1 Light What is light? 1. How does light behave? 2. What produces light? 3. What type of light is emitted? 4. What information do you get from that light?
2 Methods in Astronomy Photometry Measure total amount of light within a certain filter Study distribution and extent of object Spectroscopy Slit up light into its wavelength components Study particular absorption and emission lines Need to understand astrophysical radiation processes Understand some of the relevant physics Be able to interpret the measured light information
3 Today s Overview and Concepts 1) What is Light? Properties? 2) Analyze Black Body Radiation and understand correlations between: color dominant wavelength surface temperature flux luminosity magnitude radius 2) How can you determine those properties of stars? 3) The Hertzsprung-Russel Diagram
4 Electromagnetic Radiation Newton: Beam of light separated into rainbow colors
5 The spectrum has a much wider range; ranging from Gamma to Radio Waves The "visual" part is only a small fraction of the entire electromagnetic spectrum. Visual: 4000 to 7000 Å (1 Å = m) This is also in your toolkit.
8 Infra-Red Radiation night animals
9 How do Waves behave? Ocean Waves Interference Pattern Does light also show an Interference Pattern??
10 How do we know that light is wave? It behaves like waves What happens when two waves are interfering?
11 Demo of Joung s Double Slit Experiment
13 Medium? ---- Ether? Light waves in what?? Light is electromagnetic radiation. What is that? It is a self-perpetuation wave, where the electric field gives rise to a magnetic field which in turn gives rise to an electric field What is propagating? Space around an electric charge may be characterized by an electric field, E, which manifests itself as a force on a test charge placed nearby. If an electromagnetic wave encounters such a test charge, that charge will oscillate. Maxwell s equations say that a time varying electric field produced a perpendicular time-varying magnetic field B. This disturbance in B then gives rise to a time varying E, which in turn this therefore is a self-propagating wave of electric and magnetic fields in a vacuum.
14 Waves Wavelength is the distance from crest to crest Frequency is the number of crests passing per second Velocity of light is 300,000 km/sec h = h o sin 2πx λ c = λ ν How do we know that light is wave? It behaves like waves
15 Light Waves E B = = E B o o 2π sin λ 2π sin λ ( x ct) ( y ct) Light is electromagnetic radiation. It is a self-perpetuation disturbance, where the electric field gives rise to a magnetic field which in turn gives rise to an electric field
16 But.. How do you get shadows with waves??? How do you get photos? (do waves make photos?) Is light a particle?
17 The Photoelectric Effect Light is a Particle called "Photon"
18 The Photoelectric Effect In 1905 Einstein made 4 main discoveries: Brownian motion Photo-electric effect Special Relativity E=mc 2 He got the Nobel prize for the Photo-Electric Effect.
19 Einstein showed that: light is a particle, called "Photon" light is quantized (more later) the energy of a photon is related to the frequency of light E = hν Energy frequency
20 Relationship between the velocity of light, its wavelength and its frequency is: c = λ ν ν E = h = h c λ More Energy Frequency of light = ν Wavelength of light = λ Energy of light = E Planck s constant = h Speed of light = c Shorter Wavelength Faster rate of waves passing
21 Paradox? Can Proof that Light is a Wave Can Proof that Light is a Particle Which is correct? A Particle with a Wavelength??? (What type of animal is that?)
22 Paradox? The experiment shows that light has a wave character The experiment shows that light has a particle character Which statement is correct? We determine reality by experimenting. The experiment itself determines reality. The experiments give contradictory results How, then, do we know what is really true in Life?
