1. Note that the following lectures include animations and PowerPoint effects such as fly-ins and transitions that require you to be in PowerPoint's Slide Show mode (presentation mode).

2. The Family of Stars Chapter 9

3. Measurement is fundamental to science, but making measurements of distant celestial objects is especially difficult. To discover the properties of stars, astronomers have used their telescopes and spectrographs in clever ways to learn the secrets hidden in starlight. The result is a family portrait of the stars. In this chapter you will find answers to five important questions about stars: How far away are the stars? How much energy do stars make? How do spectra of stars allow you to determine their temperatures? How big are stars? How much mass do stars contain? Guidepost

4. Now you are leaving our sun behind and beginning your study of the billions of stars that dot the sky. In a sense, stars are the basic building blocks of the universe. If you hope to understand what the universe is, what our sun is, what our Earth is, and what we are, you must understand the stars. Once you know how to find the basic properties of stars, you will be ready to trace the history of the stars from birth to death, a story that begins in the next chapter. Guidepost (continued)

5. I.Star Distances A. The Surveyor's Triangulation Method B. The Astronomer's Triangulation Method C. Parallax and Distance D. Proper Motion II. Apparent Brightness, Intrinsic Brightness, and Luminosity A. Brightness and Distance B. Absolute Visual Magnitude and Distance C. Calculating Absolute Visual Magnitude D. Luminosity III. Stellar Spectra A. The Balmer Thermometer B. Temperature Spectral Types Outline

6. IV. Star Sizes A. Luminosity, Radius, and Temperature B. The H-R Diagram C. Giants, Supergiants, and Dwarfs D. Interferometric Observations of Star Diameters E. Luminosity Classification F. Spectroscopic Parallax V. Star Masses-Binary Stars A. Binary Stars in General B. Calculating the Masses of Binary Stars C. Visual Binary Systems D. Spectroscopic Binary Systems E. Eclipsing Binary Systems Outline (continued)

7. VI. A Census of the Stars A. Surveying the Stars B. Mass, Luminosity, and Density C. The Mass-Luminosity Relation Outline (continued)

8. The Properties of Stars We already know how to determine a star’s surface temperature chemical composition surface density In this chapter, we will learn how we can determine its distance luminosity radius mass and how all the different types of stars make up the big family of stars.

9. Distances to Stars Trigonometric Parallax: Star appears slightly shifted from different positions of the Earth on its orbit The farther away the star is (larger d), the smaller the parallax angle p d = __ p 1 d in parsec (pc) p in arc seconds 1 pc = 3.26 LY

10. The Trigonometric Parallax Example: Nearest star,  Centauri, has a parallax of p = 0.76 arc seconds d = 1/p = 1.3 pc = 4.3 LY With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec => d ≤ 50 pc This method does not work for stars farther away than 50 pc.

11. Proper Motion In addition to the periodic back-and- forth motion related to the trigonometric parallax, nearby stars also show continuous motions across the sky. These are related to the actual motion of the stars throughout the Milky Way, and are called proper motion.

12. Intrinsic Brightness/ Absolute Magnitude The more distant a light source is, the fainter it appears.

13. Intrinsic Brightness / Absolute Magnitude (2) More quantitatively: The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): F ~ L __ d2d2 Star A Star B Earth Both stars may appear equally bright, although star A is intrinsically much brighter than star B.

14. Distance and Intrinsic Brightness Betelgeuse Rigel Example: App. Magn. m V = 0.41 Recall that: Magn. Diff. Intensity Ratio 12.512 22.512*2.512 = (2.512) 2 = 6.31 …… 5(2.512) 5 = 100 App. Magn. m V = 0.14 For a magnitude difference of 0.41 – 0.14 = 0.27, we find an intensity ratio of (2.512) 0.27 = 1.28

15. Distance and Intrinsic Brightness (2) Betelgeuse Rigel Rigel is appears 1.28 times brighter than Betelgeuse, Thus, Rigel is actually (intrinsically) 1.28*(1.6) 2 = 3.3 times brighter than Betelgeuse. but Rigel is 1.6 times further away than Betelgeuse.

16. Absolute Magnitude To characterize a star’s intrinsic brightness, define Absolute Magnitude (M V ): Absolute Magnitude = Magnitude that a star would have if it were at a distance of 10 pc

17. Absolute Magnitude (2) Betelgeuse Rigel BetelgeuseRigel mVmV 0.410.14 MVMV -5.5-6.8 d152 pc244 pc Back to our example of Betelgeuse and Rigel: Difference in absolute magnitudes: 6.8 – 5.5 = 1.3 => Luminosity ratio = (2.512) 1.3 = 3.3

18. The Distance Modulus If we know a star’s absolute magnitude, we can infer its distance by comparing absolute and apparent magnitudes: Distance Modulus = m V – M V = -5 + 5 log 10 (d [pc]) Distance in units of parsec Equivalent: d = 10 (m V – M V + 5)/5 pc

19. The Balmer Thermometer Balmer line strength is sensitive to temperature: Almost all hydrogen atoms in the ground state (electrons in the n = 1 orbit) => few transitions from n = 2 => weak Balmer lines Most hydrogen atoms are ionized => weak Balmer lines

20. Measuring the Temperatures of Stars Comparing line strengths, we can measure a star’s surface temperature!

21. Spectral Classification of Stars (1) Temperature Different types of stars show different characteristic sets of absorption lines.

