1. ASTR 1200 Announcements Website http://casa.colorado.edu/~wcash/APS1200/APS1200.html Exams are at the back. Please pick up. Still have a calculator left at the exam. Problem Sets 3 and 4 posted. Due next week. Today will review equations of light and do Doppler Shift. (Necessary for PS3) Second exam will be October 30

2. The Exam mean 70.4, median 71.2 Standard deviation 13.1

3. White Dwarfs Held up by electron degeneracy About the size of the Earth R~5000km Mass Typically 0.8M  Luminosity ~.001 L  Degenerate Carbon Thin layer of “normal” H

4. Earth vs White Dwarf

5. WD Density Water has a density of 1 g/cc Lead 11 g/cc Gold 19 g/cc 100,000 times density of gold! NOT NORMAL MATTER!! 1 cubic centimeter masses one ton!

6. Surface Gravity This is 300,000 gees If you weigh 150lbs on Earth, you would weigh 45 million pounds on a White Dwarf! What would happen to you and your spaceship?

7. Escape Velocity Speed of light is 3x10 8 m/s, so escape velocity is.02c.

8. Gravitational Redshift Even light loses energy climbing out of this hole.  = 2x10 -4 At 5000Å have 1Å shift to red Looks like a 60km/s Doppler Shift

9. Magnetic Field When a star shrinks from 10 9 m to 10 7 m So B increases from 1Gauss to a Million Gauss A million Gauss can rip normal matter apart!

10. Chandrasekhar Limit A peculiarity of Degeneracy Pressure is that it has a maximum mass. Each electron added must find its own quantum state by having its own velocity. But what happens when the next electron has to go faster than light? The Chandrasekhar Limit for a White Dwarf is 1.4M  No White Dwarf Can have more than 1.4M  Otherwise it will groan and collapse under its own weight. We’ll come back to this later.

11. WDs are Common Every star with less than 5M  will end up as a White Dwarf Most stars with mass above 1.3M  have reached end of MS life. White Dwarfs are VERY common ~ 10% of all stars Closest is only 2.7pc away. (Sirius B) Will become increasing common as universe ages.

12. Immortal Stars Regular stars need thermal pressure to balance gravity, and they need nuclear reactions to maintain the pressure, so the die when they run out of fuel. Not so White Dwarfs. They are as stable as a rock. Literally. A quadrillion years in the future all the stars will be gone, but the White Dwarfs will still be here. Their glow is fossil energy left from their youth as a regular star. Might die in 10 31 years if protons prove to be unstable themselves. That’s 10,000,000,000,000,000,000,000,000,000,000 years! Really don’t know if universe will still be here.

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

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

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

16. Wien’s Law As T rises, drops Bluer with temperature Å (T in Kelvin) T 300K100,000AEarth 55005500Sun 10 6 30X-ray source Hotter stars peak at bluer wavelengths

17. 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

18. Question How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500K) λ = (3x10 7 Å K)/T T sun = 5500K T star = 11000K λ star /λ sun = ((3x10 7 Å K)/T star )/ ((3x10 7 Å K)/T sun ) = T sun /T star = 5500K /11000K = 1/2 B. Half as long

19. 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 W/m 2 /K 4 )x (6.2x10 18 m 2 ) x (5500K) 4 = 4 x 10 26 W 4x10 26 Watts = 100 billion billion MegaWatts!! A = 4πr 2 = 4 x 3.14 x (7x10 8 m) 2 = 6.2x10 18 m 2 L is luminosity in W T = 5500 K Hotter stars emit more energy per area

20. 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

21. Question If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? L = σAT 4 A stays the same (radius doesn’t change) T doubles L 2 /L 1 = (σA 2 T 2 4 )/(σA 1 T 1 4 ) = (T 2 /T 1 ) 4 = 2 4 = 16 d.) 16

22. Spectral Lines Electrons in atoms have electric potential energy Only specific energies allowed Different for each type of atom

23. Emission Lines Electron Drops Photon Escapes Electron drops to lower energy level Emits photon

24. Absorption Lines Absorbs photon Electron rises to higher energy level Electron rises Photon Absorbed

25. The Doppler Shift Another Powerful Tool Frequency of light changes depending on velocity of source. Similar to sound wave effect Higher pitch when vehicle approaches Lower when it recedes.

26. Spectral Shifts Spectrum is identifiable as known element, but lines appear shifted. Measure the shift, and we get velocity information! Shift to blueward implies approach Shift to redward implies departure

27. The Doppler Shift vt Observer D During t seconds, source emits n waves of wavelength. They move ct during that time. But source also moves vt during that time. So the n waves are scrunched into ct-vt instead of the usual ct Thus the wavelength is reduced from to ct

28. The Doppler Formula v is positive if coming toward us Wavelength decreases from lab value Frequency shifts up as source approaches

29. Doppler Examples I run toward you with laser at 3m/s c = 3x10 8 m/s, = 6328Å v/c = 10 -8 So  x v/c = 6328 x 10 -8 = 6.3x10 -5 = 6328.000063Å ---- That’s why we can’t sense a change Shuttle orbits at 6km/s v/c = 6/300,000 = 2x10 -5 100MHz becomes 100MHz + 10 8 x 2x10 -5 = 100,002,000Hz if coming at you.

30. Another Doppler Example Star has known hydrogen line at 6563Å Detect line at 6963Å  = 400Å Star is receding at 18,000km/s !! In some cases astronomers can detect shifts as small as one part in a million. That implies detection of motion as small as 300m/s.

31. What about that #@&! radar gun? Cop uses radar which typically operates near = 1cm If you are going 65mph = 65 mi/hr x 1600m/mi / (3600 s/hr) = 30m/s This creates a shift of  = 30/3x10 8 = 10 -7 in the wavelength 1cm shifts to.9999999 cm. Not much. To say you were 5mph over the limit needs to measure one part in 100million!

32. Example of How Its Used in Astronomy Stellar lines are broadened by star’s rotation.

33. Binary Stars Optical Doubleappear close together but aren’t really binary Visual Binaryorbiting, but we can see them both Astrometric Binaryproper motion wiggles to show orbit Spectrum Binaryspectra of two stars of different type Spectroscopic Binary Doppler shift shows orbital motion Eclipsing Binarylight varies Half of all stars are in binaries…. Binary stars are formed at birth. Both components will have same age and composition. Can vary in mass Can be very distant (0.1pc) or touching

34. Spectroscopic Binary