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The Dual Nature of Light It’s a particle: photon with E (ergs) It’s a wave: Wavelength , Frequency , velocity c

The Dual Nature of Light It’s a particle: photon with E (ergs) It’s a wave: Wavelength , Frequency , velocity c. . Radio: long , low , vel=c.  = c/ cm 1 Å = 10 -8 cm E = h  = hc/ ergs. X-ray: short , high , vel=c. LIGHT. c/  E=h  =hc/  ergs.

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The Dual Nature of Light It’s a particle: photon with E (ergs) It’s a wave: Wavelength , Frequency , velocity c

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  1. The Dual Nature of Light • It’s a particle: photon with E (ergs) • It’s a wave: Wavelength , Frequency , velocity c  Radio: long , low , vel=c  = c/ cm 1 Å = 10-8cm E = h = hc/ ergs X-ray: short , high , vel=c

  2. LIGHT c/ E=h=hc/ ergs The wave is the electric and magnetic fields  to each other E = Eosin[(2/) (x-ct)] IE2 Electromagnetic Spectrum: -ray X-ray UV visible IR radio MeV keV 500-3000Å 3900-7000Å µ cm-meter 1 keV=12Å 1Å=10-8cm 1µ=10,000Å GRB, SN XRB, SN O, B stars Stars Brown dwarfs Molecular remnants white dwarfs accretion disks planets clouds

  3. Half abs altitude (km) Wavelength (Å)

  4. Basic Properties of Light: • inverse square law: [E/4πd2 ergs/cm2] • reflection: angle of incidence to normal= angle of reflection [i=r] • refraction: light refracts (bends to normal) in material [n1sini = n2sinr] • dispersion: light disperses in prism or grating [spectrum] • diffraction: light passing through an aperture (telescope): [~/d(radians)=206265/d(arcsec)] x1.22 is resolution  - for a 10 cm telescope at =5000Å,  = 1 arcsec • interference[max at dsin = m] gives location of lines in spectrograph - for a grating with 12000 slits/inch, d=21,000Å

  5. Basic Properties of Light: • inverse square law: [E/4πd2 ergs/cm2]

  6. Basic Properties of Light: • reflection: angle of incidence to normal = angle of reflection [i=r]

  7. Basic Properties of Light: • refraction: light refracts (bends to normal) in material [n1sini = n2sinr]

  8. Basic Properties of Light: • diffraction: light passing through an aperture (telescope)  (radians) ~/d 1 radian=57.3 deg x 60 arcmin x 60 arcsec = 206265 arcsec resolution  (arcsec) = 206265 (/d) x 1.22 (circular correction) for a 10 cm telescope at =5000Å(5x10-5cm), ~ 1 arcsec blue vs red telescope size

  9. Basic Properties of Light: • interference[max at dsin = m] gives location of lines in spectrograph - for a grating with 12000 slits/inch, d=21,000Å

  10. Basic Properties of Light: • dispersion: light disperses in prism or grating [spectrum] n() blue is bent more than red white light

  11. 3 types of spectra: continuous, absorption line and emission line

  12. Important points about Continuum radiation: • Planck Function (Black Body) E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å • Stefan-Boltzmann Law E=T4ergs/cm2/s • Luminosity L=4πR2T4 ergs/s • Wien’s Law (Å)=2.9x107/T(°K)

  13. Continuum radiation is approximated as a Black Body • (black body is opaque and radiates as a function of its T); • amount of energy from a BB is given by the Planck function: • E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å Note there is some E at all wavelengths even if its not visible 1000Å 4000Å 7000Å 10,000Å

  14. E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å Eall  = ∫ E () d = T4 ergs/cm2/s Stefan-Boltzmann law doubling T gives 16 X more energy from a star! 1000Å4000Å 7000Å 10,000Å

  15. Stefan-Boltzmann is energy/s for each square cm on star Luminosity = total energy coming from star each sec = total emitting area (cm2) X T4 (ergs/cm2/s) = 4 R2 T4 ergs/s

  16. E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å dE/()/d = 0 (Å) = 2.9 x 107/T (˚K) Wien’s law hot stars look blue, cool stars red, color gives T 1000Å4000Å 7000Å 10,000Å

  17. Line emission is approximated by the Bohr model (Quantum physics tells the true story) E n=1 n=2 n=3 H p e • Each element has diff p, e-, n • Each element has diff E levels • e- sit at lowest E for gas T He n

