1. ASTR 1200 Announcements Website http://casa.colorado.edu/~wcash/APS1200/APS1200.html Second problem set due Lecture Notes going up on the website First Exam October 7

2. Summary: Sun as a Star Formed from cloud 4.6x10 9 years ago Collapsed to present size –stabilized by nuclear reactions Emits 4x10 26 W Runs on proton-proton chain and CNO cycle Now 20% brighter Turbulent upper envelope Magnetic Fields from Differential Rotation Sunspots, Corona, Solar Wind Activity Cycle 11 years

3. Stars are grouped in Galaxies Sun and all the stars we see are part of Milky Way Galaxy We all orbit a common center Sun is 3x10 20 m from center of MW You are here Each star orbits center Disk Stability Again

4. The Light Year Light Travels at 300,000km/s (186,000miles/s = 3x10 8 m/s) That’s one foot per nanosecond One Year is 3.15x10 7 seconds long In one year light travels 3.15x10 7 x3x10 8 = 10 16 m This is the definition of a light year. Prox Cen is at 4ly.

5. The Parsec Astronomers use the parsec as a measure of distance 1pc = 3ly 1pc = 3x10 16 m Origin of parsec comes from method of measuring distance

6. Each Star Orbits the Center

7. How Long does that Take? Takes about a hundred million years to circumnavigate the galaxy

8. Star Names Arabic Names –Antares, Capella, Mira, etc. Constellations  Orionis,  Cygni, … then 49 Ori, 50 Ori, etc. Catalogues HD80591, SAO 733421, etc RA and Dec – just position in the sky

9. Proper Motion All stars move Nearby stars move faster Appear to move against fixed field Can Take Many Years Use Old Photographic Plates 1900 2003

10. Parallax I year cycle

11. The Parsec 1AU 1 parsec 1 arcsecond 360 degrees in circle 60 arcminutes per degree 60 arcseconds per arcminute 200,000AU = 1 parsec = 3x10 16 m parsec ---- parallax second

12. Brightness Around the sky stars vary in brightness and in color. Brightness is the result of two factors 1. Intrinsic Luminosity 2. Distance Each Sphere has area A=4pd 2 Star Emits N photons per second Brightness is d photons/m 2 /s

13. Brightness (2) Brightness e.g. 10 -12 Watts/m 2 Simple and easy to understand If your eye is 10 -4 m 2, then it collects 10 -16 W 4 stars at 10 -12 W/m 2 together have 4x10 -12 W/m 2 But this would be too easy for astronomers. We use a brightness system invented by Ptolemy in the 400’s

14. The Magnitude System Ptolemy Broke Stars into 5 magnitude groups m=1 the brightest, m=5 the faintest In 1700’s it was found this was a logarithmic scale, as that is how the naked eye responds. Also, faintest were about 100x fainter than brightest. Break the factor of 100 into 5 equal factors: Start with Vegam=1 Polaris 2.51x fainter m=2 2.5x fainter than Polaris m=3 2.5x fainter than that m=4 etc

15. Magnitudes (2) Every 5 magnitudes is a factor of 100 m=5 is 100 times fainter than m=0 m=10 is 100x100 =10,000 times fainter than m=0 m=15 is (100) 3 = 1million times fainter than m=0 Works only in the visible. Really inconvenient in modern astronomy because we observe across the spectrum from radio to gamma rays. Sunm=-26.5 Full Moonm=-13 Venusm=-4 Siriusm=-1.5 Vegam=1 Polarism=2 Faintest Visiblem=6 Faintest Detectedm=28

16. Absolute Magnitude We see a star of magnitude m=10 at 100 pc. What would be its magnitude (M) if it were at 10 pc instead of 100pc? The magnitude a star would have were it at 10pc At 10 times closer the star would be 100x brighter = 5 magnitudes M = 10-5 = 5

17. Clicker A 5 magnitude difference means a factor of 100 in flux. By what factor do the fluxes differ between two stars of 20 magnitudes difference? a)2.51 b)20 c)400 d)10,000 e)100,000,000

