first classified during the late 1800s. Stars with the strongest hydrogen lines were labelled “A,” stars with somewhat weaker hydrogen lines were labelled “B stars,” and …

33. Composition: Spectral Types of Stars • Hottest stars: weak absorption by hydrogen and helium (type O). • Middle: strong hydrogen absorption (type A). • Cool stars: many different heavy elements or molecules (type M).

34. Composition: Spectral Types Subclasses Absorption lines depend mainly on the temperature. Full sequence: OBAFGKM Each spectral type is broken down into 10: 0-9. => The Sun is type G2.

35. Class Question Which of the following spectral types is the hottest? A G M O

36. Class Question Which of the following spectral types has the weakest hydrogen lines? A G M O

37. Temperature Measuring the color of a star tells us the surface temperature. The spectrum shifts to shorter wavelengths at higher temperatures. Wien’s law: “Hotter means bluer.”

38. Size With luminosity and temperature, we can calculate the size of a star. Stars have radii measuring from 1% of the Sun’s to 1000 times its radius!

39. Size (Cont.)

40. Size (Cont.)

41. Mass • To measure mass, astronomers look for the effects of gravity. • Many stars are binary stars orbiting a common center of mass. • A less massive star moves faster on a larger orbit.

42. Mass: Measuring the Mass Measure velocities from Doppler shift. Calculate total mass of both stars from Kepler’s third law. Lowest-mass stars have M = 0.08 M. Highest-mass stars appear to be greater than 200 M, but are rare.

43. Mass: Visual Binary System If we can take pictures showing the two stars separately, the system is called a visual binary. We can directly measure the size and period of the orbits of the two stars.

44. Mass: Spectroscopic Binary Stars Spectroscopic binary: individual stars cannot be resolved in images. Pairs of Doppler-shifted lines trade places indicating the presence of two stars.

45. Mass: Spectroscopic Binary Stars (Cont.)

46. Mass: Spectroscopic Binary Stars (Cont.)

47. Mass: Doppler Velocity The Doppler shifts can be converted into radial velocities, leading to the ratio of the masses of the two stars.

48. Size: Eclipsing Binary System Eclipsing binary: the total light coming from the star system decreases when one star passes in front of the other. This allows us to determine the relative sizes of the two stars.

49. H-R Diagram Hertzsprung-Russell (H-R) diagram = Plot of luminosity vs. temperature. Key to unraveling stellar evolution: how stars change with time.

50. H-R Diagram: Properties of Stars Top = brightest. Left = hottest. Some stars are cool but very luminous. Some are hot with low luminosity.