Methods in Astronomy. Light. Electromagnetic Radiation. Today s Overview and Concepts. Newton: Beam of light separated into rainbow colo.

Transcription

1 What is light? ight. How does light behave?. What produces light? 3. What type of light is emitted?. What information do you get from that light? 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 oday s Overview and Concepts ) What is ight? Properties? ) Analyze Black Body adiation and understand correlations between: color dominant wavelength surface temperature flux luminosity magnitude radius Electromagnetic adiation Newton: Beam of light separated into rainbow colo ) How can you determine those properties of stars? 3) he Hertzsprung-ussel Diagram e spectrum has a much wider ge; ranging from Gamma to dio Waves e "visual" part is only a small ction of the entire ctromagnetic spectrum. sual: 000 to 7000 Å ( Å 0-0 m) is is also in your toolkit.

2 Infra-ed adiation night animals How do Waves behave? Ocean Waves Interference Pattern Does light also show an Interference Pattern?? How do we know that light is wave? It behaves like waves What happens when two waves are interfering? Demo of Joung s Double Slit Experiment

3 Medium? ---- Ether? ight waves in what?? ight 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? 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 Waves πx h ho sin 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. his 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. c ν How do we know that light is wave? It behaves like waves ight Waves π E Eo sin π B Bo sin ( x ct) ( y ct) But.. How do you get shadows with waves??? How do you get photos? (do waves make photos?) Is light a particle? ight is electromagnetic radiation. It is a self-perpetuation isturbance, where the electric field gives rise to a magnetic eld which in turn gives rise to an electric field he Photoelectric Effect ight is a Particle called "Photon" he Photoelectric Effect In 90 Einstein made main discoveries: Brownian motion Photo-electric effect Special elativity Emc He got the Nobel prize for the Photo-Electric Effect.

4 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 elationship between the velocity of light, its wavelength and its frequency is: c ν c E hν h More Energy Energy frequency Frequency of light ν Wavelength of light Energy of light E Planck s constant h Speed of light c Shorter Wavelength Faster rate of waves passing Paradox? Paradox? Can Proof that ight is a Wave Can Proof that ight is a Particle Which is correct? A Particle with a Wavelength??? (What type of animal is that?) he experiment shows that light has a wave character he experiment shows that light has a particle character Which statement is correct? We determine reality by experimenting. he experiment itself determines reality. he experiments give contradictory results How, then, do we know what is really true in ife? Energy and Intensity of ight What produces light? c E hν h hot bodies hot gases shocks and friction electric fields magnetic fields chemical reactions nuclear reactions oday: Experiment & heory oday: Experiment only

5 he ight Bulb adiation from a dense body, i.e., from the Iron Wire inside the bulb What is a Black Body? A Perfect Absorber no eflection Perfect Emitter o be compared later to the and Def: A black body is an object that absorbs A radiation that is incident upon it. this makes it black he Spectrum of a ight bulb ed light disappears ess light ess light he Black Body Spectrum Most light Black Bodies emit ight with a characteristic Spectrum his shape is meant by that More light ess light ess light Blue light disappears ed light disappears Blue light disappears he Black Body Spectrum Black Bodies emit ight with a characteristic Spectrum Empirical formula hc I e 3 hν I ν c e hc k hν k he ight-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, emperature & Brightness

6 Experimental Findings for Black Body Graphical Illustration ) Hotter Bodies emit more light emp Flux his is Stefan-Bolzman s law ) Hotter bodies emit bluer light emp /wavelength his is Wien s law F σ Hotter bodies emit bluer light emp /wavelength [Inverse relationship] his is Wien s law otal Flux otal energy density radiated at all wavelengths Area under the curve Integrate over all wavelengths Flux F( ) d 0 hc F F 0 hc k h c F d hc F σ hc k e 0 k d hc k hc k hc k e hc dx x x e d hc k e Integrate k Multiply by hc k Substitute x hc Integral from ables 0 dx π x x e

7 Do not see this ligh Stars have colors HS image of Quintuplet Cluster - almost real colors Stars are roughly black bodies Bolometric correction V 7000 A 000 A F( ) d Since know the shape of the a Black Body Curve know how much light missing Apply so-called bolometric correction m m.log 7000 A F( ) d 000 A mbol.log + m V F d ( ) 0 Determining the emperature Method : By Eye Figure out the colors; Get ; Use Wien s law to get temperature. How do you determine the dominant wavelength? geuse: color red igel: color blue