18. Answer 5magnitudes difference is a factor of 100. By what factor do the fluxes differ between two stars of 20 magnitudes difference a)2.51 b)20 c)400 d)10,000 e)100,000,000 20 magnitudes is four factors of 10 2, which is 10 8

19. Nature of Light Light is a flux of particles called photons Each photon is both a particle and a wave (a packet of waves) 250 years after Newton we still don’t understand it Electromagnetic Theory (Maxwell’s Equations) 1860’s Quantum Electrodynamics 1948 Feynman Each photon has: direction wavelength polarization

20. Light Waves lambda is lower case Greek “L” stands for length Each photon is a sine wave moving at the speed of light Wavelength is usually measure in Angstroms 1Å = 10 -8 cm =10 -10 m about the diameter of an atom. And 10Å = 1 nm Electric and Magnetic Fields Sloshing Back And Forth

21. Color Wavelength Determines Color of Light Color is the eye’s response to different wavelengths Color is a physiological effect A photon can have any wavelength RED7000Å YELLOW5500Å VIOLET4000Å

22. Electromagnetic Spectrum visible is tiny chunk of em spectrum

23. Parts of EM Spectrum Radio  > 1mm (10 7 A) Infrared1 mm > > 10000A Visible10,000A > > 3500A Ultraviolet3500A > > 100A X-ray100A > > 0.1A Gamma-ray0.1A >

24. Clicker What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400nm-800nm, redder to bluer B) 500nm-700nm, bluer to redder C) 400nm-700nm, bluer to redder D) 300nm-600nm, redder to bluer E) None of the above

25. Answer What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400nm-800nm, redder to bluer B) 500nm-700nm, bluer to redder C) 400nm-700nm, bluer to redder D) 300nm-600nm, redder to bluer E) None of the above Answer: C

26. Speed of Light Speed of Light c = 3x10 8 m/s That’s a very odd statement 1 car at 130mph 2 cars at 65mph Cover same distance in same amount of time The Relative speeds are the same

27. Relativity.8c Clearly Approaching each other at 1.6c NO!!! per Einstein v always less than c if velocities << c, then v=v 1 +v 2 (Concept of time and space changes)

28. Frequency Moves during each cycle Frequency is the number of cycles per second, Greek “nu” Moves distance  for each of cycles each second

29. Frequency (2) 300MHz = 1m wavelength Yellow Light = 600 trillion Herz

30. Question An x-ray has a wavelength of 100Å (10nm, 1x10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) A. 3x10 16 B. 1.5x10 16 C. 3x10 13 D. 1.5x10 13

31. Question An x-ray has a wavelength of 100Å (10nm, 1x10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) A. 3x10 16 B. 1.5x10 16 C. 3x10 13 D. 1.5x10 13 Answer: A. (3E8m/s)/(1E-8m)=3E16 Hz

32. Energy of a Photon h = 6.63x10 -34 J s Planck’s Constant energy of yellow photon Sunlight is 10 4 W/m 2 Outside we have 10 23 photons/m 2 /s hit us

33. Question How many times more energy is there in an x-ray photon at 100A than the infrared light photons emitted by every living human? (Assuming 10,000nm wavelength of infrared light). A. Ten times as powerful. B. A hundred times more powerful. C. A thousand times more powerful. D. 1x10 12 (a trillion) times more powerful. E. 1x10 15 (a quadrillion) times more powerful.

34. Question How many times more energy is there in an x-ray photon at 100A than the infrared light photons emitted by every living human? (Assuming 10,000nm wavelength of infrared light). A. Ten times as powerful. B. A hundred times more powerful. C. A thousand times more powerful. D. 1x10 12 (a trillion) times more powerful. E. 1x10 15 (a quadrillion) times more powerful. Answer: C. 10,000nm/10nm = 1000

35. Spectroscopy Spectrum is plot of number of photons as a function of wavelength Tells us huge amounts about nature of object emitting light.

