Summary

1. Summary Science is based on measurement, but measurement in astronomy is very difficult. Even with the powerful modern telescope it is impossible to measure directly simple parameters such as the diameter of a star. This chapter shows how we can use the simple observations that are possible, combined with the basic laws of physics and mathematics, to discover the properties of stars. With this unit, we leave our sun behind and begin to study the billions of stars that dot the sky. In a sense, the star is the basic building block of the universe. If we hope to understand what the universe is, what our sun is, what our Earth is, and what we are, we must understand the stars. In this unit we will find out what stars are like. In this unit we will trace the life stories of the stars from their births to their deaths.

2. The Stars

3. Outline I. Measuring the Distances to Stars A. The Surveyor's Method B. The Astronomer's Method C. Proper Motion II. Intrinsic Brightness A. Brightness and Distance B. Absolute Visual Magnitude C. Calculating Absolute Visual Magnitude D. Luminosity III. The Diameters of Stars A. Luminosity, Radius, and Temperature B. The H-R Diagram C. Giants, Supergiants, and Dwarfs

4. Outline D. Luminosity Classification E. Spectroscopic Parallax IV. The Masses of 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 V. A Survey of the Stars A. Mass, Luminosity, and Density B. Surveying the Stars

5. Properties of Stars • We will learn how we can determine a stars • Distance from Earth. • Luminosity • Radius • Mass • And how the different types of stars make up what is known as the family of stars.

6. Properties of the Stars Measuring distance to a star

7. How far away is a star from Earth? Want to know d. What can we measure? Baseline. Angle BAC 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.

8. How far away is a star from Earth? d in parsec (pc) p in arc seconds __ 1 d = p Trigonometric Parallax: Star appears slightly shifted from different positions of the Earth on its orbit 1 parsec = 3.26 LY The farther away the star is (larger d), the smaller the parallax angle p. 1 LY = 63,241 AU

9. How far away is a star from Earth? Example: Nearest star, a Centauri, has a parallax of p = 0.76 arc seconds d = 1/p = 1.3 parsec = 4.3 LY With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec => d ≤ 50 parsec With ground based telescopes this method does not work for stars farther away than 50 parsecor about 160 Lightyears. Hipparcos satellite gave us measurments good to .001arc seconds or about 3000 light years.

10. 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. This is related to the actual motion of the stars throughout the Milky Way, and is called proper motion.

11. Proper Motion The Sun is also moving and this makes the stars appear to move in addition to their own motion. Example: You are walking across a fields towards a forest. What do the trees appear to be doing?

12. Brief Review Parallax: The apparent motion of stars against their more distant background stars due to the motion of the earth. Parsecs: d(parsecs) = 1/p 1 Parsec: = 3.26 Light Years 1 Light Year ~ 10,000,000,000,000km ~ 6,000,000,000,000 miles Proper Motion: The actual motion of the stars as they rotate about the center of the Milky Way.

13. Properties of the Stars Apparent Brightnessof a star

14. Apparent Magnitude Scale – brightness of a star as seen from Earth Astronomers give the brightness of objects in the sky by apparent magnitudes. Stars visible to the naked eye have magnitudes between m = –1.44 and about m = +6. Several stars in and around the constellation Orion labeled with their names and apparent magnitudes

15. Intrinsic Brightness and Distance. The more distant a light source is, the fainter it appears.

17. The Inverse Square Law. • The farther a star is from Earth, the dimmer it looks to us. Doubling the distance makes the star look one-fourth as bright. Tripling the distance decreases the star’s brightness by a factor of 9.

18. Intrinsic Brightness and Distance. • Absolute magnitude tells how bright a star actually is, no matter how far from Earth it is. • Are the car lights actually dimmer as the car moves away?

20. Intrinsic Brightness and Distance. • No. Their actual brightness (absolute magnitude) is the same no matter the distance. • But they look dimmer (apparent magnitude) to us when the car is farther away.

21. Intrinsic Brightness and Distance. More quantitatively: The amount of light received from a star (its Flux) is proportional to its actual brightness or luminosity (L) and inversely proportional to the square of the distance (d): L __ F ~ d2 Star A Earth Star B Both stars may appear equally bright, although star A is actually giving off much more light than star B.

22. Distance and Intrinsic Brightness Recall that: Betelgeuse App. Magn. mV = 0.41 For a magnitude difference of 0.41 – 0.14 = 0.27, we find an intensity ratio of (2.512)0.27 = 1.28 Rigel appears 1.28 times brighter than Betelgeuse Rigel App. Magn. mV = 0.14

23. Distance and Intrinsic Brightness 1.28 times as much light from Rigel reaches earth compared to Betelgeuse, Betelgeuse But Rigel is 1.6 times further away than Betelgeuse Amount of light received from star * (Distance)2 = Actual Brightness or Luminosity Flux * d2 = L Thus, Rigel is actually 1.28*(1.6)2 = 3.3 times brighter than Betelgeuse. Rigel

24. Brief Review Parallax: The apparent motion of stars against their more distant background stars due to the motion of the earth. Parsecs: d(parsecs) = 1/p 1 Parsec: = 3.26 Light Years 1 Light Year ~ 10,000,000,000,000km ~ 6,000,000,000,000 miles Proper Motion: The actual motion of the stars as they rotate about the center of the Milky Way.