23 Energy and Intensity of Light E = hν = h c λ
24 What produces light? hot bodies Today: Experiment & Theory hot gases Today: Experiment only shocks and friction electric fields magnetic fields chemical reactions nuclear reactions
25 The Light Bulb Radiation from a dense body, i.e., from the Iron Wire inside the bulb To be compared later to the and
26 What is a Black Body? A Perfect Absorber no Reflection Perfect Emitter Def: A black body is an object that absorbs ALL radiation that is incident upon it. this makes it black
27 The Spectrum of a Light bulb Red light disappears Less light More light Less light Blue light disappears
28 The Black Body Spectrum Less light Most light Black Bodies emit Light with a characteristic Spectrum This shape is meant by that Less light Blue light disappears Red light disappears
29 The Black Body Spectrum Black Bodies emit Light with a characteristic Spectrum Empirical formula = = kt h kt hc e c h I e hc I ν ν λ λ ν λ
30 The Light-bulb experiment Decrease electricity supply total amount of light decreases color gets redder (relatively less blue light) temperature gets colder Have a relationship between: Color, Temperature & Brightness
33 Experimental Findings for Black Body 1) Hotter Bodies emit more light Temp 4 Flux This is Stefan-Bolzman s law F = σ T 4 2) Hotter bodies emit bluer light Temp 1/wavelength This is Wien s law λ max = T
34 Graphical Illustration Hotter bodies emit bluer light Temp 1/wavelength [Inverse relationship] This is Wien s law λ max = T
35 Total Flux Total energy density radiated at all wavelengths Area under the curve Integrate over all wavelengths Flux = 0 F( λ) dλ
36 T F e x dx from Tables Integral T e x dx c h k hc kt x Substitute hc kt e hc kt hc kt d hc hc kt by Multiply e d hc d F F Integrate e hc F x x kt hc kt hc kt hc σ π λ λ λ λ λ λ λ λ λ λ λ λ = = = = = = = =
37 Stars have colors
38 HST image of Quintuplet Cluster - almost real colors
39 Stars are roughly black bodies
40 Do not see this light
41 Bolometric correction λ λ = A A V d F L ) ( Since know the shape of the a Black Body Curve know how much light missing Apply so-called bolometric correction V A A Bol m d F d F m L L m m + = = ) ( ) ( 2.5log 2.5log λ λ λ λ
42 Determining the Temperature Method 1: By Eye Figure out the colors; Get λ max ; Use Wien s law to get temperature. How do you determine the dominant wavelength? Betelgeuse: color red λ max Rigel: color blue λ max
43 Rigel: λ max is around 4000Å this is in the blue part of the spectrum Betelgeuse: λ max is around 7000Å this is in the red part of the spectrum.
44 Which star is hotter? By how much? Betelgeuse: color red λ max = 7000Å Rigel: color blueish λ max = 4000Å Recall Wien's law: T = λ max But watch out for UNITS Temperature has to be in Kelvin Wavelength in meters (e.g. 7000Å = 7000 x m = 7 x 10-7 m)
45 Temperature scale Absolute Zero In Astronomy we always use the Kelvin Scale. Why? Absolute Zero corresponds to Zero Energy
46 Recall Wien's law: T = λ max First convert units: Betelgeuse: color red λ max = 7000Å = 7 x 10-7 m Rigel: color blueish λ max = 4000Å = 4 x 10-7 m Betelgeuse Rigel TB = = 4000K m ( λ ) max ( λ ) B TR = = 7000K m max R Calculation easier in ratios T T B R ( λ ) ( λ ) o ( λmax ) R 4000 A 4 = = ( λ ) 7 max B = = o max B max R 7000 A Betelgeuse is 4/7 times as hot as Rigel
47 Quiz Question 1: Hot Human Bodies Temperature? About 37 o Celsius = 310 Kelvin λ 0 6 max = = = T K m λ λ max max = meters = 9.4 micro meters Humans emit at ~ 9µm Humans emit light at INFRA RED wavelengths
48 Quiz Question 2: Ice & Cold Dust Temperature? About 0 o Celsius = 273 Kelvin λ 0 6 max = = = T λ λ max max K = meters = 10.4 micro meters m Ice emit light at near INFRA RED wavelengths Dust has temp of ~ K And thus emits at ~ µm Which is at near to far IR wavelengths
49 Other objects
50 Filters & Experiments with Pictures (Photometry Lab) Determining the "color index Quantitative Method a) Measure the magnitudes using filters, e.g., B & V b) Determine the color index (B-V) c) Then use Wien s law to get Temperature
51 First Look at the Spectra of Stars Then look at the entire Electromagnetic Spectrum in your Toolkit The Visual Part of the Spectrum is marked in the picture below Spectrum (a): We see relatively more red light Spectrum (c): We see relatively more blue light Correlating Colors and Dominant Wavelengths Spectrum (a): Dominant Wavelength is at Long Wavelengths here in the IR Spectrum (c): Dominant Wavelength is at Short Wavelengths here in the UV Red yellow λ max in IR λ max in Visual blue λ max in UV
52 How do your "measure" colors? Use filters, take black and white pictures (not color), then measure magnitude in each filter
53 HST image of Quintuplet Cluster -- almost real colors
54 Horsehead Nebula
55 Nebulosity in Sagittarius
56 How do your "measure" colors? Use filters & take (black and white ) pictures, then measure magnitude in each filter; Then calculate the Difference in Magnitude in two Filter Bands.