22. Spectral Classification of Stars (2) Mnemonics to remember the spectral sequence: OhOhOhOhOnly BeBeBoy,Bad AAnAnAstronomers FineFForget Girl/GuyGradeGenerally KissKillsKnown MeMeMeMeMnemonics

23. Stellar Spectra O B A F G K M Surface temperature

24. The Composition of Stars From the relative strength of absorption lines (carefully accounting for their temperature dependence), one can infer the composition of stars.

25. The Size (Radius) of a Star We already know: flux increases with surface temperature (~ T 4 ); hotter stars are brighter But brightness also increases with size: A B Star B will be brighter than star A. Absolute brightness is proportional to radius squared, L ~ R 2 Quantitatively: L = 4  R 2  T 4 Surface area of the star Surface flux due to a blackbody spectrum

26. Example: Star Radii Polaris has just about the same spectral type (and thus surface temperature) as our sun, but it is 10,000 times brighter than our sun. Thus, Polaris is 100 times larger than the sun. This causes its luminosity to be 100 2 = 10,000 times more than our sun’s

27. Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Luminosity versus Temperature (or spectral type) Luminosity Temperature Spectral type: O B A F G K M Hertzsprung-Russell Diagram or Absolute mag.

28. The Hertzsprung-Russell Diagram Most stars are found along the Main Sequence

29. The Hertzsprung-Russell Diagram (2) Stars spend most of their active life time on the Main Sequence (MS). Same temperature, but much brighter than Main Sequence stars

30. The Brightest Stars The open star cluster M39 The brightest stars are either blue (=> unusually hot) or red (=> unusually cold).

31. The Radii of Stars in the Hertzsprung-Russell Diagram 10,000 times the sun’s radius 100 times the sun’s radius As large as the sun Rigel Betelgeuse Sun Polaris

32. The Relative Sizes of Stars in the HR Diagram

33. Luminosity Classes Ia Bright Supergiants Ib Supergiants II Bright Giants III Giants IV Subgiants V Main-Sequence Stars Ia Ib II III IV V

34. Example: Luminosity Classes Our Sun: G2 star on the Main Sequence: G2V Polaris: G2 star with Supergiant luminosity: G2Ib

35. Spectral Lines of Giants => Absorption lines in spectra of giants and supergiants are narrower than in main sequence stars Pressure and density in the atmospheres of giants are lower than in main sequence stars. => From the line widths, we can estimate the size and luminosity of a star.  Distance estimate (spectroscopic parallax)

36. Binary Stars More than 50 % of all stars in our Milky Way are not single stars, but belong to binaries: Pairs or multiple systems of stars which orbit their common center of mass. If we can measure and understand their orbital motion, we can estimate the stellar masses.

37. The Center of Mass center of mass = balance point of the system Both masses equal => center of mass is in the middle, r A = r B The more unequal the masses are, the more it shifts toward the more massive star.

38. Estimating Stellar Masses Recall Kepler’s 3rd Law: P y 2 = a AU 3 Valid for the Solar system: star with 1 solar mass in the center We find almost the same law for binary stars with masses M A and M B different from 1 solar mass: M A + M B = a AU 3 ____ Py2Py2 (M A and M B in units of solar masses)

39. Examples: Estimating Mass a) Binary system with period of P = 32 years and separation of a = 16 AU: M A + M B = = 4 solar masses 16 3 ____ 32 2 b) Any binary system with a combination of period P and separation a that obeys Kepler’s 3. Law must have a total mass of 1 solar mass.

40. Visual Binaries The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly.

41. Spectroscopic Binaries Usually, binary separation a can not be measured directly because the stars are too close to each other. A limit on the separation and thus the masses can be inferred in the most common case: Spectroscopic Binaries

42. Spectroscopic Binaries (2) The approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum Doppler shift  Measurement of radial velocities  Estimate of separation a  Estimate of masses

43. Spectroscopic Binaries (3) Time Typical sequence of spectra from a spectroscopic binary system

44. Eclipsing Binaries Usually, the inclination angle of binary systems is unknown  uncertainty in mass estimates Special case: Eclipsing Binaries Here, we know that we are looking at the system edge-on!

45. Eclipsing Binaries (2) Peculiar “double-dip” light curve Example: VW Cephei

46. Eclipsing Binaries (3) From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane. Example: Algol in the constellation of Perseus

47. The Light Curve of Algol

48. Surveys of Stars Ideal situation for creating a census of the stars: Determine properties of all stars within a certain volume

49. Surveys of Stars Main Problem for creating such a survey: Fainter stars are hard to observe; we might be biased towards the more luminous stars.

50. A Census of the Stars Faint, red dwarfs (low mass) are the most common stars. Giants and supergiants are extremely rare. Bright, hot, blue main-sequence stars (high- mass) are very rare.

51. Masses of Stars in the Hertzsprung- Russell Diagram The more massive a star is, the brighter it is: High-mass stars have much shorter lives than low-mass stars: Sun: ~ 10 billion yr. 10 M sun : ~ 30 million yr. 0.1 M sun : ~ 3 trillion yr. Low masses High masses Mass L ~ M 3.5 t life ~ M -2.5