25. Brief Review Distance and Brightness: Far things appear dimmer. Inverse Square Law: y = 1/x2 F ~ L / d2 Flux: The amount of light received from a star. Luminosity: The actual amount of light given off by a star.

26. Properties of the Stars Absolute magnitude (Brightness) of a Star

27. Absolute Magnitude To characterize a star’s intrinsic or actual brightness, then we must define Absolute Magnitude (MV): Absolute Magnitude = MV = Magnitude that a star would have if all stars were at the same distance from earth. That distance is 10 parsecs or 32.6LYs.

28. Absolute Magnitude Back to our example of Betelgeuse and Rigel: Betelgeuse Rigel Difference in absolute magnitudes: 6.8 – 5.5 = 1.3 => Luminosity ratio = (2.512)1.3 = 3.3

29. Distance and Brightness • What does it all mean? • Close things appear bright and far things appear dim. • Our Sun would have an apparent magnitude of approximately 11 if it were located near Betelguese. • Our Sun is not a very bright star. • So, what kind of star is our sun? • What is the difference between stars?? • Is it a difference in their age or the type of stars???

30. Properties of the Stars The size (Radius)of A star

31. The Size (Radius) of a Star • Flux (light received from a star) increases with surface temperature (~ T4). • Hotter stars are brighter. But brightness also increases with size: A B Star B will be brighter than star A if it has the same surface temperature.

32. The Size (Radius) of a Star Absolute brightness is proportional to radius and temperature, L ~ R2 and T4 L = Luminosity = EM radiation given off by a star. Quantitatively: L = 4 p R2s T4 Surface area of the star Surface flux due to a blackbody spectrum

33. 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. Quantitatively: L = 4 p R2s T4 If, RPolaris = 100RSun Then, LPolaris = 1002 LSun = 10,000LSun

34. Example: Star Radii If, LPolaris = 1002 LSun = 10,000LSun How come Polaris looks so dim?? Because it is so far away…

36. The Atom • Bohr Model • Electron Transitions • Give off photons of light. • These photons have very specific wavelengths or colors.

37. EM Spectrum, Spectral Lines and the Atom • The Electromagnetic Spectrum is the chart of all the radiation coming off a star plotted by wavelength, frequency and energy. • The radiation is sorted into 7 different categories on the spectrum…. • Radio Waves • Microwaves • Infrared Radiation • Visible Light • Ultraviolet Radiation • X-Rays • Gamma Rays

38. EM Spectrum, Spectral Lines and the Atom • Frequency is increasing left to right • Energy is increasing left to right. • Wavelength is decreasing left to right

39. EM Spectrum, Spectral Lines and the Atom • On the EM spectrum, the only types of radiation that penetrate earth’s atmosphere are radio waves and visible light. • There is not a significant amount of infrared and ultraviolet radiation that penetrate earth’s atmosphere. • The small section of visible light, is the only type of radiation our human eyes can actually see. • It is seen as a variation of seven different colors. • In order of decreasing wavelength, increasing frequency and increasing energy, the colors are… • R O Y G B I V • Red, Orange, Yellow, Green, Blue, Indigo and Violet

40. EM Spectrum, Spectral Lines and the Atom • Spectral Analysis is a practice used to learn about the composition of stars. • Scientists have studied the “spectra” of different elements. • They then look at the “spectra” of a star and compare it to the “spectra” of the different elements to determine what elements a star is made of.

42. EM Spectrum, Spectral Lines and the Atom • Scientists use spectrometers or spectroscopes to study the “spectra” of the stars and different elements. • A spectroscope has special lenses that allow scientists to see the different properties of light waves coming off a star or an element. • A spectrometer is just a spectroscope that has scales on it to measure wavelength.

43. EM Spectrum, Spectral Lines and the Atom

44. Temperature and Color (review) Hottest = blue color Medium = orange/yellow color Coolest = red color

45. Spectral Classes (Color and Temperature) “Oh, Be AFine Guy/Girl, Kiss Me!”

47. 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 Temperature (or spectral type) versus Absolute mag. Hertzsprung-Russell Diagram Luminosity or Temperature Spectral type: O B A F G K M

48. Hertzsprung-Russell (HR) Diagram • Star brightness is plotted against star spectral types (color / temperature). • Brightness and spectral type are related. • Main-sequence stars (fusing hydrogen to helium) fall along the red curve. • Giants are to the upper right and super-giants are on the top. • White dwarfs are below the main sequence.

49. Hertzsprung-Russell (HR) Diagram