1. ASTR 1020 – February 9 . Second Homework Due Today
Planetarium Next Tuesday Feb 14
First Exam Feb 21
Website

2. 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

3. Light Waves l 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 = 10-8cm =10-10m
about the diameter of an atom.
And 10Å = 1nm
Electric and Magnetic
Fields Sloshing Back
And Forth

4. Color RED 7000Å YELLOW 5500Å VIOLET 4000Å
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
RED 7000Å
YELLOW 5500Å
VIOLET 4000Å

5. Electromagnetic Spectrum
visible is tiny chunk of em spectrum

6. Parts of EM Spectrum Radio l > 1mm (107A)
Infrared 1mm> l > 10000A
Visible 10,000A > l > 3500A
Ultraviolet 3500A > l > 100A
X-ray 100A > l > 0.1A
Gamma-ray 0.1A > l

7. Question
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

8. 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

9. Speed of Light Speed of Light c = 3x108m/s That’s a very odd statement
2 cars at 65mph
1 car at 130mph
Cover same distance in same amount of time
The Relative speeds are the same

10. Relativity NO!!! .8c .8c Clearly Approaching each other at 1.6c
v always less than c
if velocities << c, then v=v1+v2
per Einstein
(Concept of time and space changes)

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

12. Frequency (2)
300MHz = 1m wavelength
Yellow Light = 600 trillion Hertz

13. Question An x-ray has a wavelength of 100Å
(10nm, 1x10-8m). What is it's frequency, in cycles per second? (aka Hertz)
A. 3x1016
B. 1.5x1016
C. 3x1013
D. 1.5x1013

14. Answer
An x-ray has a wavelength of 100Å (10nm, 1x10-8m). What is it's frequency, in cycles per second? (aka Hertz)
A. 3x1016
B. 1.5x1016
C. 3x1013
D. 1.5x1013
Answer: A. (3E8m/s)/(1E-8m)=3E16 Hz

15. Energy of a Photon h = 6.63x10-34 J s Planck’s Constant
energy of yellow photon
Sunlight is 104 W/m2
Outside we have 1023 photons/m2/s hit us

16. 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. 1x1012 (a trillion) times more powerful.
E. 1x1015 (a quadrillion) times more powerful.

17. Answer
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. 1x1012 (a trillion) times more powerful.
E. 1x1015 (a quadrillion) times more powerful.
Answer: C. 10,000nm/10nm = 1000

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

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

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

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

22. Wien’s Law Å As T rises, l drops Bluer with temperature (T in Kelvin)
300K 100,000A Earth
Sun
X-ray source

23. 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

24. Answer
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.

25. Stefan-Boltzman Law s = 5.67x10-8 W/m2/K4 A is area in m2 T in Kelvins
Example: The Sun
L = 5.7x10-8 x 4 x 3.14 x (7x108m)2 x (5500K)4 = 4 x 1026 W
4x1026 Watts = 100 billion billion MegaWatts!!

26. Question
If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? 2 4 8 16 32

27. Answer
If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? 2 4 8
16 = 24 32

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

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

30. 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

31. Answer
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

32. Stars Come in Different Colors

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

34. 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

35. 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

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

37. The Spectral Types O Stars of Orion's Belt >30,000 K
Lines of ionized helium, weak hydrogen lines
<97 nm (ultraviolet)* B
Rigel
30,000 K-10,000 K
Lines of neutral helium, moderate hydrogen lines
nm (ultraviolet)* A
Sirius
10,000 K-7,500 K
Very strong hydrogen lines
nm (violet)* F
Polaris
7,500 K-6,000 K
Moderate hydrogen lines, moderate lines of ionized calcium
nm (blue)* G
Sun, Alpha Centauri A
6,000 K-5,000 K
Weak hydrogen lines, strong lines of ionized calcium
nm (yellow) K
Arcturus
5,000 K-3,500 K
Lines of neutral and singly ionized metals, some molecules
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.

38. Stellar Classification (2)
Sun G2
a Cen G2 + K5
Sirius A1
Antares M1
Rigel B8
O5 40,000K
B5 15,500
A5 8500
F5 6580
G5 5520
K5 4130
M5 2800
Letters are odd due to confusion in sorting out temperature scale
between 1900 and 1920

39. 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.

40. 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

41. The Doppler Shift vt ct Observer D
During t seconds, source emits n waves of wavelength l.
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 l to

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

43. Doppler Examples I run toward you with laser at 3m/s
c = 3x108m/s, l = 6328Å
v/c = 10-8
So dl = l x v/c = 6328 x 10-8 = 6.3x10-5
l = Å That’s why we can’t sense a change
Shuttle orbits at 6km/s
v/c = 6/300,000 = 2x10-5
100MHz becomes 100MHz x 2x10-5 = 100,002,000Hz if coming
at you.

44. Another Doppler Example
Star has known hydrogen line at 6563Å
Detect line at 6963Å
dl = 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.

45. What about that #@&! radar gun?
Cop uses radar which typically operates near l = 1cm
If you are going 65mph = 65 mi/hr x 1600m/mi / (3600 s/hr) = 30m/s
This creates a shift of dl = 30/3x108 = 10-7 in the wavelength
1cm shifts to cm. Not much.
To say you were 5mph over the limit needs to measure one part in 100million!

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

47. Stellar Luminosity The H-R Diagram
By 1915 had lots of spectra and classifications
Had a few distances from parallax
Once distance was available, luminosity and Absolute Magnitude
could be calculated.
Herzsprung and Russel, working independently both plotted
absolute magnitude (luminosity) vs classification (temperature)
The H-R Diagram

48. The H-R Diagram Plot of Brightness vs Temperature-5
Rigel
Giants
Capella
Sirius
Brightness
Procyon
Sun
Main Sequence +5
a Cen B
White Dwarfs
+10
Sirius B
Prox Cen
+15 O B A F G K M
Spectral Type

49. The H-R Diagram

50. The Main Sequence Stars Differ By: Mass Age Composition Nothing else!
And composition doesn’t vary
Age and Mass only.
Those on main sequence are all
burning H so age drops out.
MS is function of MASS only!!!

51. Full, Artistic H-R As mass of MS star increases, both R and T increase
increasing
size
sAT4
T constant
on any vertical
line

52. Newly Formed Star M Spectral Type O +10 +5 -5 +15 B A F G K Protostar
+15 B A F G K
Sun
Sirius
a Cen B
Prox Cen
Procyon
Rigel
Capella
Sirius B
Main Sequence
Giants
White Dwarfs
Protostar
Large,
Low T.
Settles down
to MS
Then sits while
burning H

53. MS Lifetime
What determines amount of time a star stays on Main Sequence?
Just like a kerosene heater: Amount of fuel and rate of burn.
More Mass = More Fuel
More Luminosity = Greater Burn Rate
We can scale from the Sun: M = 1M L = 1L
Sun lasts 1010 years
M in solar masses
L in solar luminosities

54. Some Lifetimes Mass Luminosity Lifetime in Billion Years Sun 1 1 10
Sirius
Prox Cen
Rigel 8 10,
Dinky little stars like Prox Cen will last trillions of years
Huge stars like Rigel are gone in a few million
There aren’t many large stars out there, because they don’t last.
10,000 O stars of the 100,000,000,000 Milky Way stars