8 igel: is around 000Å this is in the blue part of the spectrum geuse: is around 7000Å this is in the red part of the spectrum. Which star is hotter? By how much? geuse: color red 7000Å igel: color blueish 000Å ecall Wien's law: But watch out for UNIS emperature has to be in Kelvin Wavelength in meters (e.g. 7000Å 7000 x 0-0 m 7 x 0-7 m emperature scale ecall Wien's law: First convert units: geuse: color red 7000Å 7 x 0-7 m igel: color blueish 000Å x 0-7 m Absolute Zero geuse igel K B 7 0 m ( ) B K 0 m ( ) In Astronomy we always use the Kelvin Scale. Why? Absolute Zero corresponds to Zero Energy Calculation easier in ratios ( ) ( ) geuse is /7 times as hot as igel o ( ) 000 A ( ) 7 B B o B 7000 A Quiz Question : Hot Human Bodies K meters 9. micro meters Humans emit at ~ 9µm Humans emit light at INFA ED wavelengths m emperature? About 37 o Celsius Kelvin Quiz Question : Ice & Cold Dust emperature? About 0 o Celsius 73 Kelvin K meters 0. micro meters Ice emit light at near INFA ED wavelengths Dust has temp of ~ K And thus emits at ~ 0-00µm Which is at near to far I wavelengths m

9 Other objects Filters & Experiments with Pictures (Photometry ab) Determining the "color index Quantitative Method a) Measure the magnitudes using filters, e.g., B & V b) Determine the color index (B-V) c) hen use Wien s law to get emperature First ook at the Spectra of Stars hen look at the entire Electromagnetic Spectrum in your oolkit he 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 How do your "measure" colors? Use filters, take black and white pictures (not color), then measure magnitude in each filter Correlating Colors and Dominant Wavelengths Spectrum (a): Dominant Wavelength is at ong Wavelengths here in the I Spectrum (c): Dominant Wavelength is at Short Wavelengths here in the UV ed yellow blue in I in Visual in UV HS image of Quintuplet Cluster -- almost real colors Horsehead Nebula

10 Nebulosity in Sagittarius How do your "measure" colors? Use filters & take (black and white ) pictures, then measure magnitude in each filter; hen calculate the Difference in Magnitude in two Filter Bands. ue star: much light in blue filter relatively less light in red filter d star: less red light than blue star but relatively more light in red filter than blue star B V.log Color Color index B-V Magnitude in B Magnitude in V Flux( ) V ( ) d Flux( ) d B ( ) Empirical relationship for solar like stars: 80 B V he Hertzsprung ussel Diagram For all stars can determine their absolute magnitudes and color Make a plot of absolute and color he Hertzsprung ussel Diagram For all stars can determine their uminosities and their emperatu Make a plot of Stellar uminosity and emperature M V uminosity emperature uminosity M V B-V emperature or B-V

11 he Hertzsprung ussel Diagram (HD) lot of uminosity and emperature If both stars have the same color Color and emperature Wien s law Color is the same emperature is the same Most stars are so-called main-sequence stars emperature and Flux Stefan-Bolzman s law Flux σ emp emperature is the same Flux is the same Which star is more luminous? uminosity and Size he Flux the amount of light assing through the green square is e SAME. hich star is more luminous? he larger or smaller? BIG Star SMA Star ecall Definitions uminosity: uminosity is an intrinsic quantity of the star. It is the energy per second emitted from the entire star. Units: Watts (or Joules/sec) Flux: he energy per second passing through a certain area. It is the energy per second per square meter. Units: Watts/m (or Joules/sec/m ) his quantity is the flux uminosity and Size he uminosity of a star is the tal amount of light emitted om its surface. hus the luminosity is obtained multiplying the flux by the ea of the star. uminosity Flux Area uminosity Flux Area uminosity ecall Stefan-Bolzman's law: Insert the value for Flux into the above equation: π F π σ πσ F π F σ he uminosity of a star depends on its adius and its emperature

12 ecall: 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: emperature, uminosity, & Size Determining the adii of Stars Can figure out radius of a star if know luminosity and temperature. πσ Aside: In general always compare the stars. Stick to SOA units. Why? he is a meaningful star for us -- so compare other stars to the For easier calculations you can use these πσ πσ or What about the size of a Star? Can you use the small angle formula? Example: geuse geuse is 00,000 times as luminous as the. geuse 0 Sun size of distance angle star 06,6" If the angle is measured in arc seconds geuse s color is red, the s, color is yellow. ed color emp ~ 3000K Yellow colors emp ~ 6000K Angle Distance to the star size of star Could put the values of the luminosities and temperatures into these formulae: Sun πσ Sun Sun πσ But there is an easier method. Again use ratios. Example: Calculation Sun πσ πσ Sun Sun So geuse is 300 times bigger than the. How big is that? he Earth Sun distance is AU 300 ~ 6AU geuse is 6 times as big as the Earth Sun distance. Procedure (on right): Write down both formulae; Add two lines to turn this into ratios; Cancel constants K 6000 K 3000K 6000K geuse is a ed Supergiant!

13 he Hertzsprung ussel Diagram (HD) geuse has a red color (~3000K) and is very luminous B 0. his puts geuse into the top right in the HD BIG adius increases from bottom left to top right geuse is much bigger than the Big stars are in the top H Small stars are in the bottom H SMA Mass increases along main sequence from bottom right to top left 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 ypes? Summary of ules: Hotter Bodies emit more light emp Flux his is Stefan-Bolzman s law F σ Hotter bodies emit bluer light emp /wavelength his is Wien s law uminosity of a star is light emitted from its surface. um emp and πσ