  18. E=hc/ photon emission line absorption line e- absorbs photon and moves to higher E level (n=2) e- emits photon to move down to lower E level (n=1)

  19. Transitions to a given level are a series: 13.6eV 12.73eV 12.07eV 10.19eV 0 eV UV optical IR

  20. Line theory - Bohr model mvr=nh/2π mv2/r=(Ze)e/r2 r= n2h2/4πme2Z E(n)=-2π2me4/h2n2 E=hc/ 1/=109678 [(1/m2)-(1/n2)] H (level 3 to 2) 1/=109678 [(1/4)-(1/9)] so =6563Å Quantum theory: N, L, S, J, M quantum numbers Level Populations: - gas T determines E which determines level occupied - number of electrons in that level and abundance determines line strength Boltzman eqtn provides excitation: N2/N1=g2/g1 e[E1-E2/kT] Saha eqtn provides ionization : N+/No=A(kT)3/2/Nee[-o/kT]

  21. Lines are broadened by: • uncertainty principle: 1/t 0.05 mÅ • Doppler : rotational and thermal • pressure: collisions • magnetic field: Zeeman splitting

  22. Sun’s spectrum

  23. Spectra of stars like the Sun

  24. Normal Star: cool atm continuum + absorption lines WL Peculiar Star: disk of hot low density gas emission lines Planet: continua and absorption of sun + planet sun planet earth

  25. Typical CV spectra in DR1 Cyclotron humps Polar CVs in DR1 in Szkody et al. 2003, AJ, 126, 1499 Strong HeII Polar Strong continuum Shows WD ZZ Cet Strong lines

  26. Important Info from Spectra: Composition (careful) Temperature Velocity

  27. Doppler Shift source moving to right source at rest red shift seen here blue shift seen here if v<< c / = v/c  = observed shift, v=object velocity,  = lab wavelength, c= 3x105 km/s if  =1Å for H (4861Å), v= 62 km/s Uses of Doppler shift: find motion of star or galaxy find rotation of planet or star determine if its a binary (star+star) or (star+planet)

  28. red shift no shift no shift blue shift only v component toward or away is measured!

  29. Useful info for telescopes: f-ratio = focal length/diameter = f/d [small f-ratio means brighter image] brightness increases as (diameter)2 resolution  = 2.1x105/d x 1.22 arcsec magnification = focal length of objective/focal length of eyepiece plate scale s = 0.01745xf cm/deg = 4.85x10-6 f cm/arcsec

  30. Plate scale s: how the linear measure on your detector corresponds to angular measure on the sky s = 0.01745 x f in cm/deg s = 4.85x10-6 x f in cm/arcsec for an f/13 telescope of 60 cm diameter: f/d = 13 f = 780 cm s = 0.0037 cm/arcsec 1 cm on detector = 265 arcsec = 4.4 arcmin

  31. Our Nationally Funded Observatories: • NSF (ground) • Kitt Peak National Obs (KPNO, Tucson) • Cerro Tololo Interamerican Obs (CTIO, Chile) • Gemini (Hawaii and Chile) • radio (VLA, New Mexico; Arecibo, Puerto Rico) • NASA (space) + ground (space-related) • HST, Chandra, XMM, GALEX + others • Infrared Telescope Facility (IRTF, Hawaii) • Keck (Hawaii)

  32. US Optical Telescopes in the Next Decade • LSST - 8.4m in Chile, 10 yr imaging survey, $400 million, start 2018 • TMT - 30m on Mauna Kea, CA, Canada, Japan, India, China, $1 billion • GMT - 7x8.4m=24.5m in Chile, CA, Harvard, Texas, Arizona, Chicago, Australia, Korea

  33. Primary Instruments • 1. Camera - Charge Coupled Device : CCD • time exposures, stars, clusters, galaxies • different filters (colors temps) • brightness, variability • 2. Spectrograph - slit, lenses, CCD • composition • temperature • velocity

  34. CCDs - invented at Bell Labs about 1970 2D grid of picture elements (pixels) that are 7-30 microns across well capacity 10,000-60,000 e- 2048x2048 with 2 bytes/pxl = 8MB picture To use: take prior bias & flats then [prep, expose, read] • Advantages: • linear over large range in brightness • good quantum efficiency (95% at 6000-9000Å) • dark current small at cold T (-100C) • Disadvantages: • large pixel sizes compared to plates, overall small coverage • low blue response • long readout times for large arrays • cosmic rays add up

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