1. Intro to Astrophysics Dr. Bill Pezzaglia 1 Updated: Nov 2007

2. III. Introduction To Astrophysics A.Distances to Stars B.Binary Stars C.HR Diagrams 2

3. A. Stellar Distances 1.Method of Parallax 2.Absolute Magnitudes 3.Magnitude-Distance Relation 3

4. 1a. Measuring Distance to Stars Parallax: the apparent change in position of object (against distant background) due to shift in position of observer 4

5. 1b. Parallax As the earth goes around sun, the close stars will appear to move relative to background stars. 5

6. 1c. Parallax So over a year the close stars would appear to move 6

7. 1d. The Parsec A star that has a parallax of 1 arcsecond is defined to be 1 parsec away Parsec is: 3.26 light years 200,000 AU 3x10 16 meters 7

8. 1e. Parallax 8

9. 1f. Parallax Closer stars will have a bigger parallax 9

10. 1g. Parallax Formula Formula: Distance (pc)=1/parallax Limiting Optical resolution of telescope (due to wave nature of light) limits smallest parallax we can measure 10 ParallaxDistanceNote 0.01”100 pcHipparchos Limit 0.25”4 pcSmallest can measure from Earth 0.74”1.35 pcClosest Star 1”1 pcDefinition of Parsec 2”0.5 pc

11. 1h. Bessel measures first parallax (61 Cygni) in 1838 11

12. 1i. Bessel measures first parallax (61 Cygni) in 1838 12

13. 2a. Apparent Magnitude “m” 13 Apparent Magnitude: how bright the star appears in the sky The sun appears very bright only because its very close Actually the sun is one of the fainter stars

14. 2b. Absolute Magnitude “M” 14 Absolute Magnitude: how bright the would be if viewed at standard distance Standard Distance: is 10 parsecs Sun is M=+4.83 Star with 100 Solar Luminosities (100 x brighter than sun) would be 5 magnitudes brighter, or have absolute magnitude of M= -0.17

15. 3a. Inverse Square Law 15

16. 3b. Inverse Square Law 16 Apparent Luminosity drops off inversely proportional to squared distance. Sun at 100 parsecs away (10x standard) would appear 1/100 as bright. A factor of 100 is 5 magnitudes. Sun’s apparent magnitude at 100 pc would be m=M+5, where M=+4.83

17. 3c. Magnitude-Distance Relation 17 M=Absolute Magnitude m=Apparent Magnitude (m-M) is called the “distance modulus” (m-M)D (pc) -51 pc 010 pc +5100 pc +101000 pc +1510,000 pc Given Sun has M=+4.83 If the sun was near the galactic core (10,000 parsecs away) it would appear as apparent magnitude: m=+19.83

18. B. Binary Stars 1.Measure Mass of Stars 2.Eclipsing Binaries measure size 3.Spectroscopic Binaries 18

19. 1a. Binary Star 19 Two stars orbit around each other

20. 1b. Center of Mass 20 The stars orbit about a common “center of mass”

21. 1c. Center of Mass 21 The stars orbit about a common “center of mass” The distances of each star to the center is inversely proportional to their masses: m 1 r 1 =m 2 r 2 The velocities of the stars are proportional to their orbital radii: v 1 /r 1 = v 2 /r 2

22. 1d. Doppler Velocity 22

23. 1e. Doppler Velocity 23 Doppler Effect: object moving away will have its wavelengths redshifted (shifted to red) Amount of shift is proportional to speed: v/c = 

24. 2a. Solving the System 24 “Spectroscopic Binaries” are so close together you only see one star, but we can see the spectral lines split and converge as the starts orbit.

25. 2b. Solving the System 25 Product of period with velocity gives size of orbit Kepler-Newton Law gives stellar Mass: a 3 /P 2 From measuring angular separation can get distance to binary star system. Hence the absolute luminosities can be determined

26. 2c. Mass Luminosity Relation 26 1913 H.N. Russell studied binary star systems and established a relationship between the masses of (main sequence) stars and their brightness. (check this) Approximately the luminosity is proportional to the (mass) 4

27. 3a. Eclipsing Binaries 27 The lengths of the eclipses give a measure of the diameters of the stars. Only a small fraction of stars are oriented so we see eclipses Algol is an eclipsing binary

28. 3b. Broadening of Spectral Lines 28 If a star is rotating, spectral lines will be broadened due to doppler effect Giant stars will show more broadening.

29. 3c. Indirectly Determining Sizes 29 If you know the absolute magnitude of the star (i.e. know the distance to the star) there is an indirect way to determine the size of a star Determine the temperature (Wien’s law) Use the Stefan-Boltzmann law to determine the size.

30. 3d. Stellar Sizes 30 Smaller stars are 1/10 the size of the sun Red Giant stars are 10x the size of the sun Supergiant stars are perhaps 100x bigger than the sun.

31. C. Stellar Sequences 1.Spectral Classes 2.H-R Diagram 3.Stellar Sequences 31

32. 1a. Color Indexing If we can measure the color of a star, we can calculate its temperature (Wien’s Law) Measure magnitude of star through color filters Color Index=C.I. = B-V is measure of temperature of star. Standard Filters U filter 370 nm B filter 440 nm V filter 550 nm 32

33. 1b. Color Ratio Recall that subtracting magnitudes is equivalent to taking a ratio of luminosities B-V = 2.5 Log(b v /b b ) b v = luminosity in yellow b b = luminosity in blue B=magnitude in blue V=magnitude in yellow 33

34. 1c. Hertzsprung’s Studies 34 Not knowing distances to stars, he didn’t know the absolute magnitudes. But, a cluster of stars will all be at the same distance So plot apparent magnitude vs temperature 1911 plotted Hyades and Pleiades clusters, found relationship between temperature and luminosity 1905 coined term “giant stars”

35. 2a. Persistence of Lines A more precise method is to look at the relative strengths of various spectral lines to determine temperature. 35

36. 2b. Spectral Classes Classes: (hot to cold): O B A F G K M Subclasses: (hot to cold) B7 B8 B9 A0 A1 A2 etc. Russell suggests Oh Be A Fine Girl Kiss Me 36

37. 2c. Spectral Classes 37

38. 2d. How we determine properties of stars 38

39. 3a. Hertzsprung-Russel Diagram 39 Combining their work, they were able to calibrate Hertzsprung’s diagram 90% of stars fall on the “main sequence”. They are all burning hydrogen into helium (like sun), and obey the mass-luminosity relation. The other 10% are giants and white dwarfs.

40. 3b. Luminosity Classes 40 Sequence V is main sequence. The sun is hence a “G2 V” The other sequences have different fuel cycles. Red giants are sequence III and are burning helium into carbon. Supergiants burn carbon into heavier elements.

41. 3c. Spectroscopic Parallax 41 The distance to a star can be estimated if we can guess which sequence to which the star belongs. From spectral class, lookup absolute magnitude on HR diagram. Use (m-M) to get distance.

42. Summary Most of the stars visible to naked eye are giants and supergiants, or the brighter main sequence stars (B, A, F). 42 M=-10 M=-5 M=0 M=+5 M=+10 M=+15