36. Thermal Radiation Planck’s Law Temperature Determines Where Spectrum Peaks Position of Peak Determines Color

37. Blue is Hotter than Red Optically Thick, But hot Sunalmost “white hot” Burner“red hot” Desk“black hot” Ice Cube “black hot”

38. Question A star with a temperature of 100,000K has what color to the naked eye? a)White b)Yellow c)Orange d)Red

39. Wien’s Law As T rises, drops Bluer with temperature Å (T in Kelvin) 300K100,000AEarth 55005500Sun 10 6 30X-ray source

40. Question How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500K) A. Twice as long B. Half as long C. Four times as long D. A fourth as long

41. Question How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500K) A. Twice as long B. Half as long C. Four times as long D. A fourth as long Answer: B. Since peak wavelength is a function of the inverse of temperature, doubling the temp of a star would cause it's peak wavelength to cut in half.

42. Stefan-Boltzman Law  = 5.67x10 -8 W/m 2 /K 4 A is area in m 2 T in Kelvins Example: The Sun L = 5.7x10 -8 x 4 x 3.14 x (7x10 8 m) 2 x (5500K) 4 = 4 x 10 26 W 4x10 26 Watts = 100 billion billion MegaWatts!!

43. Question If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? a)2 b)4 c)8 d)16 e)32

44. Question If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? a)2 b)4 c)8 d)16 = 2 4 e)32

45. Emission Lines Electron Drops Photon Escapes Can Only Happen Between Certain Pre-determined orbitals Each Element Has Different Orbitals So Each Element Has Different Lines Spectrum of Hydrogen Energy Levels of H

46. Absorption Lines Light moving through cold gas can have photons removed. Creates dark wavelengths called absorption lines

47. Question A star is viewed through a far away hydrogen gas cloud, what kind of spectrum can we expect to see? A) Absorption only B) Emission only C) Continuum only D) Emission and Continuum E) Absorption and Continuum

48. Question A star is viewed through a far away hydrogen gas cloud, what kind of spectrum can we expect to see? A) Absorption only B) Emission only C) Continuum only D) Emission and Continuum E) Absorption and Continuum

49. Stars Come in Different Colors

50. Stellar Temperature Stars come in different sizes and temperatures. Can the two be linked?

51. Question You see three stars up in the sky. One is bigger than the others and red, one is yellow, and one is white. Which one peaks at a higher frequency? A)Red B)Yellow C)White D)I need to know how far away they are

52. Question You see three stars up in the sky. One is bigger than the others and red, one is yellow, and one is white. Which one peaks at a higher frequency? A)Red B)Yellow C)White D)I need to know how far away they are

53. Stellar Classification Full range of surface temperatures from 2000 to 40,000K Spectral Classification is Based on Surface Temperature O B A F G K M Oh Be A Fine Gal Guy Kiss Me Each Letter has ten subdivisions from 0 to 9 0 is hottest, 9 is coolest Coolest Hottest { }

54. The Spectral Types O Stars of Orion's Belt >30,000 K Lines of ionized helium, weak hydrogen lines <97 nm (ultraviolet)* BRigel 30,000 K- 10,000 K Lines of neutral helium, moderate hydrogen lines 97-290 nm (ultraviolet)* ASirius 10,000 K-7,500 K Very strong hydrogen lines 290-390 nm (violet)* FPolaris 7,500 K- 6,000 K Moderate hydrogen lines, moderate lines of ionized calcium 390-480 nm (blue)* G Sun, Alpha Centauri A 6,000 K- 5,000 K Weak hydrogen lines, strong lines of ionized calcium 480-580 nm (yellow) KArcturus 5,000 K- 3,500 K Lines of neutral and singly ionized metals, some molecules 580-830 nm (red) M Betelgeuse, Proxima Centauri <3,500 K Molecular lines strong >830 nm (infrared) *All stars above 6,000 K look more or less white to the human eye because they emit plenty of radiation at all visible wavelengths.

55. Stellar Classification (2) SunG2  CenG2 + K5 SiriusA1 AntaresM1 RigelB8 O540,000K B515,500 A58500 F56580 G55520 K54130 M52800 Letters are odd due to confusion in sorting out temperature scale between 1900 and 1920