57 Blue star: much light in blue filter relatively less light in red filter Red star: less red light than blue star but relatively more light in red filter than blue star
58 Color = λ λ λ λ λ λ d R Flux d R Flux V B B V ) ( ) ( ) ( ) ( 2.5log T V B = 0 + Color index = B-V = Magnitude in B Magnitude in V Empirical relationship for solar like stars:
59 The Hertzsprung Russel Diagram For all stars can determine their absolute magnitudes and color Make a plot of absolute and color Luminosity M V Temperature B-V
60 The Hertzsprung Russel Diagram For all stars can determine their Luminosities and their Temperatures Make a plot of Stellar Luminosity and Temperature Luminosity M V Temperature or B-V
61 The Hertzsprung Russel Diagram (HRD) Plot of Luminosity and Temperature Most stars are so-called main-sequence stars
62 If both stars have the same color Color and Temperature Wien s law λ max = T Color is the same Temperature is the same Temperature and Flux Stefan-Bolzman s law Flux = σ Temp 4 Temperature is the same Flux is the same
63 Which star is more luminous? Luminosity and Size The Flux the amount of light passing through the green square is the SAME. BIG Star SMALL Star Which star is more luminous? The larger or smaller?
64 Recall Definitions Luminosity: Luminosity is an intrinsic quantity of the star. It is the energy per second emitted from the entire star. This quantity is the flux Units: Watts (or Joules/sec) Flux: The energy per second passing through a certain area. It is the energy per second per square meter. Units: Watts/m 2 (or Joules/sec/m 2 )
65 Luminosity and Size The Luminosity of a star is the total amount of light emitted from its surface. Thus the luminosity is obtained by multiplying the flux by the area of the star. Luminosity = Flux Area
66 Luminosity Luminosity = Flux Area L = F 4πR 2 Recall Stefan-Bolzman's law: F = σ T 4 Insert the value for Flux into the above equation: L = 2 2 4πR F = 4πR σ T 4 L = 2 4πσ R T 4 The Luminosity of a star depends on its Radius and its Temperature
67 Recall: redder stars are cooler Wien s law cooler stars emit less flux Stephan Bolzman s law get more light from bigger stars For Stars: Have a relationship between: Temperature, Luminosity, & Size
68 Determining the Radii of Stars Can figure out radius of a star if know luminosity and temperature. L = 2 4 4πσ R T Aside: In general always compare the stars. Stick to SOLAR units. Why? The sun is a meaningful star for us -- so compare other stars to the sun L L sun = 4πσ 4πσ R 2 4 R T 2 sun T 4 sun = 2 4 R T R 2 sun T 4 sun = R R sun 2 T T sun 4 For easier calculations you can use these L L sun R R sun R = R = sun or L L 2 sun T T T T sun sun 2 4
69 What about the size of a Star? Can you use the small angle formula? size of star = distance angle 206,265" If the angle is measured in arc seconds Angle size of star Distance to the star
70 Example: Betelgeuse Betelgeuse is 100,000 times as luminous as the sun. 5 L Betelgeuse = 10 L Sun Betelgeuse s color is red, the suns, color is yellow. Red color Temp ~ 3000K Yellow colors Temp ~ 6000K Could put the values of the luminosities and temperatures into these formulae: L Sun = 2 4 4πσ RSun TSun L Betel = 2 4 4πσ RBetel TBetel But there is an easier method. Again use ratios.
71 Example: Calculation L Betel L Sun = = 2 4 4πσ RBetel TBetel 2 4 4πσ RSun TSun Procedure (on right): Write down both formulae; Add two lines to turn this into ratios; Cancel constants L L 10 Betel sun 5 R = R R = R Betel sun Betel sun 2 2 T T Betel sun K 6000K K 6000K 10 R R R R R Betel = = = 2 16 Betel Betel sun sun Betel R R = 2 sun = = 1300R = 1300 sun 1 16
72 So Betelgeuse is 1300 times bigger than the sun. How big is that? The Earth Sun distance is 1AU 1300R sun ~ 6AU Betelgeuse is 6 times as big as the Earth Sun distance. Betelgeuse is a Red Supergiant!
73 The Hertzsprung Russel Diagram (HRD) Betelgeuse has a red color (T~3000K) and is very luminous L B =10 5 L sun. This puts Betelgeuse into the top right in the HRD Betelgeuse is much bigger than the sun Big stars are in the top RH Small stars are in the bottom LH
74 BIG Radius increases from bottom left to top right SMALL
75 Mass increases along main sequence from bottom right to top left
76 Frequencies of Stars Most are Main Sequence Stars Smaller Main sequence stars are much more numerous than luminous m.s. stars Next: What are Spectral Types?
77 Summary of Rules: 1) Hotter Bodies emit more light Temp 4 Flux This is Stefan-Bolzman s law F = σ T 4 2) Hotter bodies emit bluer light Temp 1/wavelength This is Wien s law λ max = T 3) Luminosity of a star is light emitted from its surface. Lum Temp 4 and R 2 L = 2 4πσ R T 4
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